Merge commit '498dfabf9848286be003b42941c323a045d9fa46' as 'lib/ed25519'

17 files changed, 4990 insertions, 0 deletions

diff --git a/lib/ed25519/src/add_scalar.c b/lib/ed25519/src/add_scalar.c
new file mode 100644
index 0000000..a4f2a55
--- /dev/null
+++ b/lib/ed25519/src/add_scalar.c
@@ -0,0 +1,56 @@
+#include "ed25519.h"
+#include "ge.h"
+#include "sc.h"
+
+
+/* see http://crypto.stackexchange.com/a/6215/4697 */
+void ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar) {
+    const unsigned char SC_1[32] = {1}; /* scalar with value 1 */
+    
+    unsigned char n[32]; 
+    ge_p3 nB;
+    ge_p1p1 A_p1p1;
+    ge_p3 A;
+    ge_p3 public_key_unpacked;
+    ge_cached T;
+
+    int i;
+
+    /* copy the scalar and clear highest bit */
+    for (i = 0; i < 31; ++i) {
+        n[i] = scalar[i];
+    }
+    n[31] = scalar[31] & 127;
+
+    /* private key: a = n + t */
+    if (private_key) {
+        sc_muladd(private_key, SC_1, n, private_key);
+    }
+
+    /* public key: A = nB + T */
+    if (public_key) {
+        /* if we know the private key we don't need a point addition, which is faster */
+        /* using a "timing attack" you could find out wether or not we know the private
+           key, but this information seems rather useless - if this is important pass
+           public_key and private_key seperately in 2 function calls */
+        if (private_key) {
+            ge_scalarmult_base(&A, private_key);
+        } else {
+            /* unpack public key into T */
+            ge_frombytes_negate_vartime(&public_key_unpacked, public_key);
+            fe_neg(public_key_unpacked.X, public_key_unpacked.X); /* undo negate */
+            fe_neg(public_key_unpacked.T, public_key_unpacked.T); /* undo negate */
+            ge_p3_to_cached(&T, &public_key_unpacked);
+
+            /* calculate n*B */
+            ge_scalarmult_base(&nB, n);
+
+            /* A = n*B + T */
+            ge_add(&A_p1p1, &nB, &T);
+            ge_p1p1_to_p3(&A, &A_p1p1);
+        }
+            
+        /* pack public key */
+        ge_p3_tobytes(public_key, &A);
+    }
+}
diff --git a/lib/ed25519/src/ed25519.h b/lib/ed25519/src/ed25519.h
new file mode 100644
index 0000000..8924659
--- /dev/null
+++ b/lib/ed25519/src/ed25519.h
@@ -0,0 +1,38 @@
+#ifndef ED25519_H
+#define ED25519_H
+
+#include <stddef.h>
+
+#if defined(_WIN32)
+    #if defined(ED25519_BUILD_DLL)
+        #define ED25519_DECLSPEC __declspec(dllexport)
+    #elif defined(ED25519_DLL)
+        #define ED25519_DECLSPEC __declspec(dllimport)
+    #else
+        #define ED25519_DECLSPEC
+    #endif
+#else
+    #define ED25519_DECLSPEC
+#endif
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef ED25519_NO_SEED
+int ED25519_DECLSPEC ed25519_create_seed(unsigned char *seed);
+#endif
+
+void ED25519_DECLSPEC ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed);
+void ED25519_DECLSPEC ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key);
+int ED25519_DECLSPEC ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key);
+void ED25519_DECLSPEC ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar);
+void ED25519_DECLSPEC ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key);
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/lib/ed25519/src/fe.c b/lib/ed25519/src/fe.c
new file mode 100644
index 0000000..448e3e9
--- /dev/null
+++ b/lib/ed25519/src/fe.c
@@ -0,0 +1,1491 @@
+#include "fixedint.h"
+#include "fe.h"
+
+
+/*
+    helper functions
+*/
+static uint64_t load_3(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+
+    return result;
+}
+
+static uint64_t load_4(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+    result |= ((uint64_t) in[3]) << 24;
+    
+    return result;
+}
+
+
+
+/*
+    h = 0
+*/
+
+void fe_0(fe h) {
+    h[0] = 0;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+    h[4] = 0;
+    h[5] = 0;
+    h[6] = 0;
+    h[7] = 0;
+    h[8] = 0;
+    h[9] = 0;
+}
+
+
+
+/*
+    h = 1
+*/
+
+void fe_1(fe h) {
+    h[0] = 1;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+    h[4] = 0;
+    h[5] = 0;
+    h[6] = 0;
+    h[7] = 0;
+    h[8] = 0;
+    h[9] = 0;
+}
+
+
+
+/*
+    h = f + g
+    Can overlap h with f or g.
+
+    Preconditions:
+       |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+       |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+    Postconditions:
+       |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_add(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t h0 = f0 + g0;
+    int32_t h1 = f1 + g1;
+    int32_t h2 = f2 + g2;
+    int32_t h3 = f3 + g3;
+    int32_t h4 = f4 + g4;
+    int32_t h5 = f5 + g5;
+    int32_t h6 = f6 + g6;
+    int32_t h7 = f7 + g7;
+    int32_t h8 = f8 + g8;
+    int32_t h9 = f9 + g9;
+    
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+
+/*
+    Replace (f,g) with (g,g) if b == 1;
+    replace (f,g) with (f,g) if b == 0.
+
+    Preconditions: b in {0,1}.
+*/
+
+void fe_cmov(fe f, const fe g, unsigned int b) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t x0 = f0 ^ g0;
+    int32_t x1 = f1 ^ g1;
+    int32_t x2 = f2 ^ g2;
+    int32_t x3 = f3 ^ g3;
+    int32_t x4 = f4 ^ g4;
+    int32_t x5 = f5 ^ g5;
+    int32_t x6 = f6 ^ g6;
+    int32_t x7 = f7 ^ g7;
+    int32_t x8 = f8 ^ g8;
+    int32_t x9 = f9 ^ g9;
+
+    b = (unsigned int) (- (int) b); /* silence warning */
+    x0 &= b;
+    x1 &= b;
+    x2 &= b;
+    x3 &= b;
+    x4 &= b;
+    x5 &= b;
+    x6 &= b;
+    x7 &= b;
+    x8 &= b;
+    x9 &= b;
+    
+    f[0] = f0 ^ x0;
+    f[1] = f1 ^ x1;
+    f[2] = f2 ^ x2;
+    f[3] = f3 ^ x3;
+    f[4] = f4 ^ x4;
+    f[5] = f5 ^ x5;
+    f[6] = f6 ^ x6;
+    f[7] = f7 ^ x7;
+    f[8] = f8 ^ x8;
+    f[9] = f9 ^ x9;
+}
+
+/*
+    Replace (f,g) with (g,f) if b == 1;
+    replace (f,g) with (f,g) if b == 0.
+
+    Preconditions: b in {0,1}.
+*/
+
+void fe_cswap(fe f,fe g,unsigned int b) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t x0 = f0 ^ g0;
+    int32_t x1 = f1 ^ g1;
+    int32_t x2 = f2 ^ g2;
+    int32_t x3 = f3 ^ g3;
+    int32_t x4 = f4 ^ g4;
+    int32_t x5 = f5 ^ g5;
+    int32_t x6 = f6 ^ g6;
+    int32_t x7 = f7 ^ g7;
+    int32_t x8 = f8 ^ g8;
+    int32_t x9 = f9 ^ g9;
+    b = -b;
+    x0 &= b;
+    x1 &= b;
+    x2 &= b;
+    x3 &= b;
+    x4 &= b;
+    x5 &= b;
+    x6 &= b;
+    x7 &= b;
+    x8 &= b;
+    x9 &= b;
+    f[0] = f0 ^ x0;
+    f[1] = f1 ^ x1;
+    f[2] = f2 ^ x2;
+    f[3] = f3 ^ x3;
+    f[4] = f4 ^ x4;
+    f[5] = f5 ^ x5;
+    f[6] = f6 ^ x6;
+    f[7] = f7 ^ x7;
+    f[8] = f8 ^ x8;
+    f[9] = f9 ^ x9;
+    g[0] = g0 ^ x0;
+    g[1] = g1 ^ x1;
+    g[2] = g2 ^ x2;
+    g[3] = g3 ^ x3;
+    g[4] = g4 ^ x4;
+    g[5] = g5 ^ x5;
+    g[6] = g6 ^ x6;
+    g[7] = g7 ^ x7;
+    g[8] = g8 ^ x8;
+    g[9] = g9 ^ x9;
+}
+
+
+
+/*
+    h = f
+*/
+
+void fe_copy(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    
+    h[0] = f0;
+    h[1] = f1;
+    h[2] = f2;
+    h[3] = f3;
+    h[4] = f4;
+    h[5] = f5;
+    h[6] = f6;
+    h[7] = f7;
+    h[8] = f8;
+    h[9] = f9;
+}
+
+
+
+/*
+    Ignores top bit of h.
+*/
+
+void fe_frombytes(fe h, const unsigned char *s) {
+    int64_t h0 = load_4(s);
+    int64_t h1 = load_3(s + 4) << 6;
+    int64_t h2 = load_3(s + 7) << 5;
+    int64_t h3 = load_3(s + 10) << 3;
+    int64_t h4 = load_3(s + 13) << 2;
+    int64_t h5 = load_4(s + 16);
+    int64_t h6 = load_3(s + 20) << 7;
+    int64_t h7 = load_3(s + 23) << 5;
+    int64_t h8 = load_3(s + 26) << 4;
+    int64_t h9 = (load_3(s + 29) & 8388607) << 2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+
+void fe_invert(fe out, const fe z) {
+    fe t0;
+    fe t1;
+    fe t2;
+    fe t3;
+    int i;
+
+    fe_sq(t0, z);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t2, t0);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t1, t2);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t2, t2, t1);
+    fe_sq(t3, t2);
+
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t3, t3);
+    }
+
+    fe_mul(t2, t3, t2);
+    fe_sq(t2, t2);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t2, t2, t1);
+    fe_sq(t3, t2);
+
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t3, t3);
+    }
+
+    fe_mul(t2, t3, t2);
+    fe_sq(t2, t2);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(out, t1, t0);
+}
+
+
+
+/*
+    return 1 if f is in {1,3,5,...,q-2}
+    return 0 if f is in {0,2,4,...,q-1}
+
+    Preconditions:
+       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnegative(const fe f) {
+    unsigned char s[32];
+
+    fe_tobytes(s, f);
+    
+    return s[0] & 1;
+}
+
+
+
+/*
+    return 1 if f == 0
+    return 0 if f != 0
+
+    Preconditions:
+       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnonzero(const fe f) {
+    unsigned char s[32];
+    unsigned char r;
+
+    fe_tobytes(s, f);
+
+    r = s[0];
+    #define F(i) r |= s[i]
+    F(1);
+    F(2);
+    F(3);
+    F(4);
+    F(5);
+    F(6);
+    F(7);
+    F(8);
+    F(9);
+    F(10);
+    F(11);
+    F(12);
+    F(13);
+    F(14);
+    F(15);
+    F(16);
+    F(17);
+    F(18);
+    F(19);
+    F(20);
+    F(21);
+    F(22);
+    F(23);
+    F(24);
+    F(25);
+    F(26);
+    F(27);
+    F(28);
+    F(29);
+    F(30);
+    F(31);
+    #undef F
+
+    return r != 0;
+}
+
+
+
+/*
+    h = f * g
+    Can overlap h with f or g.
+
+    Preconditions:
+       |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+       |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+    Postconditions:
+       |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+    */
+
+    /*
+    Notes on implementation strategy:
+
+    Using schoolbook multiplication.
+    Karatsuba would save a little in some cost models.
+
+    Most multiplications by 2 and 19 are 32-bit precomputations;
+    cheaper than 64-bit postcomputations.
+
+    There is one remaining multiplication by 19 in the carry chain;
+    one *19 precomputation can be merged into this,
+    but the resulting data flow is considerably less clean.
+
+    There are 12 carries below.
+    10 of them are 2-way parallelizable and vectorizable.
+    Can get away with 11 carries, but then data flow is much deeper.
+
+    With tighter constraints on inputs can squeeze carries into int32.
+*/
+
+void fe_mul(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
+    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+    int32_t g3_19 = 19 * g3;
+    int32_t g4_19 = 19 * g4;
+    int32_t g5_19 = 19 * g5;
+    int32_t g6_19 = 19 * g6;
+    int32_t g7_19 = 19 * g7;
+    int32_t g8_19 = 19 * g8;
+    int32_t g9_19 = 19 * g9;
+    int32_t f1_2 = 2 * f1;
+    int32_t f3_2 = 2 * f3;
+    int32_t f5_2 = 2 * f5;
+    int32_t f7_2 = 2 * f7;
+    int32_t f9_2 = 2 * f9;
+    int64_t f0g0    = f0   * (int64_t) g0;
+    int64_t f0g1    = f0   * (int64_t) g1;
+    int64_t f0g2    = f0   * (int64_t) g2;
+    int64_t f0g3    = f0   * (int64_t) g3;
+    int64_t f0g4    = f0   * (int64_t) g4;
+    int64_t f0g5    = f0   * (int64_t) g5;
+    int64_t f0g6    = f0   * (int64_t) g6;
+    int64_t f0g7    = f0   * (int64_t) g7;
+    int64_t f0g8    = f0   * (int64_t) g8;
+    int64_t f0g9    = f0   * (int64_t) g9;
+    int64_t f1g0    = f1   * (int64_t) g0;
+    int64_t f1g1_2  = f1_2 * (int64_t) g1;
+    int64_t f1g2    = f1   * (int64_t) g2;
+    int64_t f1g3_2  = f1_2 * (int64_t) g3;
+    int64_t f1g4    = f1   * (int64_t) g4;
+    int64_t f1g5_2  = f1_2 * (int64_t) g5;
+    int64_t f1g6    = f1   * (int64_t) g6;
+    int64_t f1g7_2  = f1_2 * (int64_t) g7;
+    int64_t f1g8    = f1   * (int64_t) g8;
+    int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
+    int64_t f2g0    = f2   * (int64_t) g0;
+    int64_t f2g1    = f2   * (int64_t) g1;
+    int64_t f2g2    = f2   * (int64_t) g2;
+    int64_t f2g3    = f2   * (int64_t) g3;
+    int64_t f2g4    = f2   * (int64_t) g4;
+    int64_t f2g5    = f2   * (int64_t) g5;
+    int64_t f2g6    = f2   * (int64_t) g6;
+    int64_t f2g7    = f2   * (int64_t) g7;
+    int64_t f2g8_19 = f2   * (int64_t) g8_19;
+    int64_t f2g9_19 = f2   * (int64_t) g9_19;
+    int64_t f3g0    = f3   * (int64_t) g0;
+    int64_t f3g1_2  = f3_2 * (int64_t) g1;
+    int64_t f3g2    = f3   * (int64_t) g2;
+    int64_t f3g3_2  = f3_2 * (int64_t) g3;
+    int64_t f3g4    = f3   * (int64_t) g4;
+    int64_t f3g5_2  = f3_2 * (int64_t) g5;
+    int64_t f3g6    = f3   * (int64_t) g6;
+    int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
+    int64_t f3g8_19 = f3   * (int64_t) g8_19;
+    int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
+    int64_t f4g0    = f4   * (int64_t) g0;
+    int64_t f4g1    = f4   * (int64_t) g1;
+    int64_t f4g2    = f4   * (int64_t) g2;
+    int64_t f4g3    = f4   * (int64_t) g3;
+    int64_t f4g4    = f4   * (int64_t) g4;
+    int64_t f4g5    = f4   * (int64_t) g5;
+    int64_t f4g6_19 = f4   * (int64_t) g6_19;
+    int64_t f4g7_19 = f4   * (int64_t) g7_19;
+    int64_t f4g8_19 = f4   * (int64_t) g8_19;
+    int64_t f4g9_19 = f4   * (int64_t) g9_19;
+    int64_t f5g0    = f5   * (int64_t) g0;
+    int64_t f5g1_2  = f5_2 * (int64_t) g1;
+    int64_t f5g2    = f5   * (int64_t) g2;
+    int64_t f5g3_2  = f5_2 * (int64_t) g3;
+    int64_t f5g4    = f5   * (int64_t) g4;
+    int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
+    int64_t f5g6_19 = f5   * (int64_t) g6_19;
+    int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
+    int64_t f5g8_19 = f5   * (int64_t) g8_19;
+    int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
+    int64_t f6g0    = f6   * (int64_t) g0;
+    int64_t f6g1    = f6   * (int64_t) g1;
+    int64_t f6g2    = f6   * (int64_t) g2;
+    int64_t f6g3    = f6   * (int64_t) g3;
+    int64_t f6g4_19 = f6   * (int64_t) g4_19;
+    int64_t f6g5_19 = f6   * (int64_t) g5_19;
+    int64_t f6g6_19 = f6   * (int64_t) g6_19;
+    int64_t f6g7_19 = f6   * (int64_t) g7_19;
+    int64_t f6g8_19 = f6   * (int64_t) g8_19;
+    int64_t f6g9_19 = f6   * (int64_t) g9_19;
+    int64_t f7g0    = f7   * (int64_t) g0;
+    int64_t f7g1_2  = f7_2 * (int64_t) g1;
+    int64_t f7g2    = f7   * (int64_t) g2;
+    int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
+    int64_t f7g4_19 = f7   * (int64_t) g4_19;
+    int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
+    int64_t f7g6_19 = f7   * (int64_t) g6_19;
+    int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
+    int64_t f7g8_19 = f7   * (int64_t) g8_19;
+    int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
+    int64_t f8g0    = f8   * (int64_t) g0;
+    int64_t f8g1    = f8   * (int64_t) g1;
+    int64_t f8g2_19 = f8   * (int64_t) g2_19;
+    int64_t f8g3_19 = f8   * (int64_t) g3_19;
+    int64_t f8g4_19 = f8   * (int64_t) g4_19;
+    int64_t f8g5_19 = f8   * (int64_t) g5_19;
+    int64_t f8g6_19 = f8   * (int64_t) g6_19;
+    int64_t f8g7_19 = f8   * (int64_t) g7_19;
+    int64_t f8g8_19 = f8   * (int64_t) g8_19;
+    int64_t f8g9_19 = f8   * (int64_t) g9_19;
+    int64_t f9g0    = f9   * (int64_t) g0;
+    int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
+    int64_t f9g2_19 = f9   * (int64_t) g2_19;
+    int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
+    int64_t f9g4_19 = f9   * (int64_t) g4_19;
+    int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
+    int64_t f9g6_19 = f9   * (int64_t) g6_19;
+    int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
+    int64_t f9g8_19 = f9   * (int64_t) g8_19;
+    int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
+    int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
+    int64_t h1 = f0g1 + f1g0   + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
+    int64_t h2 = f0g2 + f1g1_2 + f2g0   + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
+    int64_t h3 = f0g3 + f1g2   + f2g1   + f3g0   + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
+    int64_t h4 = f0g4 + f1g3_2 + f2g2   + f3g1_2 + f4g0   + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
+    int64_t h5 = f0g5 + f1g4   + f2g3   + f3g2   + f4g1   + f5g0   + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
+    int64_t h6 = f0g6 + f1g5_2 + f2g4   + f3g3_2 + f4g2   + f5g1_2 + f6g0   + f7g9_38 + f8g8_19 + f9g7_38;
+    int64_t h7 = f0g7 + f1g6   + f2g5   + f3g4   + f4g3   + f5g2   + f6g1   + f7g0   + f8g9_19 + f9g8_19;
+    int64_t h8 = f0g8 + f1g7_2 + f2g6   + f3g5_2 + f4g4   + f5g3_2 + f6g2   + f7g1_2 + f8g0   + f9g9_38;
+    int64_t h9 = f0g9 + f1g8   + f2g7   + f3g6   + f4g5   + f5g4   + f6g3   + f7g2   + f8g1   + f9g0   ;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = f * 121666
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_mul121666(fe h, fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int64_t h0 = f0 * (int64_t) 121666;
+    int64_t h1 = f1 * (int64_t) 121666;
+    int64_t h2 = f2 * (int64_t) 121666;
+    int64_t h3 = f3 * (int64_t) 121666;
+    int64_t h4 = f4 * (int64_t) 121666;
+    int64_t h5 = f5 * (int64_t) 121666;
+    int64_t h6 = f6 * (int64_t) 121666;
+    int64_t h7 = f7 * (int64_t) 121666;
+    int64_t h8 = f8 * (int64_t) 121666;
+    int64_t h9 = f9 * (int64_t) 121666;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+    carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+    carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+    carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+    carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+    carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+    carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+    carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+    carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+    carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+/*
+h = -f
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_neg(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t h0 = -f0;
+    int32_t h1 = -f1;
+    int32_t h2 = -f2;
+    int32_t h3 = -f3;
+    int32_t h4 = -f4;
+    int32_t h5 = -f5;
+    int32_t h6 = -f6;
+    int32_t h7 = -f7;
+    int32_t h8 = -f8;
+    int32_t h9 = -f9;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+void fe_pow22523(fe out, const fe z) {
+    fe t0;
+    fe t1;
+    fe t2;
+    int i;
+    fe_sq(t0, z);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t0, t0);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t0, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_mul(out, t0, z);
+    return;
+}
+
+
+/*
+h = f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0  + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4 + f2f2   + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4   + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = 2 * f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq2(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0  + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4 + f2f2   + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4   + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    h0 += h0;
+    h1 += h1;
+    h2 += h2;
+    h3 += h3;
+    h4 += h4;
+    h5 += h5;
+    h6 += h6;
+    h7 += h7;
+    h8 += h8;
+    h9 += h9;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_sub(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t h0 = f0 - g0;
+    int32_t h1 = f1 - g1;
+    int32_t h2 = f2 - g2;
+    int32_t h3 = f3 - g3;
+    int32_t h4 = f4 - g4;
+    int32_t h5 = f5 - g5;
+    int32_t h6 = f6 - g6;
+    int32_t h7 = f7 - g7;
+    int32_t h8 = f8 - g8;
+    int32_t h9 = f9 - g9;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+
+/*
+Preconditions:
+  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Write p=2^255-19; q=floor(h/p).
+Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+Proof:
+  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+  Then 0<y<1.
+
+  Write r=h-pq.
+  Have 0<=r<=p-1=2^255-20.
+  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+
+  Write x=r+19(2^-255)r+y.
+  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+
+  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+*/
+
+void fe_tobytes(unsigned char *s, const fe h) {
+    int32_t h0 = h[0];
+    int32_t h1 = h[1];
+    int32_t h2 = h[2];
+    int32_t h3 = h[3];
+    int32_t h4 = h[4];
+    int32_t h5 = h[5];
+    int32_t h6 = h[6];
+    int32_t h7 = h[7];
+    int32_t h8 = h[8];
+    int32_t h9 = h[9];
+    int32_t q;
+    int32_t carry0;
+    int32_t carry1;
+    int32_t carry2;
+    int32_t carry3;
+    int32_t carry4;
+    int32_t carry5;
+    int32_t carry6;
+    int32_t carry7;
+    int32_t carry8;
+    int32_t carry9;
+    q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
+    q = (h0 + q) >> 26;
+    q = (h1 + q) >> 25;
+    q = (h2 + q) >> 26;
+    q = (h3 + q) >> 25;
+    q = (h4 + q) >> 26;
+    q = (h5 + q) >> 25;
+    q = (h6 + q) >> 26;
+    q = (h7 + q) >> 25;
+    q = (h8 + q) >> 26;
+    q = (h9 + q) >> 25;
+    /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+    h0 += 19 * q;
+    /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+    carry0 = h0 >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry1 = h1 >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry2 = h2 >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry3 = h3 >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry4 = h4 >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry5 = h5 >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry6 = h6 >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry7 = h7 >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry8 = h8 >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = h9 >> 25;
+    h9 -= carry9 << 25;
+
+    /* h10 = carry9 */
+    /*
+    Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+    Have h0+...+2^230 h9 between 0 and 2^255-1;
+    evidently 2^255 h10-2^255 q = 0.
+    Goal: Output h0+...+2^230 h9.
+    */
+    s[0] = (unsigned char) (h0 >> 0);
+    s[1] = (unsigned char) (h0 >> 8);
+    s[2] = (unsigned char) (h0 >> 16);
+    s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2));
+    s[4] = (unsigned char) (h1 >> 6);
+    s[5] = (unsigned char) (h1 >> 14);
+    s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3));
+    s[7] = (unsigned char) (h2 >> 5);
+    s[8] = (unsigned char) (h2 >> 13);
+    s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5));
+    s[10] = (unsigned char) (h3 >> 3);
+    s[11] = (unsigned char) (h3 >> 11);
+    s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6));
+    s[13] = (unsigned char) (h4 >> 2);
+    s[14] = (unsigned char) (h4 >> 10);
+    s[15] = (unsigned char) (h4 >> 18);
+    s[16] = (unsigned char) (h5 >> 0);
+    s[17] = (unsigned char) (h5 >> 8);
+    s[18] = (unsigned char) (h5 >> 16);
+    s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1));
+    s[20] = (unsigned char) (h6 >> 7);
+    s[21] = (unsigned char) (h6 >> 15);
+    s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3));
+    s[23] = (unsigned char) (h7 >> 5);
+    s[24] = (unsigned char) (h7 >> 13);
+    s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4));
+    s[26] = (unsigned char) (h8 >> 4);
+    s[27] = (unsigned char) (h8 >> 12);
+    s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6));
+    s[29] = (unsigned char) (h9 >> 2);
+    s[30] = (unsigned char) (h9 >> 10);
+    s[31] = (unsigned char) (h9 >> 18);
+}
diff --git a/lib/ed25519/src/fe.h b/lib/ed25519/src/fe.h
new file mode 100644
index 0000000..b4b62d2
--- /dev/null
+++ b/lib/ed25519/src/fe.h
@@ -0,0 +1,41 @@
+#ifndef FE_H
+#define FE_H
+
+#include "fixedint.h"
+
+
+/*
+    fe means field element.
+    Here the field is \Z/(2^255-19).
+    An element t, entries t[0]...t[9], represents the integer
+    t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
+    Bounds on each t[i] vary depending on context.
+*/
+
+
+typedef int32_t fe[10];
+
+
+void fe_0(fe h);
+void fe_1(fe h);
+
+void fe_frombytes(fe h, const unsigned char *s);
+void fe_tobytes(unsigned char *s, const fe h);
+
+void fe_copy(fe h, const fe f);
+int fe_isnegative(const fe f);
+int fe_isnonzero(const fe f);
+void fe_cmov(fe f, const fe g, unsigned int b);
+void fe_cswap(fe f, fe g, unsigned int b);
+
+void fe_neg(fe h, const fe f);
+void fe_add(fe h, const fe f, const fe g);
+void fe_invert(fe out, const fe z);
+void fe_sq(fe h, const fe f);
+void fe_sq2(fe h, const fe f);
+void fe_mul(fe h, const fe f, const fe g);
+void fe_mul121666(fe h, fe f);
+void fe_pow22523(fe out, const fe z);
+void fe_sub(fe h, const fe f, const fe g);
+
+#endif
diff --git a/lib/ed25519/src/fixedint.h b/lib/ed25519/src/fixedint.h
new file mode 100644
index 0000000..1a8745b
--- /dev/null
+++ b/lib/ed25519/src/fixedint.h
@@ -0,0 +1,72 @@
+/*
+    Portable header to provide the 32 and 64 bits type.
+
+    Not a compatible replacement for <stdint.h>, do not blindly use it as such.
+*/
+
+#if ((defined(__STDC__) && __STDC__ && __STDC_VERSION__ >= 199901L) || (defined(__WATCOMC__) && (defined(_STDINT_H_INCLUDED) || __WATCOMC__ >= 1250)) || (defined(__GNUC__) && (defined(_STDINT_H) || defined(_STDINT_H_) || defined(__UINT_FAST64_TYPE__)) )) && !defined(FIXEDINT_H_INCLUDED)
+    #include <stdint.h>
+    #define FIXEDINT_H_INCLUDED
+
+    #if defined(__WATCOMC__) && __WATCOMC__ >= 1250 && !defined(UINT64_C)
+        #include <limits.h>
+        #define UINT64_C(x) (x + (UINT64_MAX - UINT64_MAX))
+    #endif
+#endif
+
+
+#ifndef FIXEDINT_H_INCLUDED
+    #define FIXEDINT_H_INCLUDED
+    
+    #include <limits.h>
+
+    /* (u)int32_t */
+    #ifndef uint32_t
+        #if (ULONG_MAX == 0xffffffffUL)
+            typedef unsigned long uint32_t;
+        #elif (UINT_MAX == 0xffffffffUL)
+            typedef unsigned int uint32_t;
+        #elif (USHRT_MAX == 0xffffffffUL)
+            typedef unsigned short uint32_t;
+        #endif
+    #endif
+
+
+    #ifndef int32_t
+        #if (LONG_MAX == 0x7fffffffL)
+            typedef signed long int32_t;
+        #elif (INT_MAX == 0x7fffffffL)
+            typedef signed int int32_t;
+        #elif (SHRT_MAX == 0x7fffffffL)
+            typedef signed short int32_t;
+        #endif
+    #endif
+
+
+    /* (u)int64_t */
+    #if (defined(__STDC__) && defined(__STDC_VERSION__) && __STDC__ && __STDC_VERSION__ >= 199901L)
+        typedef long long int64_t;
+        typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif defined(__GNUC__)
+        __extension__ typedef long long int64_t;
+        __extension__ typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif defined(__MWERKS__) || defined(__SUNPRO_C) || defined(__SUNPRO_CC) || defined(__APPLE_CC__) || defined(_LONG_LONG) || defined(_CRAYC)
+        typedef long long int64_t;
+        typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif (defined(__WATCOMC__) && defined(__WATCOM_INT64__)) || (defined(_MSC_VER) && _INTEGRAL_MAX_BITS >= 64) || (defined(__BORLANDC__) && __BORLANDC__ > 0x460) || defined(__alpha) || defined(__DECC)
+        typedef __int64 int64_t;
+        typedef unsigned __int64 uint64_t;
+
+        #define UINT64_C(v) v ##UI64
+        #define INT64_C(v) v ##I64
+    #endif
+#endif
diff --git a/lib/ed25519/src/ge.c b/lib/ed25519/src/ge.c
new file mode 100644
index 0000000..3c342b1
--- /dev/null
+++ b/lib/ed25519/src/ge.c
@@ -0,0 +1,467 @@
+#include "ge.h"
+#include "precomp_data.h"
+
+
+/*
+r = p + q
+*/
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+    fe t0;
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YplusX);
+    fe_mul(r->Y, r->Y, q->YminusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
+}
+
+
+static void slide(signed char *r, const unsigned char *a) {
+    int i;
+    int b;
+    int k;
+
+    for (i = 0; i < 256; ++i) {
+        r[i] = 1 & (a[i >> 3] >> (i & 7));
+    }
+
+    for (i = 0; i < 256; ++i)
+        if (r[i]) {
+            for (b = 1; b <= 6 && i + b < 256; ++b) {
+                if (r[i + b]) {
+                    if (r[i] + (r[i + b] << b) <= 15) {
+                        r[i] += r[i + b] << b;
+                        r[i + b] = 0;
+                    } else if (r[i] - (r[i + b] << b) >= -15) {
+                        r[i] -= r[i + b] << b;
+
+                        for (k = i + b; k < 256; ++k) {
+                            if (!r[k]) {
+                                r[k] = 1;
+                                break;
+                            }
+
+                            r[k] = 0;
+                        }
+                    } else {
+                        break;
+                    }
+                }
+            }
+        }
+}
+
+/*
+r = a * A + b * B
+where a = a[0]+256*a[1]+...+256^31 a[31].
+and b = b[0]+256*b[1]+...+256^31 b[31].
+B is the Ed25519 base point (x,4/5) with x positive.
+*/
+
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) {
+    signed char aslide[256];
+    signed char bslide[256];
+    ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+    ge_p1p1 t;
+    ge_p3 u;
+    ge_p3 A2;
+    int i;
+    slide(aslide, a);
+    slide(bslide, b);
+    ge_p3_to_cached(&Ai[0], A);
+    ge_p3_dbl(&t, A);
+    ge_p1p1_to_p3(&A2, &t);
+    ge_add(&t, &A2, &Ai[0]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[1], &u);
+    ge_add(&t, &A2, &Ai[1]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[2], &u);
+    ge_add(&t, &A2, &Ai[2]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[3], &u);
+    ge_add(&t, &A2, &Ai[3]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[4], &u);
+    ge_add(&t, &A2, &Ai[4]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[5], &u);
+    ge_add(&t, &A2, &Ai[5]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[6], &u);
+    ge_add(&t, &A2, &Ai[6]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[7], &u);
+    ge_p2_0(r);
+
+    for (i = 255; i >= 0; --i) {
+        if (aslide[i] || bslide[i]) {
+            break;
+        }
+    }
+
+    for (; i >= 0; --i) {
+        ge_p2_dbl(&t, r);
+
+        if (aslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_add(&t, &u, &Ai[aslide[i] / 2]);
+        } else if (aslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
+        }
+
+        if (bslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_madd(&t, &u, &Bi[bslide[i] / 2]);
+        } else if (bslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
+        }
+
+        ge_p1p1_to_p2(r, &t);
+    }
+}
+
+
+static const fe d = {
+    -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116
+};
+
+static const fe sqrtm1 = {
+    -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482
+};
+
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s) {
+    fe u;
+    fe v;
+    fe v3;
+    fe vxx;
+    fe check;
+    fe_frombytes(h->Y, s);
+    fe_1(h->Z);
+    fe_sq(u, h->Y);
+    fe_mul(v, u, d);
+    fe_sub(u, u, h->Z);     /* u = y^2-1 */
+    fe_add(v, v, h->Z);     /* v = dy^2+1 */
+    fe_sq(v3, v);
+    fe_mul(v3, v3, v);      /* v3 = v^3 */
+    fe_sq(h->X, v3);
+    fe_mul(h->X, h->X, v);
+    fe_mul(h->X, h->X, u);  /* x = uv^7 */
+    fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
+    fe_mul(h->X, h->X, v3);
+    fe_mul(h->X, h->X, u);  /* x = uv^3(uv^7)^((q-5)/8) */
+    fe_sq(vxx, h->X);
+    fe_mul(vxx, vxx, v);
+    fe_sub(check, vxx, u);  /* vx^2-u */
+
+    if (fe_isnonzero(check)) {
+        fe_add(check, vxx, u); /* vx^2+u */
+
+        if (fe_isnonzero(check)) {
+            return -1;
+        }
+
+        fe_mul(h->X, h->X, sqrtm1);
+    }
+
+    if (fe_isnegative(h->X) == (s[31] >> 7)) {
+        fe_neg(h->X, h->X);
+    }
+
+    fe_mul(h->T, h->X, h->Y);
+    return 0;
+}
+
+
+/*
+r = p + q
+*/
+
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+    fe t0;
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yplusx);
+    fe_mul(r->Y, r->Y, q->yminusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
+}
+
+
+/*
+r = p - q
+*/
+
+void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+    fe t0;
+
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yminusx);
+    fe_mul(r->Y, r->Y, q->yplusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
+}
+
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+}
+
+
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+    fe_mul(r->T, p->X, p->Y);
+}
+
+
+void ge_p2_0(ge_p2 *h) {
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+}
+
+
+
+/*
+r = 2 * p
+*/
+
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
+    fe t0;
+
+    fe_sq(r->X, p->X);
+    fe_sq(r->Z, p->Y);
+    fe_sq2(r->T, p->Z);
+    fe_add(r->Y, p->X, p->Y);
+    fe_sq(t0, r->Y);
+    fe_add(r->Y, r->Z, r->X);
+    fe_sub(r->Z, r->Z, r->X);
+    fe_sub(r->X, t0, r->Y);
+    fe_sub(r->T, r->T, r->Z);
+}
+
+
+void ge_p3_0(ge_p3 *h) {
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+    fe_0(h->T);
+}
+
+
+/*
+r = 2 * p
+*/
+
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
+    ge_p2 q;
+    ge_p3_to_p2(&q, p);
+    ge_p2_dbl(r, &q);
+}
+
+
+
+/*
+r = p
+*/
+
+static const fe d2 = {
+    -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199
+};
+
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
+    fe_add(r->YplusX, p->Y, p->X);
+    fe_sub(r->YminusX, p->Y, p->X);
+    fe_copy(r->Z, p->Z);
+    fe_mul(r->T2d, p->T, d2);
+}
+
+
+/*
+r = p
+*/
+
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
+    fe_copy(r->X, p->X);
+    fe_copy(r->Y, p->Y);
+    fe_copy(r->Z, p->Z);
+}
+
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) {
+    fe recip;
+    fe x;
+    fe y;
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}
+
+
+static unsigned char equal(signed char b, signed char c) {
+    unsigned char ub = b;
+    unsigned char uc = c;
+    unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
+    uint64_t y = x; /* 0: yes; 1..255: no */
+    y -= 1; /* large: yes; 0..254: no */
+    y >>= 63; /* 1: yes; 0: no */
+    return (unsigned char) y;
+}
+
+static unsigned char negative(signed char b) {
+    uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+    x >>= 63; /* 1: yes; 0: no */
+    return (unsigned char) x;
+}
+
+static void cmov(ge_precomp *t, ge_precomp *u, unsigned char b) {
+    fe_cmov(t->yplusx, u->yplusx, b);
+    fe_cmov(t->yminusx, u->yminusx, b);
+    fe_cmov(t->xy2d, u->xy2d, b);
+}
+
+
+static void select(ge_precomp *t, int pos, signed char b) {
+    ge_precomp minust;
+    unsigned char bnegative = negative(b);
+    unsigned char babs = b - (((-bnegative) & b) << 1);
+    fe_1(t->yplusx);
+    fe_1(t->yminusx);
+    fe_0(t->xy2d);
+    cmov(t, &base[pos][0], equal(babs, 1));
+    cmov(t, &base[pos][1], equal(babs, 2));
+    cmov(t, &base[pos][2], equal(babs, 3));
+    cmov(t, &base[pos][3], equal(babs, 4));
+    cmov(t, &base[pos][4], equal(babs, 5));
+    cmov(t, &base[pos][5], equal(babs, 6));
+    cmov(t, &base[pos][6], equal(babs, 7));
+    cmov(t, &base[pos][7], equal(babs, 8));
+    fe_copy(minust.yplusx, t->yminusx);
+    fe_copy(minust.yminusx, t->yplusx);
+    fe_neg(minust.xy2d, t->xy2d);
+    cmov(t, &minust, bnegative);
+}
+
+/*
+h = a * B
+where a = a[0]+256*a[1]+...+256^31 a[31]
+B is the Ed25519 base point (x,4/5) with x positive.
+
+Preconditions:
+  a[31] <= 127
+*/
+
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) {
+    signed char e[64];
+    signed char carry;
+    ge_p1p1 r;
+    ge_p2 s;
+    ge_precomp t;
+    int i;
+
+    for (i = 0; i < 32; ++i) {
+        e[2 * i + 0] = (a[i] >> 0) & 15;
+        e[2 * i + 1] = (a[i] >> 4) & 15;
+    }
+
+    /* each e[i] is between 0 and 15 */
+    /* e[63] is between 0 and 7 */
+    carry = 0;
+
+    for (i = 0; i < 63; ++i) {
+        e[i] += carry;
+        carry = e[i] + 8;
+        carry >>= 4;
+        e[i] -= carry << 4;
+    }
+
+    e[63] += carry;
+    /* each e[i] is between -8 and 8 */
+    ge_p3_0(h);
+
+    for (i = 1; i < 64; i += 2) {
+        select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+
+    ge_p3_dbl(&r, h);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p3(h, &r);
+
+    for (i = 0; i < 64; i += 2) {
+        select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+}
+
+
+/*
+r = p - q
+*/
+
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+    fe t0;
+    
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YminusX);
+    fe_mul(r->Y, r->Y, q->YplusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
+}
+
+
+void ge_tobytes(unsigned char *s, const ge_p2 *h) {
+    fe recip;
+    fe x;
+    fe y;
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}
diff --git a/lib/ed25519/src/ge.h b/lib/ed25519/src/ge.h
new file mode 100644
index 0000000..17fde2d
--- /dev/null
+++ b/lib/ed25519/src/ge.h
@@ -0,0 +1,74 @@
+#ifndef GE_H
+#define GE_H
+
+#include "fe.h"
+
+
+/*
+ge means group element.
+
+Here the group is the set of pairs (x,y) of field elements (see fe.h)
+satisfying -x^2 + y^2 = 1 + d x^2y^2
+where d = -121665/121666.
+
+Representations:
+  ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
+  ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+  ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+  ge_precomp (Duif): (y+x,y-x,2dxy)
+*/
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+} ge_p2;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p3;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p1p1;
+
+typedef struct {
+  fe yplusx;
+  fe yminusx;
+  fe xy2d;
+} ge_precomp;
+
+typedef struct {
+  fe YplusX;
+  fe YminusX;
+  fe Z;
+  fe T2d;
+} ge_cached;
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h);
+void ge_tobytes(unsigned char *s, const ge_p2 *h);
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s);
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b);
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q);
+void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q);
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a);
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p);
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p);
+void ge_p2_0(ge_p2 *h);
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p);
+void ge_p3_0(ge_p3 *h);
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p);
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p);
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p);
+
+#endif
diff --git a/lib/ed25519/src/key_exchange.c b/lib/ed25519/src/key_exchange.c
new file mode 100644
index 0000000..abd75da
--- /dev/null
+++ b/lib/ed25519/src/key_exchange.c
@@ -0,0 +1,79 @@
+#include "ed25519.h"
+#include "fe.h"
+
+void ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key) {
+    unsigned char e[32];
+    unsigned int i;
+    
+    fe x1;
+    fe x2;
+    fe z2;
+    fe x3;
+    fe z3;
+    fe tmp0;
+    fe tmp1;
+
+    int pos;
+    unsigned int swap;
+    unsigned int b;
+
+    /* copy the private key and make sure it's valid */
+    for (i = 0; i < 32; ++i) {
+        e[i] = private_key[i];
+    }
+
+    e[0] &= 248;
+    e[31] &= 63;
+    e[31] |= 64;
+
+    /* unpack the public key and convert edwards to montgomery */
+    /* due to CodesInChaos: montgomeryX = (edwardsY + 1)*inverse(1 - edwardsY) mod p */
+    fe_frombytes(x1, public_key);
+    fe_1(tmp1);
+    fe_add(tmp0, x1, tmp1);
+    fe_sub(tmp1, tmp1, x1);
+    fe_invert(tmp1, tmp1);
+    fe_mul(x1, tmp0, tmp1);
+
+    fe_1(x2);
+    fe_0(z2);
+    fe_copy(x3, x1);
+    fe_1(z3);
+
+    swap = 0;
+    for (pos = 254; pos >= 0; --pos) {
+        b = e[pos / 8] >> (pos & 7);
+        b &= 1;
+        swap ^= b;
+        fe_cswap(x2, x3, swap);
+        fe_cswap(z2, z3, swap);
+        swap = b;
+
+        /* from montgomery.h */
+        fe_sub(tmp0, x3, z3);
+        fe_sub(tmp1, x2, z2);
+        fe_add(x2, x2, z2);
+        fe_add(z2, x3, z3);
+        fe_mul(z3, tmp0, x2);
+        fe_mul(z2, z2, tmp1);
+        fe_sq(tmp0, tmp1);
+        fe_sq(tmp1, x2);
+        fe_add(x3, z3, z2);
+        fe_sub(z2, z3, z2);
+        fe_mul(x2, tmp1, tmp0);
+        fe_sub(tmp1, tmp1, tmp0);
+        fe_sq(z2, z2);
+        fe_mul121666(z3, tmp1);
+        fe_sq(x3, x3);
+        fe_add(tmp0, tmp0, z3);
+        fe_mul(z3, x1, z2);
+        fe_mul(z2, tmp1, tmp0);
+    }
+
+    fe_cswap(x2, x3, swap);
+    fe_cswap(z2, z3, swap);
+
+    fe_invert(z2, z2);
+    fe_mul(x2, x2, z2);
+    fe_tobytes(shared_secret, x2);
+}
diff --git a/lib/ed25519/src/keypair.c b/lib/ed25519/src/keypair.c
new file mode 100644
index 0000000..dc1b8ec
--- /dev/null
+++ b/lib/ed25519/src/keypair.c
@@ -0,0 +1,16 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+
+
+void ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed) {
+    ge_p3 A;
+
+    sha512(seed, 32, private_key);
+    private_key[0] &= 248;
+    private_key[31] &= 63;
+    private_key[31] |= 64;
+
+    ge_scalarmult_base(&A, private_key);
+    ge_p3_tobytes(public_key, &A);
+}
diff --git a/lib/ed25519/src/precomp_data.h b/lib/ed25519/src/precomp_data.h
new file mode 100644
index 0000000..776b84f
--- /dev/null
+++ b/lib/ed25519/src/precomp_data.h
@@ -0,0 +1,1391 @@
+static ge_precomp Bi[8] = {
+    {
+        { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
+        { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
+        { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
+    },
+    {
+        { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
+        { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
+        { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
+    },
+    {
+        { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
+        { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
+        { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
+    },
+    {
+        { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
+        { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
+        { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
+    },
+    {
+        { -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877 },
+        { -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951 },
+        { 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784 },
+    },
+    {
+        { -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436 },
+        { 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918 },
+        { 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877 },
+    },
+    {
+        { -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800 },
+        { -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305 },
+        { -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300 },
+    },
+    {
+        { -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876 },
+        { -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619 },
+        { -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683 },
+    },
+};
+
+
+/* base[i][j] = (j+1)*256^i*B */
+static ge_precomp base[32][8] = {
+    {
+        {
+            { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
+            { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
+            { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
+        },
+        {
+            { -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303 },
+            { -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081 },
+            { 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697 },
+        },
+        {
+            { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
+            { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
+            { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
+        },
+        {
+            { -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540 },
+            { 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397 },
+            { 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325 },
+        },
+        {
+            { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
+            { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
+            { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
+        },
+        {
+            { -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777 },
+            { -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737 },
+            { -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652 },
+        },
+        {
+            { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
+            { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
+            { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
+        },
+        {
+            { 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726 },
+            { -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955 },
+            { 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425 },
+        },
+    },
+    {
+        {
+            { -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171 },
+            { 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510 },
+            { 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660 },
+        },
+        {
+            { -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639 },
+            { 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963 },
+            { 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950 },
+        },
+        {
+            { -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568 },
+            { 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335 },
+            { 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628 },
+        },
+        {
+            { -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007 },
+            { -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772 },
+            { -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653 },
+        },
+        {
+            { 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567 },
+            { 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686 },
+            { 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372 },
+        },
+        {
+            { -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887 },
+            { -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954 },
+            { -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953 },
+        },
+        {
+            { 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833 },
+            { -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532 },
+            { -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876 },
+        },
+        {
+            { 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268 },
+            { 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214 },
+            { 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038 },
+        },
+    },
+    {
+        {
+            { 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800 },
+            { 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645 },
+            { -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664 },
+        },
+        {
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+            { 4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278 },
+        },
+        {
+            { 31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045 },
+            { 19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377 },
+            { 24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480 },
+        },
+        {
+            { 17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016 },
+            { 510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426 },
+            { 18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525 },
+        },
+        {
+            { 13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396 },
+            { 9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080 },
+            { 12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892 },
+        },
+        {
+            { 15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275 },
+            { 11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074 },
+            { 20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140 },
+        },
+        {
+            { -16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717 },
+            { -1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101 },
+            { 24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127 },
+        },
+    },
+    {
+        {
+            { -12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632 },
+            { -26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415 },
+            { -31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160 },
+        },
+        {
+            { 31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876 },
+            { 22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625 },
+            { -15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478 },
+        },
+        {
+            { 27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164 },
+            { 26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595 },
+            { -7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248 },
+        },
+        {
+            { -16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858 },
+            { 15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193 },
+            { 8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184 },
+        },
+        {
+            { -18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942 },
+            { -1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635 },
+            { 21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948 },
+        },
+        {
+            { 11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935 },
+            { -25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415 },
+            { -15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416 },
+        },
+        {
+            { -7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018 },
+            { 4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778 },
+            { 366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659 },
+        },
+        {
+            { -24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385 },
+            { 18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503 },
+            { 476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329 },
+        },
+    },
+    {
+        {
+            { 20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056 },
+            { -13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838 },
+            { 24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948 },
+        },
+        {
+            { -3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691 },
+            { -15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118 },
+            { -23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517 },
+        },
+        {
+            { -20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269 },
+            { -6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904 },
+            { -23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589 },
+        },
+        {
+            { -28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193 },
+            { -7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910 },
+            { -30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930 },
+        },
+        {
+            { -7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667 },
+            { 25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481 },
+            { -9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876 },
+        },
+        {
+            { 22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640 },
+            { -8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278 },
+            { -21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112 },
+        },
+        {
+            { 26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272 },
+            { 17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012 },
+            { -10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221 },
+        },
+        {
+            { 30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046 },
+            { 13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345 },
+            { -19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310 },
+        },
+    },
+    {
+        {
+            { 19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937 },
+            { 31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636 },
+            { -9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008 },
+        },
+        {
+            { -2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429 },
+            { -15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576 },
+            { 31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066 },
+        },
+        {
+            { -9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490 },
+            { -12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104 },
+            { 33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053 },
+        },
+        {
+            { 31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275 },
+            { -20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511 },
+            { 22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095 },
+        },
+        {
+            { -28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439 },
+            { 23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939 },
+            { -23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424 },
+        },
+        {
+            { 2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310 },
+            { 3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608 },
+            { -32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079 },
+        },
+        {
+            { -23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101 },
+            { 21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418 },
+            { 18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576 },
+        },
+        {
+            { 30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356 },
+            { 9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996 },
+            { -26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099 },
+        },
+    },
+    {
+        {
+            { -26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728 },
+            { -13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658 },
+            { -10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242 },
+        },
+        {
+            { -21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001 },
+            { -4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766 },
+            { 18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373 },
+        },
+        {
+            { 26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458 },
+            { -17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628 },
+            { -13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657 },
+        },
+        {
+            { -23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062 },
+            { 25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616 },
+            { 31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014 },
+        },
+        {
+            { 24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383 },
+            { -25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814 },
+            { -20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718 },
+        },
+        {
+            { 30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417 },
+            { 2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222 },
+            { 33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444 },
+        },
+        {
+            { -20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597 },
+            { 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970 },
+            { 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799 },
+        },
+        {
+            { -5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647 },
+            { 13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511 },
+            { -29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032 },
+        },
+    },
+    {
+        {
+            { 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834 },
+            { -23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461 },
+            { 29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062 },
+        },
+        {
+            { -25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516 },
+            { -20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547 },
+            { -24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240 },
+        },
+        {
+            { -17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038 },
+            { -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741 },
+            { 16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103 },
+        },
+        {
+            { -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747 },
+            { -1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323 },
+            { 31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016 },
+        },
+        {
+            { -14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373 },
+            { 15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228 },
+            { -2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141 },
+        },
+        {
+            { 16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399 },
+            { 11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831 },
+            { -185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376 },
+        },
+        {
+            { -32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 },
+            { -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 },
+            { -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 },
+        },
+        {
+            { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 },
+            { 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 },
+            { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 },
+        },
+    },
+};
\ No newline at end of file
diff --git a/lib/ed25519/src/sc.c b/lib/ed25519/src/sc.c
new file mode 100644
index 0000000..ca5bad2
--- /dev/null
+++ b/lib/ed25519/src/sc.c
@@ -0,0 +1,809 @@
+#include "fixedint.h"
+#include "sc.h"
+
+static uint64_t load_3(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+
+    return result;
+}
+
+static uint64_t load_4(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+    result |= ((uint64_t) in[3]) << 24;
+    
+    return result;
+}
+
+/*
+Input:
+  s[0]+256*s[1]+...+256^63*s[63] = s
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = s mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+  Overwrites s in place.
+*/
+
+void sc_reduce(unsigned char *s) {
+    int64_t s0 = 2097151 & load_3(s);
+    int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
+    int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
+    int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
+    int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
+    int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
+    int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
+    int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
+    int64_t s8 = 2097151 & load_3(s + 21);
+    int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
+    int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
+    int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
+    int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
+    int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
+    int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
+    int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
+    int64_t s16 = 2097151 & load_3(s + 42);
+    int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
+    int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
+    int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
+    int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
+    int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
+    int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
+    int64_t s23 = (load_4(s + 60) >> 3);
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23 = 0;
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22 = 0;
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21 = 0;
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20 = 0;
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19 = 0;
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18 = 0;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17 = 0;
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+    s16 = 0;
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+    s15 = 0;
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+    s14 = 0;
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+    s13 = 0;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+
+    s[0] = (unsigned char) (s0 >> 0);
+    s[1] = (unsigned char) (s0 >> 8);
+    s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
+    s[3] = (unsigned char) (s1 >> 3);
+    s[4] = (unsigned char) (s1 >> 11);
+    s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
+    s[6] = (unsigned char) (s2 >> 6);
+    s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
+    s[8] = (unsigned char) (s3 >> 1);
+    s[9] = (unsigned char) (s3 >> 9);
+    s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
+    s[11] = (unsigned char) (s4 >> 4);
+    s[12] = (unsigned char) (s4 >> 12);
+    s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
+    s[14] = (unsigned char) (s5 >> 7);
+    s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
+    s[16] = (unsigned char) (s6 >> 2);
+    s[17] = (unsigned char) (s6 >> 10);
+    s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
+    s[19] = (unsigned char) (s7 >> 5);
+    s[20] = (unsigned char) (s7 >> 13);
+    s[21] = (unsigned char) (s8 >> 0);
+    s[22] = (unsigned char) (s8 >> 8);
+    s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
+    s[24] = (unsigned char) (s9 >> 3);
+    s[25] = (unsigned char) (s9 >> 11);
+    s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
+    s[27] = (unsigned char) (s10 >> 6);
+    s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
+    s[29] = (unsigned char) (s11 >> 1);
+    s[30] = (unsigned char) (s11 >> 9);
+    s[31] = (unsigned char) (s11 >> 17);
+}
+
+
+
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+  c[0]+256*c[1]+...+256^31*c[31] = c
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) {
+    int64_t a0 = 2097151 & load_3(a);
+    int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+    int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+    int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+    int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+    int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+    int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+    int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+    int64_t a8 = 2097151 & load_3(a + 21);
+    int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+    int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+    int64_t a11 = (load_4(a + 28) >> 7);
+    int64_t b0 = 2097151 & load_3(b);
+    int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+    int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+    int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+    int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+    int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+    int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+    int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+    int64_t b8 = 2097151 & load_3(b + 21);
+    int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+    int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+    int64_t b11 = (load_4(b + 28) >> 7);
+    int64_t c0 = 2097151 & load_3(c);
+    int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
+    int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
+    int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
+    int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
+    int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
+    int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
+    int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
+    int64_t c8 = 2097151 & load_3(c + 21);
+    int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
+    int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
+    int64_t c11 = (load_4(c + 28) >> 7);
+    int64_t s0;
+    int64_t s1;
+    int64_t s2;
+    int64_t s3;
+    int64_t s4;
+    int64_t s5;
+    int64_t s6;
+    int64_t s7;
+    int64_t s8;
+    int64_t s9;
+    int64_t s10;
+    int64_t s11;
+    int64_t s12;
+    int64_t s13;
+    int64_t s14;
+    int64_t s15;
+    int64_t s16;
+    int64_t s17;
+    int64_t s18;
+    int64_t s19;
+    int64_t s20;
+    int64_t s21;
+    int64_t s22;
+    int64_t s23;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+    int64_t carry17;
+    int64_t carry18;
+    int64_t carry19;
+    int64_t carry20;
+    int64_t carry21;
+    int64_t carry22;
+
+    s0 = c0 + a0 * b0;
+    s1 = c1 + a0 * b1 + a1 * b0;
+    s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
+    s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
+    s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
+    s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
+    s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
+    s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
+    s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
+    s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
+    s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
+    s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
+    s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
+    s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
+    s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
+    s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
+    s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
+    s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
+    s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
+    s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
+    s20 = a9 * b11 + a10 * b10 + a11 * b9;
+    s21 = a10 * b11 + a11 * b10;
+    s22 = a11 * b11;
+    s23 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry18 = (s18 + (1 << 20)) >> 21;
+    s19 += carry18;
+    s18 -= carry18 << 21;
+    carry20 = (s20 + (1 << 20)) >> 21;
+    s21 += carry20;
+    s20 -= carry20 << 21;
+    carry22 = (s22 + (1 << 20)) >> 21;
+    s23 += carry22;
+    s22 -= carry22 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    carry17 = (s17 + (1 << 20)) >> 21;
+    s18 += carry17;
+    s17 -= carry17 << 21;
+    carry19 = (s19 + (1 << 20)) >> 21;
+    s20 += carry19;
+    s19 -= carry19 << 21;
+    carry21 = (s21 + (1 << 20)) >> 21;
+    s22 += carry21;
+    s21 -= carry21 << 21;
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23 = 0;
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22 = 0;
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21 = 0;
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20 = 0;
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19 = 0;
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18 = 0;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17 = 0;
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+    s16 = 0;
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+    s15 = 0;
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+    s14 = 0;
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+    s13 = 0;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    
+    s[0] = (unsigned char) (s0 >> 0);
+    s[1] = (unsigned char) (s0 >> 8);
+    s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
+    s[3] = (unsigned char) (s1 >> 3);
+    s[4] = (unsigned char) (s1 >> 11);
+    s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
+    s[6] = (unsigned char) (s2 >> 6);
+    s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
+    s[8] = (unsigned char) (s3 >> 1);
+    s[9] = (unsigned char) (s3 >> 9);
+    s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
+    s[11] = (unsigned char) (s4 >> 4);
+    s[12] = (unsigned char) (s4 >> 12);
+    s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
+    s[14] = (unsigned char) (s5 >> 7);
+    s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
+    s[16] = (unsigned char) (s6 >> 2);
+    s[17] = (unsigned char) (s6 >> 10);
+    s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
+    s[19] = (unsigned char) (s7 >> 5);
+    s[20] = (unsigned char) (s7 >> 13);
+    s[21] = (unsigned char) (s8 >> 0);
+    s[22] = (unsigned char) (s8 >> 8);
+    s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
+    s[24] = (unsigned char) (s9 >> 3);
+    s[25] = (unsigned char) (s9 >> 11);
+    s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
+    s[27] = (unsigned char) (s10 >> 6);
+    s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
+    s[29] = (unsigned char) (s11 >> 1);
+    s[30] = (unsigned char) (s11 >> 9);
+    s[31] = (unsigned char) (s11 >> 17);
+}
diff --git a/lib/ed25519/src/sc.h b/lib/ed25519/src/sc.h
new file mode 100644
index 0000000..8fa727e
--- /dev/null
+++ b/lib/ed25519/src/sc.h
@@ -0,0 +1,12 @@
+#ifndef SC_H
+#define SC_H
+
+/*
+The set of scalars is \Z/l
+where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_reduce(unsigned char *s);
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c);
+
+#endif
\ No newline at end of file
diff --git a/lib/ed25519/src/seed.c b/lib/ed25519/src/seed.c
new file mode 100644
index 0000000..25e5182
--- /dev/null
+++ b/lib/ed25519/src/seed.c
@@ -0,0 +1,40 @@
+#include "ed25519.h"
+
+#ifndef ED25519_NO_SEED
+
+#ifdef _WIN32
+#include <Windows.h>
+#include <Wincrypt.h>
+#else
+#include <stdio.h>
+#endif
+
+int ed25519_create_seed(unsigned char *seed) {
+#ifdef _WIN32
+    HCRYPTPROV prov;
+
+    if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT))  {
+        return 1;
+    }
+
+    if (!CryptGenRandom(prov, 32, seed))  {
+        CryptReleaseContext(prov, 0);
+        return 1;
+    }
+
+    CryptReleaseContext(prov, 0);
+#else
+    FILE *f = fopen("/dev/urandom", "rb");
+
+    if (f == NULL) {
+        return 1;
+    }
+
+    fread(seed, 1, 32, f);
+    fclose(f);
+#endif
+
+    return 0;
+}
+
+#endif
\ No newline at end of file
diff --git a/lib/ed25519/src/sha512.c b/lib/ed25519/src/sha512.c
new file mode 100644
index 0000000..cb8ae71
--- /dev/null
+++ b/lib/ed25519/src/sha512.c
@@ -0,0 +1,275 @@
+/* LibTomCrypt, modular cryptographic library -- Tom St Denis
+ *
+ * LibTomCrypt is a library that provides various cryptographic
+ * algorithms in a highly modular and flexible manner.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+#include "fixedint.h"
+#include "sha512.h"
+
+/* the K array */
+static const uint64_t K[80] = {
+    UINT64_C(0x428a2f98d728ae22), UINT64_C(0x7137449123ef65cd), 
+    UINT64_C(0xb5c0fbcfec4d3b2f), UINT64_C(0xe9b5dba58189dbbc),
+    UINT64_C(0x3956c25bf348b538), UINT64_C(0x59f111f1b605d019), 
+    UINT64_C(0x923f82a4af194f9b), UINT64_C(0xab1c5ed5da6d8118),
+    UINT64_C(0xd807aa98a3030242), UINT64_C(0x12835b0145706fbe), 
+    UINT64_C(0x243185be4ee4b28c), UINT64_C(0x550c7dc3d5ffb4e2),
+    UINT64_C(0x72be5d74f27b896f), UINT64_C(0x80deb1fe3b1696b1), 
+    UINT64_C(0x9bdc06a725c71235), UINT64_C(0xc19bf174cf692694),
+    UINT64_C(0xe49b69c19ef14ad2), UINT64_C(0xefbe4786384f25e3), 
+    UINT64_C(0x0fc19dc68b8cd5b5), UINT64_C(0x240ca1cc77ac9c65),
+    UINT64_C(0x2de92c6f592b0275), UINT64_C(0x4a7484aa6ea6e483), 
+    UINT64_C(0x5cb0a9dcbd41fbd4), UINT64_C(0x76f988da831153b5),
+    UINT64_C(0x983e5152ee66dfab), UINT64_C(0xa831c66d2db43210), 
+    UINT64_C(0xb00327c898fb213f), UINT64_C(0xbf597fc7beef0ee4),
+    UINT64_C(0xc6e00bf33da88fc2), UINT64_C(0xd5a79147930aa725), 
+    UINT64_C(0x06ca6351e003826f), UINT64_C(0x142929670a0e6e70),
+    UINT64_C(0x27b70a8546d22ffc), UINT64_C(0x2e1b21385c26c926), 
+    UINT64_C(0x4d2c6dfc5ac42aed), UINT64_C(0x53380d139d95b3df),
+    UINT64_C(0x650a73548baf63de), UINT64_C(0x766a0abb3c77b2a8), 
+    UINT64_C(0x81c2c92e47edaee6), UINT64_C(0x92722c851482353b),
+    UINT64_C(0xa2bfe8a14cf10364), UINT64_C(0xa81a664bbc423001),
+    UINT64_C(0xc24b8b70d0f89791), UINT64_C(0xc76c51a30654be30),
+    UINT64_C(0xd192e819d6ef5218), UINT64_C(0xd69906245565a910), 
+    UINT64_C(0xf40e35855771202a), UINT64_C(0x106aa07032bbd1b8),
+    UINT64_C(0x19a4c116b8d2d0c8), UINT64_C(0x1e376c085141ab53), 
+    UINT64_C(0x2748774cdf8eeb99), UINT64_C(0x34b0bcb5e19b48a8),
+    UINT64_C(0x391c0cb3c5c95a63), UINT64_C(0x4ed8aa4ae3418acb), 
+    UINT64_C(0x5b9cca4f7763e373), UINT64_C(0x682e6ff3d6b2b8a3),
+    UINT64_C(0x748f82ee5defb2fc), UINT64_C(0x78a5636f43172f60), 
+    UINT64_C(0x84c87814a1f0ab72), UINT64_C(0x8cc702081a6439ec),
+    UINT64_C(0x90befffa23631e28), UINT64_C(0xa4506cebde82bde9), 
+    UINT64_C(0xbef9a3f7b2c67915), UINT64_C(0xc67178f2e372532b),
+    UINT64_C(0xca273eceea26619c), UINT64_C(0xd186b8c721c0c207), 
+    UINT64_C(0xeada7dd6cde0eb1e), UINT64_C(0xf57d4f7fee6ed178),
+    UINT64_C(0x06f067aa72176fba), UINT64_C(0x0a637dc5a2c898a6), 
+    UINT64_C(0x113f9804bef90dae), UINT64_C(0x1b710b35131c471b),
+    UINT64_C(0x28db77f523047d84), UINT64_C(0x32caab7b40c72493), 
+    UINT64_C(0x3c9ebe0a15c9bebc), UINT64_C(0x431d67c49c100d4c),
+    UINT64_C(0x4cc5d4becb3e42b6), UINT64_C(0x597f299cfc657e2a), 
+    UINT64_C(0x5fcb6fab3ad6faec), UINT64_C(0x6c44198c4a475817)
+};
+
+/* Various logical functions */
+
+#define ROR64c(x, y) \
+    ( ((((x)&UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)(y)&UINT64_C(63))) | \
+      ((x)<<((uint64_t)(64-((y)&UINT64_C(63)))))) & UINT64_C(0xFFFFFFFFFFFFFFFF))
+
+#define STORE64H(x, y)                                                                     \
+   { (y)[0] = (unsigned char)(((x)>>56)&255); (y)[1] = (unsigned char)(((x)>>48)&255);     \
+     (y)[2] = (unsigned char)(((x)>>40)&255); (y)[3] = (unsigned char)(((x)>>32)&255);     \
+     (y)[4] = (unsigned char)(((x)>>24)&255); (y)[5] = (unsigned char)(((x)>>16)&255);     \
+     (y)[6] = (unsigned char)(((x)>>8)&255); (y)[7] = (unsigned char)((x)&255); }
+
+#define LOAD64H(x, y)                                                      \
+   { x = (((uint64_t)((y)[0] & 255))<<56)|(((uint64_t)((y)[1] & 255))<<48) | \
+         (((uint64_t)((y)[2] & 255))<<40)|(((uint64_t)((y)[3] & 255))<<32) | \
+         (((uint64_t)((y)[4] & 255))<<24)|(((uint64_t)((y)[5] & 255))<<16) | \
+         (((uint64_t)((y)[6] & 255))<<8)|(((uint64_t)((y)[7] & 255))); }
+
+
+#define Ch(x,y,z)       (z ^ (x & (y ^ z)))
+#define Maj(x,y,z)      (((x | y) & z) | (x & y)) 
+#define S(x, n)         ROR64c(x, n)
+#define R(x, n)         (((x) &UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)n))
+#define Sigma0(x)       (S(x, 28) ^ S(x, 34) ^ S(x, 39))
+#define Sigma1(x)       (S(x, 14) ^ S(x, 18) ^ S(x, 41))
+#define Gamma0(x)       (S(x, 1) ^ S(x, 8) ^ R(x, 7))
+#define Gamma1(x)       (S(x, 19) ^ S(x, 61) ^ R(x, 6))
+#ifndef MIN
+   #define MIN(x, y) ( ((x)<(y))?(x):(y) )
+#endif
+
+/* compress 1024-bits */
+static int sha512_compress(sha512_context *md, unsigned char *buf)
+{
+    uint64_t S[8], W[80], t0, t1;
+    int i;
+
+    /* copy state into S */
+    for (i = 0; i < 8; i++) {
+        S[i] = md->state[i];
+    }
+
+    /* copy the state into 1024-bits into W[0..15] */
+    for (i = 0; i < 16; i++) {
+        LOAD64H(W[i], buf + (8*i));
+    }
+
+    /* fill W[16..79] */
+    for (i = 16; i < 80; i++) {
+        W[i] = Gamma1(W[i - 2]) + W[i - 7] + Gamma0(W[i - 15]) + W[i - 16];
+    }        
+
+/* Compress */
+    #define RND(a,b,c,d,e,f,g,h,i) \
+    t0 = h + Sigma1(e) + Ch(e, f, g) + K[i] + W[i]; \
+    t1 = Sigma0(a) + Maj(a, b, c);\
+    d += t0; \
+    h  = t0 + t1;
+
+    for (i = 0; i < 80; i += 8) {
+       RND(S[0],S[1],S[2],S[3],S[4],S[5],S[6],S[7],i+0);
+       RND(S[7],S[0],S[1],S[2],S[3],S[4],S[5],S[6],i+1);
+       RND(S[6],S[7],S[0],S[1],S[2],S[3],S[4],S[5],i+2);
+       RND(S[5],S[6],S[7],S[0],S[1],S[2],S[3],S[4],i+3);
+       RND(S[4],S[5],S[6],S[7],S[0],S[1],S[2],S[3],i+4);
+       RND(S[3],S[4],S[5],S[6],S[7],S[0],S[1],S[2],i+5);
+       RND(S[2],S[3],S[4],S[5],S[6],S[7],S[0],S[1],i+6);
+       RND(S[1],S[2],S[3],S[4],S[5],S[6],S[7],S[0],i+7);
+   }
+
+   #undef RND
+
+
+
+    /* feedback */
+   for (i = 0; i < 8; i++) {
+        md->state[i] = md->state[i] + S[i];
+    }
+
+    return 0;
+}
+
+
+/**
+   Initialize the hash state
+   @param md   The hash state you wish to initialize
+   @return 0 if successful
+*/
+int sha512_init(sha512_context * md) {
+    if (md == NULL) return 1;
+
+    md->curlen = 0;
+    md->length = 0;
+    md->state[0] = UINT64_C(0x6a09e667f3bcc908);
+    md->state[1] = UINT64_C(0xbb67ae8584caa73b);
+    md->state[2] = UINT64_C(0x3c6ef372fe94f82b);
+    md->state[3] = UINT64_C(0xa54ff53a5f1d36f1);
+    md->state[4] = UINT64_C(0x510e527fade682d1);
+    md->state[5] = UINT64_C(0x9b05688c2b3e6c1f);
+    md->state[6] = UINT64_C(0x1f83d9abfb41bd6b);
+    md->state[7] = UINT64_C(0x5be0cd19137e2179);
+
+    return 0;
+}
+
+/**
+   Process a block of memory though the hash
+   @param md     The hash state
+   @param in     The data to hash
+   @param inlen  The length of the data (octets)
+   @return 0 if successful
+*/
+int sha512_update (sha512_context * md, const unsigned char *in, size_t inlen)               
+{                                                                                           
+    size_t n;
+    size_t i;                                                                        
+    int           err;     
+    if (md == NULL) return 1;  
+    if (in == NULL) return 1;                                                              
+    if (md->curlen > sizeof(md->buf)) {                             
+       return 1;                                                            
+    }                                                                                       
+    while (inlen > 0) {                                                                     
+        if (md->curlen == 0 && inlen >= 128) {                           
+           if ((err = sha512_compress (md, (unsigned char *)in)) != 0) {               
+              return err;                                                                   
+           }                                                                                
+           md->length += 128 * 8;                                        
+           in             += 128;                                                    
+           inlen          -= 128;                                                    
+        } else {                                                                            
+           n = MIN(inlen, (128 - md->curlen));
+
+           for (i = 0; i < n; i++) {
+            md->buf[i + md->curlen] = in[i];
+           }
+
+
+           md->curlen += n;                                                     
+           in             += n;                                                             
+           inlen          -= n;                                                             
+           if (md->curlen == 128) {                                      
+              if ((err = sha512_compress (md, md->buf)) != 0) {            
+                 return err;                                                                
+              }                                                                             
+              md->length += 8*128;                                       
+              md->curlen = 0;                                                   
+           }                                                                                
+       }                                                                                    
+    }                                                                                       
+    return 0;                                                                        
+}
+
+/**
+   Terminate the hash to get the digest
+   @param md  The hash state
+   @param out [out] The destination of the hash (64 bytes)
+   @return 0 if successful
+*/
+   int sha512_final(sha512_context * md, unsigned char *out)
+   {
+    int i;
+
+    if (md == NULL) return 1;
+    if (out == NULL) return 1;
+
+    if (md->curlen >= sizeof(md->buf)) {
+     return 1;
+ }
+
+    /* increase the length of the message */
+ md->length += md->curlen * UINT64_C(8);
+
+    /* append the '1' bit */
+ md->buf[md->curlen++] = (unsigned char)0x80;
+
+    /* if the length is currently above 112 bytes we append zeros
+     * then compress.  Then we can fall back to padding zeros and length
+     * encoding like normal.
+     */
+     if (md->curlen > 112) {
+        while (md->curlen < 128) {
+            md->buf[md->curlen++] = (unsigned char)0;
+        }
+        sha512_compress(md, md->buf);
+        md->curlen = 0;
+    }
+
+    /* pad upto 120 bytes of zeroes 
+     * note: that from 112 to 120 is the 64 MSB of the length.  We assume that you won't hash
+     * > 2^64 bits of data... :-)
+     */
+while (md->curlen < 120) {
+    md->buf[md->curlen++] = (unsigned char)0;
+}
+
+    /* store length */
+STORE64H(md->length, md->buf+120);
+sha512_compress(md, md->buf);
+
+    /* copy output */
+for (i = 0; i < 8; i++) {
+    STORE64H(md->state[i], out+(8*i));
+}
+
+return 0;
+}
+
+int sha512(const unsigned char *message, size_t message_len, unsigned char *out)
+{
+    sha512_context ctx;
+    int ret;
+    if ((ret = sha512_init(&ctx))) return ret;
+    if ((ret = sha512_update(&ctx, message, message_len))) return ret;
+    if ((ret = sha512_final(&ctx, out))) return ret;
+    return 0;
+}
diff --git a/lib/ed25519/src/sha512.h b/lib/ed25519/src/sha512.h
new file mode 100644
index 0000000..e56b00e
--- /dev/null
+++ b/lib/ed25519/src/sha512.h
@@ -0,0 +1,21 @@
+#ifndef SHA512_H
+#define SHA512_H
+
+#include <stddef.h>
+
+#include "fixedint.h"
+
+/* state */
+typedef struct sha512_context_ {
+    uint64_t  length, state[8];
+    size_t curlen;
+    unsigned char buf[128];
+} sha512_context;
+
+
+int sha512_init(sha512_context * md);
+int sha512_final(sha512_context * md, unsigned char *out);
+int sha512_update(sha512_context * md, const unsigned char *in, size_t inlen);
+int sha512(const unsigned char *message, size_t message_len, unsigned char *out);
+
+#endif
\ No newline at end of file
diff --git a/lib/ed25519/src/sign.c b/lib/ed25519/src/sign.c
new file mode 100644
index 0000000..199a839
--- /dev/null
+++ b/lib/ed25519/src/sign.c
@@ -0,0 +1,31 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+
+void ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key) {
+    sha512_context hash;
+    unsigned char hram[64];
+    unsigned char r[64];
+    ge_p3 R;
+
+
+    sha512_init(&hash);
+    sha512_update(&hash, private_key + 32, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, r);
+
+    sc_reduce(r);
+    ge_scalarmult_base(&R, r);
+    ge_p3_tobytes(signature, &R);
+
+    sha512_init(&hash);
+    sha512_update(&hash, signature, 32);
+    sha512_update(&hash, public_key, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, hram);
+
+    sc_reduce(hram);
+    sc_muladd(signature + 32, hram, private_key, r);
+}
diff --git a/lib/ed25519/src/verify.c b/lib/ed25519/src/verify.c
new file mode 100644
index 0000000..32f988e
--- /dev/null
+++ b/lib/ed25519/src/verify.c
@@ -0,0 +1,77 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+static int consttime_equal(const unsigned char *x, const unsigned char *y) {
+    unsigned char r = 0;
+
+    r = x[0] ^ y[0];
+    #define F(i) r |= x[i] ^ y[i]
+    F(1);
+    F(2);
+    F(3);
+    F(4);
+    F(5);
+    F(6);
+    F(7);
+    F(8);
+    F(9);
+    F(10);
+    F(11);
+    F(12);
+    F(13);
+    F(14);
+    F(15);
+    F(16);
+    F(17);
+    F(18);
+    F(19);
+    F(20);
+    F(21);
+    F(22);
+    F(23);
+    F(24);
+    F(25);
+    F(26);
+    F(27);
+    F(28);
+    F(29);
+    F(30);
+    F(31);
+    #undef F
+
+    return !r;
+}
+
+int ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key) {
+    unsigned char h[64];
+    unsigned char checker[32];
+    sha512_context hash;
+    ge_p3 A;
+    ge_p2 R;
+
+    if (signature[63] & 224) {
+        return 0;
+    }
+
+    if (ge_frombytes_negate_vartime(&A, public_key) != 0) {
+        return 0;
+    }
+
+    sha512_init(&hash);
+    sha512_update(&hash, signature, 32);
+    sha512_update(&hash, public_key, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, h);
+    
+    sc_reduce(h);
+    ge_double_scalarmult_vartime(&R, h, &A, signature + 32);
+    ge_tobytes(checker, &R);
+
+    if (!consttime_equal(checker, signature)) {
+        return 0;
+    }
+
+    return 1;
+}