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-rw-r--r--.gitignore12
-rw-r--r--LICENSE.md46
-rw-r--r--Makefile56
-rw-r--r--README40
-rw-r--r--contrib/Curve25519Donna.c118
-rw-r--r--contrib/Curve25519Donna.h53
-rw-r--r--contrib/Curve25519Donna.java77
-rw-r--r--contrib/make-snippets68
-rw-r--r--curve25519-donna-c64.c449
-rw-r--r--curve25519-donna.c860
-rw-r--r--curve25519-donna.podspec13
-rw-r--r--python-src/curve25519/__init__.py4
-rw-r--r--python-src/curve25519/curve25519module.c105
-rw-r--r--python-src/curve25519/keys.py46
-rw-r--r--python-src/curve25519/test/__init__.py0
-rwxr-xr-xpython-src/curve25519/test/test_curve25519.py99
-rwxr-xr-xpython-src/curve25519/test/test_speed.py46
-rwxr-xr-xsetup.py38
-rw-r--r--speed-curve25519.c50
-rw-r--r--test-curve25519.c54
-rw-r--r--test-noncanon.c39
-rw-r--r--test-sc-curve25519.c72
-rw-r--r--test-sc-curve25519.s8
23 files changed, 2353 insertions, 0 deletions
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ccabede
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,12 @@
+/curve25519-donna-c64.a
+/curve25519-donna.a
+/test-curve25519-donna
+/speed-curve25519-donna
+/test-curve25519-donna-c64
+/speed-curve25519-donna-c64
+/test-sc-curve25519-donna-c64
+/build
+*.o
+*.pyc
+/dist
+/MANIFEST
diff --git a/LICENSE.md b/LICENSE.md
new file mode 100644
index 0000000..33a3240
--- /dev/null
+++ b/LICENSE.md
@@ -0,0 +1,46 @@
+Copyright 2008, Google Inc.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+* Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+* Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+* Neither the name of Google Inc. nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+curve25519-donna: Curve25519 elliptic curve, public key function
+
+http://code.google.com/p/curve25519-donna/
+
+Adam Langley <agl@imperialviolet.org>
+
+Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
+
+More information about curve25519 can be found here
+ http://cr.yp.to/ecdh.html
+
+djb's sample implementation of curve25519 is written in a special assembly
+language called qhasm and uses the floating point registers.
+
+This is, almost, a clean room reimplementation from the curve25519 paper. It
+uses many of the tricks described therein. Only the crecip function is taken
+from the sample implementation.
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..e31fcca
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,56 @@
+CFLAGS=-Wmissing-prototypes -Wdeclaration-after-statement -O2 -Wall
+CFLAGS_32=-m32
+
+targets: curve25519-donna.a curve25519-donna-c64.a
+
+test: test-donna test-donna-c64
+
+clean:
+ rm -f *.o *.a *.pp test-curve25519-donna test-curve25519-donna-c64 speed-curve25519-donna speed-curve25519-donna-c64 test-noncanon-curve25519-donna test-noncanon-curve25519-donna-c64
+
+curve25519-donna.a: curve25519-donna.o
+ ar -rc curve25519-donna.a curve25519-donna.o
+ ranlib curve25519-donna.a
+
+curve25519-donna.o: curve25519-donna.c
+ gcc -c curve25519-donna.c $(CFLAGS) $(CFLAGS_32)
+
+curve25519-donna-c64.a: curve25519-donna-c64.o
+ ar -rc curve25519-donna-c64.a curve25519-donna-c64.o
+ ranlib curve25519-donna-c64.a
+
+curve25519-donna-c64.o: curve25519-donna-c64.c
+ gcc -c curve25519-donna-c64.c $(CFLAGS)
+
+test-donna: test-curve25519-donna
+ ./test-curve25519-donna | head -123456 | tail -1
+
+test-donna-c64: test-curve25519-donna-c64
+ ./test-curve25519-donna-c64 | head -123456 | tail -1
+
+test-curve25519-donna: test-curve25519.c curve25519-donna.a
+ gcc -o test-curve25519-donna test-curve25519.c curve25519-donna.a $(CFLAGS) $(CFLAGS_32)
+
+test-curve25519-donna-c64: test-curve25519.c curve25519-donna-c64.a
+ gcc -o test-curve25519-donna-c64 test-curve25519.c curve25519-donna-c64.a $(CFLAGS)
+
+speed-curve25519-donna: speed-curve25519.c curve25519-donna.a
+ gcc -o speed-curve25519-donna speed-curve25519.c curve25519-donna.a $(CFLAGS) $(CFLAGS_32)
+
+speed-curve25519-donna-c64: speed-curve25519.c curve25519-donna-c64.a
+ gcc -o speed-curve25519-donna-c64 speed-curve25519.c curve25519-donna-c64.a $(CFLAGS)
+
+test-sc-curve25519-donna-c64: test-sc-curve25519.c curve25519-donna-c64.a
+ gcc -o test-sc-curve25519-donna-c64 -O test-sc-curve25519.c curve25519-donna-c64.a test-sc-curve25519.s $(CFLAGS)
+
+test-noncanon-donna: test-noncanon-curve25519-donna
+ ./test-noncanon-curve25519-donna
+
+test-noncanon-donna-c64: test-noncanon-curve25519-donna-c64
+ ./test-noncanon-curve25519-donna-c64
+
+test-noncanon-curve25519-donna: test-noncanon.c curve25519-donna.a
+ gcc -o test-noncanon-curve25519-donna test-noncanon.c curve25519-donna.a $(CFLAGS) $(CFLAGS_32)
+
+test-noncanon-curve25519-donna-c64: test-noncanon.c curve25519-donna-c64.a
+ gcc -o test-noncanon-curve25519-donna-c64 test-noncanon.c curve25519-donna-c64.a $(CFLAGS)
diff --git a/README b/README
new file mode 100644
index 0000000..9adf9be
--- /dev/null
+++ b/README
@@ -0,0 +1,40 @@
+See http://code.google.com/p/curve25519-donna/ for details.
+
+BUILDING:
+
+If you run `make`, two .a archives will be built, similar to djb's curve25519
+code. Alternatively, read on:
+
+The C implementation is contained within curve25519-donna.c. It has no external
+dependancies and is BSD licenced. You can copy/include/link it directly in with
+your program. Recommended C flags: -O2
+
+The x86-64 bit implementation is contained within curve25519-donna-x86-64.c and
+curve25519-donna-x86-64.s. Build like this:
+
+% cpp curve25519-donna-x86-64.s > curve25519-donna-x86-64.s.pp
+% as -o curve25519-donna-x86-64.s.o curve25519-donna-x86-64.s.pp
+% gcc -O2 -c curve25519-donna-x86-64.c
+
+Then the two .o files can be linked in
+
+USAGE:
+
+The usage is exactly the same as djb's code (as described at
+http://cr.yp.to/ecdh.html) expect that the function is called curve25519_donna.
+
+In short,
+
+To generate a private key just generate 32 random bytes.
+
+To generate the public key, just do:
+
+ static const uint8_t basepoint[32] = {9};
+ curve25519_donna(mypublic, mysecret, basepoint);
+
+To generate an agreed key do:
+
+ uint8_t shared_key[32];
+ curve25519_donna(shared_key, mysecret, theirpublic);
+
+And hash the shared_key with a cryptographic hash function before using.
diff --git a/contrib/Curve25519Donna.c b/contrib/Curve25519Donna.c
new file mode 100644
index 0000000..71b816c
--- /dev/null
+++ b/contrib/Curve25519Donna.c
@@ -0,0 +1,118 @@
+/*
+ James Robson
+ Public domain.
+*/
+
+#include "Curve25519Donna.h"
+#include <stdio.h>
+#include <stdlib.h>
+
+extern void curve25519_donna(unsigned char *output, const unsigned char *a,
+ const unsigned char *b);
+
+unsigned char*
+as_unsigned_char_array(JNIEnv* env, jbyteArray array, int* len);
+
+jbyteArray as_byte_array(JNIEnv* env, unsigned char* buf, int len);
+
+
+jbyteArray as_byte_array(JNIEnv* env, unsigned char* buf, int len) {
+ jbyteArray array = (*env)->NewByteArray(env, len);
+ (*env)->SetByteArrayRegion(env, array, 0, len, (jbyte*)buf);
+
+ //int i;
+ //for (i = 0;i < len;++i) printf("%02x",(unsigned int) buf[i]); printf(" ");
+ //printf("\n");
+
+ return array;
+}
+
+unsigned char*
+as_unsigned_char_array(JNIEnv* env, jbyteArray array, int* len) {
+
+ *len = (*env)->GetArrayLength(env, array);
+ unsigned char* buf = (unsigned char*)calloc(*len+1, sizeof(char));
+ (*env)->GetByteArrayRegion (env, array, 0, *len, (jbyte*)buf);
+ return buf;
+
+}
+
+JNIEXPORT jbyteArray JNICALL Java_Curve25519Donna_curve25519Donna
+ (JNIEnv *env, jobject obj, jbyteArray a, jbyteArray b) {
+
+ unsigned char o[32] = {0};
+ int l1, l2;
+ unsigned char* a1 = as_unsigned_char_array(env, a, &l1);
+ unsigned char* b1 = as_unsigned_char_array(env, b, &l2);
+
+ if ( !(l1 == 32 && l2 == 32) ) {
+ fprintf(stderr, "Error, must be length 32");
+ return NULL;
+ }
+
+
+ curve25519_donna(o, (const unsigned char*)a1, (const unsigned char*)b1);
+
+ free(a1);
+ free(b1);
+
+ return as_byte_array(env, (unsigned char*)o, 32);
+}
+
+JNIEXPORT jbyteArray JNICALL Java_Curve25519Donna_makePrivate
+ (JNIEnv *env, jobject obj, jbyteArray secret) {
+
+ int len;
+ unsigned char* k = as_unsigned_char_array(env, secret, &len);
+
+ if (len != 32) {
+ fprintf(stderr, "Error, must be length 32");
+ return NULL;
+ }
+
+ k[0] &= 248;
+ k[31] &= 127;
+ k[31] |= 64;
+ return as_byte_array(env, k, 32);
+}
+
+JNIEXPORT jbyteArray JNICALL Java_Curve25519Donna_getPublic
+ (JNIEnv *env, jobject obj, jbyteArray privkey) {
+
+ int len;
+ unsigned char* private = as_unsigned_char_array(env, privkey, &len);
+
+ if (len != 32) {
+ fprintf(stderr, "Error, must be length 32");
+ return NULL;
+ }
+
+ unsigned char pubkey[32];
+ unsigned char basepoint[32] = {9};
+
+ curve25519_donna(pubkey, private, basepoint);
+ return as_byte_array(env, (unsigned char*)pubkey, 32);
+}
+
+JNIEXPORT jbyteArray JNICALL Java_Curve25519Donna_makeSharedSecret
+ (JNIEnv *env, jobject obj, jbyteArray privkey, jbyteArray their_pubkey) {
+
+ unsigned char shared_secret[32];
+
+ int l1, l2;
+ unsigned char* private = as_unsigned_char_array(env, privkey, &l1);
+ unsigned char* pubkey = as_unsigned_char_array(env, their_pubkey, &l2);
+
+ if ( !(l1 == 32 && l2 == 32) ) {
+ fprintf(stderr, "Error, must be length 32");
+ return NULL;
+ }
+
+ curve25519_donna(shared_secret, private, pubkey);
+ return as_byte_array(env, (unsigned char*)shared_secret, 32);
+}
+
+JNIEXPORT void JNICALL Java_Curve25519Donna_helowrld
+ (JNIEnv *env, jobject obj) {
+ printf("helowrld\n");
+}
diff --git a/contrib/Curve25519Donna.h b/contrib/Curve25519Donna.h
new file mode 100644
index 0000000..3cd4ca0
--- /dev/null
+++ b/contrib/Curve25519Donna.h
@@ -0,0 +1,53 @@
+/* DO NOT EDIT THIS FILE - it is machine generated */
+#include <jni.h>
+/* Header for class Curve25519Donna */
+
+#ifndef _Included_Curve25519Donna
+#define _Included_Curve25519Donna
+#ifdef __cplusplus
+extern "C" {
+#endif
+/*
+ * Class: Curve25519Donna
+ * Method: curve25519Donna
+ * Signature: ([B[B)[B
+ */
+JNIEXPORT jbyteArray JNICALL Java_Curve25519Donna_curve25519Donna
+ (JNIEnv *, jobject, jbyteArray, jbyteArray);
+
+/*
+ * Class: Curve25519Donna
+ * Method: makePrivate
+ * Signature: ([B)[B
+ */
+JNIEXPORT jbyteArray JNICALL Java_Curve25519Donna_makePrivate
+ (JNIEnv *, jobject, jbyteArray);
+
+/*
+ * Class: Curve25519Donna
+ * Method: getPublic
+ * Signature: ([B)[B
+ */
+JNIEXPORT jbyteArray JNICALL Java_Curve25519Donna_getPublic
+ (JNIEnv *, jobject, jbyteArray);
+
+/*
+ * Class: Curve25519Donna
+ * Method: makeSharedSecret
+ * Signature: ([B[B)[B
+ */
+JNIEXPORT jbyteArray JNICALL Java_Curve25519Donna_makeSharedSecret
+ (JNIEnv *, jobject, jbyteArray, jbyteArray);
+
+/*
+ * Class: Curve25519Donna
+ * Method: helowrld
+ * Signature: ()V
+ */
+JNIEXPORT void JNICALL Java_Curve25519Donna_helowrld
+ (JNIEnv *, jobject);
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/contrib/Curve25519Donna.java b/contrib/Curve25519Donna.java
new file mode 100644
index 0000000..e28cb53
--- /dev/null
+++ b/contrib/Curve25519Donna.java
@@ -0,0 +1,77 @@
+/*
+ James Robson
+ Public domain.
+*/
+
+public class Curve25519Donna {
+
+ final protected static char[] hexArray = "0123456789ABCDEF".toCharArray();
+
+ public static String bytesToHex(byte[] bytes) {
+ char[] hexChars = new char[bytes.length * 2];
+ int v;
+ for ( int j = 0; j < bytes.length; j++ ) {
+ v = bytes[j] & 0xFF;
+ hexChars[j * 2] = hexArray[v >>> 4];
+ hexChars[j * 2 + 1] = hexArray[v & 0x0F];
+ }
+ return new String(hexChars);
+ }
+
+ public native byte[] curve25519Donna(byte[] a, byte[] b);
+ public native byte[] makePrivate(byte[] secret);
+ public native byte[] getPublic(byte[] privkey);
+ public native byte[] makeSharedSecret(byte[] privkey, byte[] theirPubKey);
+ public native void helowrld();
+
+ // Uncomment if your Java is 32-bit:
+ //static { System.loadLibrary("Curve25519Donna"); }
+
+ // Otherwise, load this 64-bit .jnilib:
+ static { System.loadLibrary("Curve25519Donna_64"); }
+
+ /*
+ To give the old tires a kick (OSX):
+ java -cp `pwd` Curve25519Donna
+ */
+ public static void main (String[] args) {
+
+ Curve25519Donna c = new Curve25519Donna();
+
+ // These should be 32 bytes long
+ byte[] user1Secret = "abcdefghijklmnopqrstuvwxyz123456".getBytes();
+ byte[] user2Secret = "654321zyxwvutsrqponmlkjihgfedcba".getBytes();
+
+
+ // You can use the curve function directly...
+
+ //byte[] o = c.curve25519Donna(a, b);
+ //System.out.println("o = " + bytesToHex(o));
+
+
+ // ... but it's not really necessary. Just use the following
+ // convenience methods:
+
+ byte[] privKey = c.makePrivate(user1Secret);
+ byte[] pubKey = c.getPublic(privKey);
+
+ byte[] privKey2 = c.makePrivate(user2Secret);
+ byte[] pubKey2 = c.getPublic(privKey2);
+
+ System.out.println("'user1' privKey = " + bytesToHex(privKey));
+ System.out.println("'user1' pubKey = " + bytesToHex(pubKey));
+ System.out.println("===================================================");
+
+ System.out.println("'user2' privKey = " + bytesToHex(privKey2));
+ System.out.println("'user2' pubKey = " + bytesToHex(pubKey2));
+ System.out.println("===================================================");
+
+
+ byte[] ss1 = c.makeSharedSecret(privKey, pubKey2);
+ System.out.println("'user1' computes shared secret: " + bytesToHex(ss1));
+
+ byte[] ss2 = c.makeSharedSecret(privKey2, pubKey);
+ System.out.println("'user2' computes shared secret: " + bytesToHex(ss2));
+
+ }
+}
diff --git a/contrib/make-snippets b/contrib/make-snippets
new file mode 100644
index 0000000..4568721
--- /dev/null
+++ b/contrib/make-snippets
@@ -0,0 +1,68 @@
+CFLAGS=-Wmissing-prototypes -Wdeclaration-after-statement -O2 -Wall
+CC=clang
+
+
+targets: curve25519-donna.a curve25519-donna-c64.a
+
+test: test-donna test-donna-c64
+
+
+clean:
+ rm -f java-src/*.class java-src/*.jnilib *.dylib *.o *.a *.pp test-curve25519-donna test-curve25519-donna-c64 speed-curve25519-donna speed-curve25519-donna-c64
+
+curve25519-donna.a: curve25519-donna.o
+ ar -rc curve25519-donna.a curve25519-donna.o
+ ranlib curve25519-donna.a
+
+
+##### OSX dynamic library (32- & 64-bit)
+
+curve25519donna.dylib: curve25519-donna.a curve25519-donna-c64.a
+ $(CC) -m32 -fpic -shared -Wl,-all_load curve25519-donna.a -Wl,-all_load -o libcurve25519donna.dylib
+ $(CC) -fpic -shared -Wl,-all_load curve25519-donna-c64.a -Wl,-all_load -o libcurve25519donna_64.dylib
+
+##### OSX/Java section hence
+
+# Java JNI - compiled for OSX (32- & 64-bit)
+Curve25519Donna.class:
+ cd java-src; javah -jni Curve25519Donna; cd ..
+ cd java-src; javac Curve25519Donna.java; cd ..
+
+Curve25519Donna.jnilib: curve25519-donna.a curve25519-donna-c64.a Curve25519Donna.class
+ @echo "Building 32-bit..."
+ clang -o java-src/libCurve25519Donna.jnilib $(CFLAGS) -lc -shared -m32 -I /System/Library/Frameworks/JavaVM.framework/Headers curve25519-donna.o java-src/Curve25519Donna.c
+ @echo "Building 64-bit..."
+ clang -o java-src/libCurve25519Donna_64.jnilib $(CFLAGS) -lc -shared -I /System/Library/Frameworks/JavaVM.framework/Headers curve25519-donna-c64.o java-src/Curve25519Donna.c
+
+##### OSX/Java section end
+
+curve25519-donna.o: curve25519-donna.c
+ $(CC) -c curve25519-donna.c $(CFLAGS) -m32
+
+curve25519-donna-c64.a: curve25519-donna-c64.o
+ ar -rc curve25519-donna-c64.a curve25519-donna-c64.o
+ ranlib curve25519-donna-c64.a
+
+curve25519-donna-c64.o: curve25519-donna-c64.c
+ $(CC) -c curve25519-donna-c64.c $(CFLAGS)
+
+test-donna: test-curve25519-donna
+ ./test-curve25519-donna | head -123456 | tail -1
+
+test-donna-c64: test-curve25519-donna-c64
+ ./test-curve25519-donna-c64 | head -123456 | tail -1
+
+test-curve25519-donna: test-curve25519.c curve25519-donna.a
+ $(CC) -o test-curve25519-donna test-curve25519.c curve25519-donna.a $(CFLAGS) -m32
+
+test-curve25519-donna-c64: test-curve25519.c curve25519-donna-c64.a
+ $(CC) -o test-curve25519-donna-c64 test-curve25519.c curve25519-donna-c64.a $(CFLAGS)
+
+speed-curve25519-donna: speed-curve25519.c curve25519-donna.a
+ $(CC) -o speed-curve25519-donna speed-curve25519.c curve25519-donna.a $(CFLAGS) -m32
+
+speed-curve25519-donna-c64: speed-curve25519.c curve25519-donna-c64.a
+ $(CC) -o speed-curve25519-donna-c64 speed-curve25519.c curve25519-donna-c64.a $(CFLAGS)
+
+test-sc-curve25519-donna-c64: test-sc-curve25519.c curve25519-donna-c64.a
+ $(CC) -o test-sc-curve25519-donna-c64 -O test-sc-curve25519.c curve25519-donna-c64.a test-sc-curve25519.s $(CFLAGS)
diff --git a/curve25519-donna-c64.c b/curve25519-donna-c64.c
new file mode 100644
index 0000000..9ebd8a1
--- /dev/null
+++ b/curve25519-donna-c64.c
@@ -0,0 +1,449 @@
+/* Copyright 2008, Google Inc.
+ * All rights reserved.
+ *
+ * Code released into the public domain.
+ *
+ * curve25519-donna: Curve25519 elliptic curve, public key function
+ *
+ * http://code.google.com/p/curve25519-donna/
+ *
+ * Adam Langley <agl@imperialviolet.org>
+ *
+ * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
+ *
+ * More information about curve25519 can be found here
+ * http://cr.yp.to/ecdh.html
+ *
+ * djb's sample implementation of curve25519 is written in a special assembly
+ * language called qhasm and uses the floating point registers.
+ *
+ * This is, almost, a clean room reimplementation from the curve25519 paper. It
+ * uses many of the tricks described therein. Only the crecip function is taken
+ * from the sample implementation.
+ */
+
+#include <string.h>
+#include <stdint.h>
+
+typedef uint8_t u8;
+typedef uint64_t limb;
+typedef limb felem[5];
+// This is a special gcc mode for 128-bit integers. It's implemented on 64-bit
+// platforms only as far as I know.
+typedef unsigned uint128_t __attribute__((mode(TI)));
+
+#undef force_inline
+#define force_inline __attribute__((always_inline))
+
+/* Sum two numbers: output += in */
+static inline void force_inline
+fsum(limb *output, const limb *in) {
+ output[0] += in[0];
+ output[1] += in[1];
+ output[2] += in[2];
+ output[3] += in[3];
+ output[4] += in[4];
+}
+
+/* Find the difference of two numbers: output = in - output
+ * (note the order of the arguments!)
+ *
+ * Assumes that out[i] < 2**52
+ * On return, out[i] < 2**55
+ */
+static inline void force_inline
+fdifference_backwards(felem out, const felem in) {
+ /* 152 is 19 << 3 */
+ static const limb two54m152 = (((limb)1) << 54) - 152;
+ static const limb two54m8 = (((limb)1) << 54) - 8;
+
+ out[0] = in[0] + two54m152 - out[0];
+ out[1] = in[1] + two54m8 - out[1];
+ out[2] = in[2] + two54m8 - out[2];
+ out[3] = in[3] + two54m8 - out[3];
+ out[4] = in[4] + two54m8 - out[4];
+}
+
+/* Multiply a number by a scalar: output = in * scalar */
+static inline void force_inline
+fscalar_product(felem output, const felem in, const limb scalar) {
+ uint128_t a;
+
+ a = ((uint128_t) in[0]) * scalar;
+ output[0] = ((limb)a) & 0x7ffffffffffff;
+
+ a = ((uint128_t) in[1]) * scalar + ((limb) (a >> 51));
+ output[1] = ((limb)a) & 0x7ffffffffffff;
+
+ a = ((uint128_t) in[2]) * scalar + ((limb) (a >> 51));
+ output[2] = ((limb)a) & 0x7ffffffffffff;
+
+ a = ((uint128_t) in[3]) * scalar + ((limb) (a >> 51));
+ output[3] = ((limb)a) & 0x7ffffffffffff;
+
+ a = ((uint128_t) in[4]) * scalar + ((limb) (a >> 51));
+ output[4] = ((limb)a) & 0x7ffffffffffff;
+
+ output[0] += (a >> 51) * 19;
+}
+
+/* Multiply two numbers: output = in2 * in
+ *
+ * output must be distinct to both inputs. The inputs are reduced coefficient
+ * form, the output is not.
+ *
+ * Assumes that in[i] < 2**55 and likewise for in2.
+ * On return, output[i] < 2**52
+ */
+static inline void force_inline
+fmul(felem output, const felem in2, const felem in) {
+ uint128_t t[5];
+ limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
+
+ r0 = in[0];
+ r1 = in[1];
+ r2 = in[2];
+ r3 = in[3];
+ r4 = in[4];
+
+ s0 = in2[0];
+ s1 = in2[1];
+ s2 = in2[2];
+ s3 = in2[3];
+ s4 = in2[4];
+
+ t[0] = ((uint128_t) r0) * s0;
+ t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
+ t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
+ t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
+ t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
+
+ r4 *= 19;
+ r1 *= 19;
+ r2 *= 19;
+ r3 *= 19;
+
+ t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
+ t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
+ t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
+ t[3] += ((uint128_t) r4) * s4;
+
+ r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
+ t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
+ t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
+ t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
+ t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
+ r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
+ r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
+ r2 += c;
+
+ output[0] = r0;
+ output[1] = r1;
+ output[2] = r2;
+ output[3] = r3;
+ output[4] = r4;
+}
+
+static inline void force_inline
+fsquare_times(felem output, const felem in, limb count) {
+ uint128_t t[5];
+ limb r0,r1,r2,r3,r4,c;
+ limb d0,d1,d2,d4,d419;
+
+ r0 = in[0];
+ r1 = in[1];
+ r2 = in[2];
+ r3 = in[3];
+ r4 = in[4];
+
+ do {
+ d0 = r0 * 2;
+ d1 = r1 * 2;
+ d2 = r2 * 2 * 19;
+ d419 = r4 * 19;
+ d4 = d419 * 2;
+
+ t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
+ t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
+ t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
+ t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
+ t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
+
+ r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
+ t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
+ t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
+ t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
+ t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
+ r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
+ r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
+ r2 += c;
+ } while(--count);
+
+ output[0] = r0;
+ output[1] = r1;
+ output[2] = r2;
+ output[3] = r3;
+ output[4] = r4;
+}
+
+/* Load a little-endian 64-bit number */
+static limb
+load_limb(const u8 *in) {
+ return
+ ((limb)in[0]) |
+ (((limb)in[1]) << 8) |
+ (((limb)in[2]) << 16) |
+ (((limb)in[3]) << 24) |
+ (((limb)in[4]) << 32) |
+ (((limb)in[5]) << 40) |
+ (((limb)in[6]) << 48) |
+ (((limb)in[7]) << 56);
+}
+
+static void
+store_limb(u8 *out, limb in) {
+ out[0] = in & 0xff;
+ out[1] = (in >> 8) & 0xff;
+ out[2] = (in >> 16) & 0xff;
+ out[3] = (in >> 24) & 0xff;
+ out[4] = (in >> 32) & 0xff;
+ out[5] = (in >> 40) & 0xff;
+ out[6] = (in >> 48) & 0xff;
+ out[7] = (in >> 56) & 0xff;
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static void
+fexpand(limb *output, const u8 *in) {
+ output[0] = load_limb(in) & 0x7ffffffffffff;
+ output[1] = (load_limb(in+6) >> 3) & 0x7ffffffffffff;
+ output[2] = (load_limb(in+12) >> 6) & 0x7ffffffffffff;
+ output[3] = (load_limb(in+19) >> 1) & 0x7ffffffffffff;
+ output[4] = (load_limb(in+24) >> 12) & 0x7ffffffffffff;
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+static void
+fcontract(u8 *output, const felem input) {
+ uint128_t t[5];
+
+ t[0] = input[0];
+ t[1] = input[1];
+ t[2] = input[2];
+ t[3] = input[3];
+ t[4] = input[4];
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
+
+ /* now t is between 0 and 2^255-1, properly carried. */
+ /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
+
+ t[0] += 19;
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
+
+ /* now between 19 and 2^255-1 in both cases, and offset by 19. */
+
+ t[0] += 0x8000000000000 - 19;
+ t[1] += 0x8000000000000 - 1;
+ t[2] += 0x8000000000000 - 1;
+ t[3] += 0x8000000000000 - 1;
+ t[4] += 0x8000000000000 - 1;
+
+ /* now between 2^255 and 2^256-20, and offset by 2^255. */
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
+ t[4] &= 0x7ffffffffffff;
+
+ store_limb(output, t[0] | (t[1] << 51));
+ store_limb(output+8, (t[1] >> 13) | (t[2] << 38));
+ store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
+ store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
+}
+
+/* Input: Q, Q', Q-Q'
+ * Output: 2Q, Q+Q'
+ *
+ * x2 z3: long form
+ * x3 z3: long form
+ * x z: short form, destroyed
+ * xprime zprime: short form, destroyed
+ * qmqp: short form, preserved
+ */
+static void
+fmonty(limb *x2, limb *z2, /* output 2Q */
+ limb *x3, limb *z3, /* output Q + Q' */
+ limb *x, limb *z, /* input Q */
+ limb *xprime, limb *zprime, /* input Q' */
+ const limb *qmqp /* input Q - Q' */) {
+ limb origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5],
+ zzprime[5], zzzprime[5];
+
+ memcpy(origx, x, 5 * sizeof(limb));
+ fsum(x, z);
+ fdifference_backwards(z, origx); // does x - z
+
+ memcpy(origxprime, xprime, sizeof(limb) * 5);
+ fsum(xprime, zprime);
+ fdifference_backwards(zprime, origxprime);
+ fmul(xxprime, xprime, z);
+ fmul(zzprime, x, zprime);
+ memcpy(origxprime, xxprime, sizeof(limb) * 5);
+ fsum(xxprime, zzprime);
+ fdifference_backwards(zzprime, origxprime);
+ fsquare_times(x3, xxprime, 1);
+ fsquare_times(zzzprime, zzprime, 1);
+ fmul(z3, zzzprime, qmqp);
+
+ fsquare_times(xx, x, 1);
+ fsquare_times(zz, z, 1);
+ fmul(x2, xx, zz);
+ fdifference_backwards(zz, xx); // does zz = xx - zz
+ fscalar_product(zzz, zz, 121665);
+ fsum(zzz, xx);
+ fmul(z2, zz, zzz);
+}
+
+// -----------------------------------------------------------------------------
+// Maybe swap the contents of two limb arrays (@a and @b), each @len elements
+// long. Perform the swap iff @swap is non-zero.
+//
+// This function performs the swap without leaking any side-channel
+// information.
+// -----------------------------------------------------------------------------
+static void
+swap_conditional(limb a[5], limb b[5], limb iswap) {
+ unsigned i;
+ const limb swap = -iswap;
+
+ for (i = 0; i < 5; ++i) {
+ const limb x = swap & (a[i] ^ b[i]);
+ a[i] ^= x;
+ b[i] ^= x;
+ }
+}
+
+/* Calculates nQ where Q is the x-coordinate of a point on the curve
+ *
+ * resultx/resultz: the x coordinate of the resulting curve point (short form)
+ * n: a little endian, 32-byte number
+ * q: a point of the curve (short form)
+ */
+static void
+cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) {
+ limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
+ limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
+ limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
+ limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
+
+ unsigned i, j;
+
+ memcpy(nqpqx, q, sizeof(limb) * 5);
+
+ for (i = 0; i < 32; ++i) {
+ u8 byte = n[31 - i];
+ for (j = 0; j < 8; ++j) {
+ const limb bit = byte >> 7;
+
+ swap_conditional(nqx, nqpqx, bit);
+ swap_conditional(nqz, nqpqz, bit);
+ fmonty(nqx2, nqz2,
+ nqpqx2, nqpqz2,
+ nqx, nqz,
+ nqpqx, nqpqz,
+ q);
+ swap_conditional(nqx2, nqpqx2, bit);
+ swap_conditional(nqz2, nqpqz2, bit);
+
+ t = nqx;
+ nqx = nqx2;
+ nqx2 = t;
+ t = nqz;
+ nqz = nqz2;
+ nqz2 = t;
+ t = nqpqx;
+ nqpqx = nqpqx2;
+ nqpqx2 = t;
+ t = nqpqz;
+ nqpqz = nqpqz2;
+ nqpqz2 = t;
+
+ byte <<= 1;
+ }
+ }
+
+ memcpy(resultx, nqx, sizeof(limb) * 5);
+ memcpy(resultz, nqz, sizeof(limb) * 5);
+}
+
+
+// -----------------------------------------------------------------------------
+// Shamelessly copied from djb's code, tightened a little
+// -----------------------------------------------------------------------------
+static void
+crecip(felem out, const felem z) {
+ felem a,t0,b,c;
+
+ /* 2 */ fsquare_times(a, z, 1); // a = 2
+ /* 8 */ fsquare_times(t0, a, 2);
+ /* 9 */ fmul(b, t0, z); // b = 9
+ /* 11 */ fmul(a, b, a); // a = 11
+ /* 22 */ fsquare_times(t0, a, 1);
+ /* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
+ /* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
+ /* 2^10 - 2^0 */ fmul(b, t0, b);
+ /* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
+ /* 2^20 - 2^0 */ fmul(c, t0, b);
+ /* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
+ /* 2^40 - 2^0 */ fmul(t0, t0, c);
+ /* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
+ /* 2^50 - 2^0 */ fmul(b, t0, b);
+ /* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
+ /* 2^100 - 2^0 */ fmul(c, t0, b);
+ /* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
+ /* 2^200 - 2^0 */ fmul(t0, t0, c);
+ /* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
+ /* 2^250 - 2^0 */ fmul(t0, t0, b);
+ /* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
+ /* 2^255 - 21 */ fmul(out, t0, a);
+}
+
+int curve25519_donna(u8 *, const u8 *, const u8 *);
+
+int
+curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) {
+ limb bp[5], x[5], z[5], zmone[5];
+ uint8_t e[32];
+ int i;
+
+ for (i = 0;i < 32;++i) e[i] = secret[i];
+ e[0] &= 248;
+ e[31] &= 127;
+ e[31] |= 64;
+
+ fexpand(bp, basepoint);
+ cmult(x, z, e, bp);
+ crecip(zmone, z);
+ fmul(z, x, zmone);
+ fcontract(mypublic, z);
+ return 0;
+}
diff --git a/curve25519-donna.c b/curve25519-donna.c
new file mode 100644
index 0000000..ed15d6c
--- /dev/null
+++ b/curve25519-donna.c
@@ -0,0 +1,860 @@
+/* Copyright 2008, Google Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are
+ * met:
+ *
+ * * Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above
+ * copyright notice, this list of conditions and the following disclaimer
+ * in the documentation and/or other materials provided with the
+ * distribution.
+ * * Neither the name of Google Inc. nor the names of its
+ * contributors may be used to endorse or promote products derived from
+ * this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+ * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+ * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * curve25519-donna: Curve25519 elliptic curve, public key function
+ *
+ * http://code.google.com/p/curve25519-donna/
+ *
+ * Adam Langley <agl@imperialviolet.org>
+ *
+ * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
+ *
+ * More information about curve25519 can be found here
+ * http://cr.yp.to/ecdh.html
+ *
+ * djb's sample implementation of curve25519 is written in a special assembly
+ * language called qhasm and uses the floating point registers.
+ *
+ * This is, almost, a clean room reimplementation from the curve25519 paper. It
+ * uses many of the tricks described therein. Only the crecip function is taken
+ * from the sample implementation. */
+
+#include <string.h>
+#include <stdint.h>
+
+#ifdef _MSC_VER
+#define inline __inline
+#endif
+
+typedef uint8_t u8;
+typedef int32_t s32;
+typedef int64_t limb;
+
+/* Field element representation:
+ *
+ * Field elements are written as an array of signed, 64-bit limbs, least
+ * significant first. The value of the field element is:
+ * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
+ *
+ * i.e. the limbs are 26, 25, 26, 25, ... bits wide. */
+
+/* Sum two numbers: output += in */
+static void fsum(limb *output, const limb *in) {
+ unsigned i;
+ for (i = 0; i < 10; i += 2) {
+ output[0+i] = output[0+i] + in[0+i];
+ output[1+i] = output[1+i] + in[1+i];
+ }
+}
+
+/* Find the difference of two numbers: output = in - output
+ * (note the order of the arguments!). */
+static void fdifference(limb *output, const limb *in) {
+ unsigned i;
+ for (i = 0; i < 10; ++i) {
+ output[i] = in[i] - output[i];
+ }
+}
+
+/* Multiply a number by a scalar: output = in * scalar */
+static void fscalar_product(limb *output, const limb *in, const limb scalar) {
+ unsigned i;
+ for (i = 0; i < 10; ++i) {
+ output[i] = in[i] * scalar;
+ }
+}
+
+/* Multiply two numbers: output = in2 * in
+ *
+ * output must be distinct to both inputs. The inputs are reduced coefficient
+ * form, the output is not.
+ *
+ * output[x] <= 14 * the largest product of the input limbs. */
+static void fproduct(limb *output, const limb *in2, const limb *in) {
+ output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]);
+ output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[0]);
+ output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[0]);
+ output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[0]);
+ output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
+ 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[0])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[0]);
+ output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[0]);
+ output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[2])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[0]);
+ output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[0]);
+ output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
+ 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[2])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[0]);
+ output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[0]);
+ output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[4])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[2]);
+ output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[2]);
+ output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
+ 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[3])) +
+ ((limb) ((s32) in2[4])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[4]);
+ output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[4]);
+ output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[5])) +
+ ((limb) ((s32) in2[6])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[6]);
+ output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[6]);
+ output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[7]));
+ output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[8]);
+ output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]);
+}
+
+/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
+ *
+ * On entry: |output[i]| < 14*2^54
+ * On exit: |output[0..8]| < 280*2^54 */
+static void freduce_degree(limb *output) {
+ /* Each of these shifts and adds ends up multiplying the value by 19.
+ *
+ * For output[0..8], the absolute entry value is < 14*2^54 and we add, at
+ * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */
+ output[8] += output[18] << 4;
+ output[8] += output[18] << 1;
+ output[8] += output[18];
+ output[7] += output[17] << 4;
+ output[7] += output[17] << 1;
+ output[7] += output[17];
+ output[6] += output[16] << 4;
+ output[6] += output[16] << 1;
+ output[6] += output[16];
+ output[5] += output[15] << 4;
+ output[5] += output[15] << 1;
+ output[5] += output[15];
+ output[4] += output[14] << 4;
+ output[4] += output[14] << 1;
+ output[4] += output[14];
+ output[3] += output[13] << 4;
+ output[3] += output[13] << 1;
+ output[3] += output[13];
+ output[2] += output[12] << 4;
+ output[2] += output[12] << 1;
+ output[2] += output[12];
+ output[1] += output[11] << 4;
+ output[1] += output[11] << 1;
+ output[1] += output[11];
+ output[0] += output[10] << 4;
+ output[0] += output[10] << 1;
+ output[0] += output[10];
+}
+
+#if (-1 & 3) != 3
+#error "This code only works on a two's complement system"
+#endif
+
+/* return v / 2^26, using only shifts and adds.
+ *
+ * On entry: v can take any value. */
+static inline limb
+div_by_2_26(const limb v)
+{
+ /* High word of v; no shift needed. */
+ const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
+ /* Set to all 1s if v was negative; else set to 0s. */
+ const int32_t sign = ((int32_t) highword) >> 31;
+ /* Set to 0x3ffffff if v was negative; else set to 0. */
+ const int32_t roundoff = ((uint32_t) sign) >> 6;
+ /* Should return v / (1<<26) */
+ return (v + roundoff) >> 26;
+}
+
+/* return v / (2^25), using only shifts and adds.
+ *
+ * On entry: v can take any value. */
+static inline limb
+div_by_2_25(const limb v)
+{
+ /* High word of v; no shift needed*/
+ const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
+ /* Set to all 1s if v was negative; else set to 0s. */
+ const int32_t sign = ((int32_t) highword) >> 31;
+ /* Set to 0x1ffffff if v was negative; else set to 0. */
+ const int32_t roundoff = ((uint32_t) sign) >> 7;
+ /* Should return v / (1<<25) */
+ return (v + roundoff) >> 25;
+}
+
+/* Reduce all coefficients of the short form input so that |x| < 2^26.
+ *
+ * On entry: |output[i]| < 280*2^54 */
+static void freduce_coefficients(limb *output) {
+ unsigned i;
+
+ output[10] = 0;
+
+ for (i = 0; i < 10; i += 2) {
+ limb over = div_by_2_26(output[i]);
+ /* The entry condition (that |output[i]| < 280*2^54) means that over is, at
+ * most, 280*2^28 in the first iteration of this loop. This is added to the
+ * next limb and we can approximate the resulting bound of that limb by
+ * 281*2^54. */
+ output[i] -= over << 26;
+ output[i+1] += over;
+
+ /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
+ * 281*2^29. When this is added to the next limb, the resulting bound can
+ * be approximated as 281*2^54.
+ *
+ * For subsequent iterations of the loop, 281*2^54 remains a conservative
+ * bound and no overflow occurs. */
+ over = div_by_2_25(output[i+1]);
+ output[i+1] -= over << 25;
+ output[i+2] += over;
+ }
+ /* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
+ output[0] += output[10] << 4;
+ output[0] += output[10] << 1;
+ output[0] += output[10];
+
+ output[10] = 0;
+
+ /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
+ * So |over| will be no more than 2^16. */
+ {
+ limb over = div_by_2_26(output[0]);
+ output[0] -= over << 26;
+ output[1] += over;
+ }
+
+ /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
+ * bound on |output[1]| is sufficient to meet our needs. */
+}
+
+/* A helpful wrapper around fproduct: output = in * in2.
+ *
+ * On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
+ *
+ * output must be distinct to both inputs. The output is reduced degree
+ * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */
+static void
+fmul(limb *output, const limb *in, const limb *in2) {
+ limb t[19];
+ fproduct(t, in, in2);
+ /* |t[i]| < 14*2^54 */
+ freduce_degree(t);
+ freduce_coefficients(t);
+ /* |t[i]| < 2^26 */
+ memcpy(output, t, sizeof(limb) * 10);
+}
+
+/* Square a number: output = in**2
+ *
+ * output must be distinct from the input. The inputs are reduced coefficient
+ * form, the output is not.
+ *
+ * output[x] <= 14 * the largest product of the input limbs. */
+static void fsquare_inner(limb *output, const limb *in) {
+ output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
+ output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
+ output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
+ ((limb) ((s32) in[0])) * ((s32) in[2]));
+ output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
+ ((limb) ((s32) in[0])) * ((s32) in[3]));
+ output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
+ 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
+ 2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
+ output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
+ ((limb) ((s32) in[1])) * ((s32) in[4]) +
+ ((limb) ((s32) in[0])) * ((s32) in[5]));
+ output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
+ ((limb) ((s32) in[2])) * ((s32) in[4]) +
+ ((limb) ((s32) in[0])) * ((s32) in[6]) +
+ 2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
+ output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
+ ((limb) ((s32) in[2])) * ((s32) in[5]) +
+ ((limb) ((s32) in[1])) * ((s32) in[6]) +
+ ((limb) ((s32) in[0])) * ((s32) in[7]));
+ output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
+ 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
+ ((limb) ((s32) in[0])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[5])));
+ output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
+ ((limb) ((s32) in[3])) * ((s32) in[6]) +
+ ((limb) ((s32) in[2])) * ((s32) in[7]) +
+ ((limb) ((s32) in[1])) * ((s32) in[8]) +
+ ((limb) ((s32) in[0])) * ((s32) in[9]));
+ output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
+ ((limb) ((s32) in[4])) * ((s32) in[6]) +
+ ((limb) ((s32) in[2])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
+ ((limb) ((s32) in[1])) * ((s32) in[9])));
+ output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
+ ((limb) ((s32) in[4])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[8]) +
+ ((limb) ((s32) in[2])) * ((s32) in[9]));
+ output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
+ 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[9])));
+ output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
+ ((limb) ((s32) in[5])) * ((s32) in[8]) +
+ ((limb) ((s32) in[4])) * ((s32) in[9]));
+ output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
+ ((limb) ((s32) in[6])) * ((s32) in[8]) +
+ 2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
+ output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
+ ((limb) ((s32) in[6])) * ((s32) in[9]));
+ output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
+ 4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
+ output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
+ output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]);
+}
+
+/* fsquare sets output = in^2.
+ *
+ * On entry: The |in| argument is in reduced coefficients form and |in[i]| <
+ * 2^27.
+ *
+ * On exit: The |output| argument is in reduced coefficients form (indeed, one
+ * need only provide storage for 10 limbs) and |out[i]| < 2^26. */
+static void
+fsquare(limb *output, const limb *in) {
+ limb t[19];
+ fsquare_inner(t, in);
+ /* |t[i]| < 14*2^54 because the largest product of two limbs will be <
+ * 2^(27+27) and fsquare_inner adds together, at most, 14 of those
+ * products. */
+ freduce_degree(t);
+ freduce_coefficients(t);
+ /* |t[i]| < 2^26 */
+ memcpy(output, t, sizeof(limb) * 10);
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static void
+fexpand(limb *output, const u8 *input) {
+#define F(n,start,shift,mask) \
+ output[n] = ((((limb) input[start + 0]) | \
+ ((limb) input[start + 1]) << 8 | \
+ ((limb) input[start + 2]) << 16 | \
+ ((limb) input[start + 3]) << 24) >> shift) & mask;
+ F(0, 0, 0, 0x3ffffff);
+ F(1, 3, 2, 0x1ffffff);
+ F(2, 6, 3, 0x3ffffff);
+ F(3, 9, 5, 0x1ffffff);
+ F(4, 12, 6, 0x3ffffff);
+ F(5, 16, 0, 0x1ffffff);
+ F(6, 19, 1, 0x3ffffff);
+ F(7, 22, 3, 0x1ffffff);
+ F(8, 25, 4, 0x3ffffff);
+ F(9, 28, 6, 0x1ffffff);
+#undef F
+}
+
+#if (-32 >> 1) != -16
+#error "This code only works when >> does sign-extension on negative numbers"
+#endif
+
+/* s32_eq returns 0xffffffff iff a == b and zero otherwise. */
+static s32 s32_eq(s32 a, s32 b) {
+ a = ~(a ^ b);
+ a &= a << 16;
+ a &= a << 8;
+ a &= a << 4;
+ a &= a << 2;
+ a &= a << 1;
+ return a >> 31;
+}
+
+/* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
+ * both non-negative. */
+static s32 s32_gte(s32 a, s32 b) {
+ a -= b;
+ /* a >= 0 iff a >= b. */
+ return ~(a >> 31);
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array.
+ *
+ * On entry: |input_limbs[i]| < 2^26 */
+static void
+fcontract(u8 *output, limb *input_limbs) {
+ int i;
+ int j;
+ s32 input[10];
+ s32 mask;
+
+ /* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */
+ for (i = 0; i < 10; i++) {
+ input[i] = input_limbs[i];
+ }
+
+ for (j = 0; j < 2; ++j) {
+ for (i = 0; i < 9; ++i) {
+ if ((i & 1) == 1) {
+ /* This calculation is a time-invariant way to make input[i]
+ * non-negative by borrowing from the next-larger limb. */
+ const s32 mask = input[i] >> 31;
+ const s32 carry = -((input[i] & mask) >> 25);
+ input[i] = input[i] + (carry << 25);
+ input[i+1] = input[i+1] - carry;
+ } else {
+ const s32 mask = input[i] >> 31;
+ const s32 carry = -((input[i] & mask) >> 26);
+ input[i] = input[i] + (carry << 26);
+ input[i+1] = input[i+1] - carry;
+ }
+ }
+
+ /* There's no greater limb for input[9] to borrow from, but we can multiply
+ * by 19 and borrow from input[0], which is valid mod 2^255-19. */
+ {
+ const s32 mask = input[9] >> 31;
+ const s32 carry = -((input[9] & mask) >> 25);
+ input[9] = input[9] + (carry << 25);
+ input[0] = input[0] - (carry * 19);
+ }
+
+ /* After the first iteration, input[1..9] are non-negative and fit within
+ * 25 or 26 bits, depending on position. However, input[0] may be
+ * negative. */
+ }
+
+ /* The first borrow-propagation pass above ended with every limb
+ except (possibly) input[0] non-negative.
+
+ If input[0] was negative after the first pass, then it was because of a
+ carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
+ one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
+
+ In the second pass, each limb is decreased by at most one. Thus the second
+ borrow-propagation pass could only have wrapped around to decrease
+ input[0] again if the first pass left input[0] negative *and* input[1]
+ through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
+ and this last borrow-propagation step will leave input[1] non-negative. */
+ {
+ const s32 mask = input[0] >> 31;
+ const s32 carry = -((input[0] & mask) >> 26);
+ input[0] = input[0] + (carry << 26);
+ input[1] = input[1] - carry;
+ }
+
+ /* All input[i] are now non-negative. However, there might be values between
+ * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */
+ for (j = 0; j < 2; j++) {
+ for (i = 0; i < 9; i++) {
+ if ((i & 1) == 1) {
+ const s32 carry = input[i] >> 25;
+ input[i] &= 0x1ffffff;
+ input[i+1] += carry;
+ } else {
+ const s32 carry = input[i] >> 26;
+ input[i] &= 0x3ffffff;
+ input[i+1] += carry;
+ }
+ }
+
+ {
+ const s32 carry = input[9] >> 25;
+ input[9] &= 0x1ffffff;
+ input[0] += 19*carry;
+ }
+ }
+
+ /* If the first carry-chain pass, just above, ended up with a carry from
+ * input[9], and that caused input[0] to be out-of-bounds, then input[0] was
+ * < 2^26 + 2*19, because the carry was, at most, two.
+ *
+ * If the second pass carried from input[9] again then input[0] is < 2*19 and
+ * the input[9] -> input[0] carry didn't push input[0] out of bounds. */
+
+ /* It still remains the case that input might be between 2^255-19 and 2^255.
+ * In this case, input[1..9] must take their maximum value and input[0] must
+ * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */
+ mask = s32_gte(input[0], 0x3ffffed);
+ for (i = 1; i < 10; i++) {
+ if ((i & 1) == 1) {
+ mask &= s32_eq(input[i], 0x1ffffff);
+ } else {
+ mask &= s32_eq(input[i], 0x3ffffff);
+ }
+ }
+
+ /* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
+ * this conditionally subtracts 2^255-19. */
+ input[0] -= mask & 0x3ffffed;
+
+ for (i = 1; i < 10; i++) {
+ if ((i & 1) == 1) {
+ input[i] -= mask & 0x1ffffff;
+ } else {
+ input[i] -= mask & 0x3ffffff;
+ }
+ }
+
+ input[1] <<= 2;
+ input[2] <<= 3;
+ input[3] <<= 5;
+ input[4] <<= 6;
+ input[6] <<= 1;
+ input[7] <<= 3;
+ input[8] <<= 4;
+ input[9] <<= 6;
+#define F(i, s) \
+ output[s+0] |= input[i] & 0xff; \
+ output[s+1] = (input[i] >> 8) & 0xff; \
+ output[s+2] = (input[i] >> 16) & 0xff; \
+ output[s+3] = (input[i] >> 24) & 0xff;
+ output[0] = 0;
+ output[16] = 0;
+ F(0,0);
+ F(1,3);
+ F(2,6);
+ F(3,9);
+ F(4,12);
+ F(5,16);
+ F(6,19);
+ F(7,22);
+ F(8,25);
+ F(9,28);
+#undef F
+}
+
+/* Input: Q, Q', Q-Q'
+ * Output: 2Q, Q+Q'
+ *
+ * x2 z3: long form
+ * x3 z3: long form
+ * x z: short form, destroyed
+ * xprime zprime: short form, destroyed
+ * qmqp: short form, preserved
+ *
+ * On entry and exit, the absolute value of the limbs of all inputs and outputs
+ * are < 2^26. */
+static void fmonty(limb *x2, limb *z2, /* output 2Q */
+ limb *x3, limb *z3, /* output Q + Q' */
+ limb *x, limb *z, /* input Q */
+ limb *xprime, limb *zprime, /* input Q' */
+ const limb *qmqp /* input Q - Q' */) {
+ limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
+ zzprime[19], zzzprime[19], xxxprime[19];
+
+ memcpy(origx, x, 10 * sizeof(limb));
+ fsum(x, z);
+ /* |x[i]| < 2^27 */
+ fdifference(z, origx); /* does x - z */
+ /* |z[i]| < 2^27 */
+
+ memcpy(origxprime, xprime, sizeof(limb) * 10);
+ fsum(xprime, zprime);
+ /* |xprime[i]| < 2^27 */
+ fdifference(zprime, origxprime);
+ /* |zprime[i]| < 2^27 */
+ fproduct(xxprime, xprime, z);
+ /* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
+ * 2^(27+27) and fproduct adds together, at most, 14 of those products.
+ * (Approximating that to 2^58 doesn't work out.) */
+ fproduct(zzprime, x, zprime);
+ /* |zzprime[i]| < 14*2^54 */
+ freduce_degree(xxprime);
+ freduce_coefficients(xxprime);
+ /* |xxprime[i]| < 2^26 */
+ freduce_degree(zzprime);
+ freduce_coefficients(zzprime);
+ /* |zzprime[i]| < 2^26 */
+ memcpy(origxprime, xxprime, sizeof(limb) * 10);
+ fsum(xxprime, zzprime);
+ /* |xxprime[i]| < 2^27 */
+ fdifference(zzprime, origxprime);
+ /* |zzprime[i]| < 2^27 */
+ fsquare(xxxprime, xxprime);
+ /* |xxxprime[i]| < 2^26 */
+ fsquare(zzzprime, zzprime);
+ /* |zzzprime[i]| < 2^26 */
+ fproduct(zzprime, zzzprime, qmqp);
+ /* |zzprime[i]| < 14*2^52 */
+ freduce_degree(zzprime);
+ freduce_coefficients(zzprime);
+ /* |zzprime[i]| < 2^26 */
+ memcpy(x3, xxxprime, sizeof(limb) * 10);
+ memcpy(z3, zzprime, sizeof(limb) * 10);
+
+ fsquare(xx, x);
+ /* |xx[i]| < 2^26 */
+ fsquare(zz, z);
+ /* |zz[i]| < 2^26 */
+ fproduct(x2, xx, zz);
+ /* |x2[i]| < 14*2^52 */
+ freduce_degree(x2);
+ freduce_coefficients(x2);
+ /* |x2[i]| < 2^26 */
+ fdifference(zz, xx); // does zz = xx - zz
+ /* |zz[i]| < 2^27 */
+ memset(zzz + 10, 0, sizeof(limb) * 9);
+ fscalar_product(zzz, zz, 121665);
+ /* |zzz[i]| < 2^(27+17) */
+ /* No need to call freduce_degree here:
+ fscalar_product doesn't increase the degree of its input. */
+ freduce_coefficients(zzz);
+ /* |zzz[i]| < 2^26 */
+ fsum(zzz, xx);
+ /* |zzz[i]| < 2^27 */
+ fproduct(z2, zz, zzz);
+ /* |z2[i]| < 14*2^(26+27) */
+ freduce_degree(z2);
+ freduce_coefficients(z2);
+ /* |z2|i| < 2^26 */
+}
+
+/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
+ * them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
+ * side-channel attacks.
+ *
+ * NOTE that this function requires that 'iswap' be 1 or 0; other values give
+ * wrong results. Also, the two limb arrays must be in reduced-coefficient,
+ * reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
+ * and all all values in a[0..9],b[0..9] must have magnitude less than
+ * INT32_MAX. */
+static void
+swap_conditional(limb a[19], limb b[19], limb iswap) {
+ unsigned i;
+ const s32 swap = (s32) -iswap;
+
+ for (i = 0; i < 10; ++i) {
+ const s32 x = swap & ( ((s32)a[i]) ^ ((s32)b[i]) );
+ a[i] = ((s32)a[i]) ^ x;
+ b[i] = ((s32)b[i]) ^ x;
+ }
+}
+
+/* Calculates nQ where Q is the x-coordinate of a point on the curve
+ *
+ * resultx/resultz: the x coordinate of the resulting curve point (short form)
+ * n: a little endian, 32-byte number
+ * q: a point of the curve (short form) */
+static void
+cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) {
+ limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
+ limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
+ limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
+ limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
+
+ unsigned i, j;
+
+ memcpy(nqpqx, q, sizeof(limb) * 10);
+
+ for (i = 0; i < 32; ++i) {
+ u8 byte = n[31 - i];
+ for (j = 0; j < 8; ++j) {
+ const limb bit = byte >> 7;
+
+ swap_conditional(nqx, nqpqx, bit);
+ swap_conditional(nqz, nqpqz, bit);
+ fmonty(nqx2, nqz2,
+ nqpqx2, nqpqz2,
+ nqx, nqz,
+ nqpqx, nqpqz,
+ q);
+ swap_conditional(nqx2, nqpqx2, bit);
+ swap_conditional(nqz2, nqpqz2, bit);
+
+ t = nqx;
+ nqx = nqx2;
+ nqx2 = t;
+ t = nqz;
+ nqz = nqz2;
+ nqz2 = t;
+ t = nqpqx;
+ nqpqx = nqpqx2;
+ nqpqx2 = t;
+ t = nqpqz;
+ nqpqz = nqpqz2;
+ nqpqz2 = t;
+
+ byte <<= 1;
+ }
+ }
+
+ memcpy(resultx, nqx, sizeof(limb) * 10);
+ memcpy(resultz, nqz, sizeof(limb) * 10);
+}
+
+// -----------------------------------------------------------------------------
+// Shamelessly copied from djb's code
+// -----------------------------------------------------------------------------
+static void
+crecip(limb *out, const limb *z) {
+ limb z2[10];
+ limb z9[10];
+ limb z11[10];
+ limb z2_5_0[10];
+ limb z2_10_0[10];
+ limb z2_20_0[10];
+ limb z2_50_0[10];
+ limb z2_100_0[10];
+ limb t0[10];
+ limb t1[10];
+ int i;
+
+ /* 2 */ fsquare(z2,z);
+ /* 4 */ fsquare(t1,z2);
+ /* 8 */ fsquare(t0,t1);
+ /* 9 */ fmul(z9,t0,z);
+ /* 11 */ fmul(z11,z9,z2);
+ /* 22 */ fsquare(t0,z11);
+ /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
+
+ /* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
+ /* 2^7 - 2^2 */ fsquare(t1,t0);
+ /* 2^8 - 2^3 */ fsquare(t0,t1);
+ /* 2^9 - 2^4 */ fsquare(t1,t0);
+ /* 2^10 - 2^5 */ fsquare(t0,t1);
+ /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
+
+ /* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
+ /* 2^12 - 2^2 */ fsquare(t1,t0);
+ /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
+ /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
+
+ /* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
+ /* 2^22 - 2^2 */ fsquare(t1,t0);
+ /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
+ /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
+
+ /* 2^41 - 2^1 */ fsquare(t1,t0);
+ /* 2^42 - 2^2 */ fsquare(t0,t1);
+ /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
+ /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
+
+ /* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
+ /* 2^52 - 2^2 */ fsquare(t1,t0);
+ /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
+ /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
+
+ /* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
+ /* 2^102 - 2^2 */ fsquare(t0,t1);
+ /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
+ /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
+
+ /* 2^201 - 2^1 */ fsquare(t0,t1);
+ /* 2^202 - 2^2 */ fsquare(t1,t0);
+ /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
+ /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
+
+ /* 2^251 - 2^1 */ fsquare(t1,t0);
+ /* 2^252 - 2^2 */ fsquare(t0,t1);
+ /* 2^253 - 2^3 */ fsquare(t1,t0);
+ /* 2^254 - 2^4 */ fsquare(t0,t1);
+ /* 2^255 - 2^5 */ fsquare(t1,t0);
+ /* 2^255 - 21 */ fmul(out,t1,z11);
+}
+
+int
+curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) {
+ limb bp[10], x[10], z[11], zmone[10];
+ uint8_t e[32];
+ int i;
+
+ for (i = 0; i < 32; ++i) e[i] = secret[i];
+ e[0] &= 248;
+ e[31] &= 127;
+ e[31] |= 64;
+
+ fexpand(bp, basepoint);
+ cmult(x, z, e, bp);
+ crecip(zmone, z);
+ fmul(z, x, zmone);
+ fcontract(mypublic, z);
+ return 0;
+}
diff --git a/curve25519-donna.podspec b/curve25519-donna.podspec
new file mode 100644
index 0000000..0f2f31a
--- /dev/null
+++ b/curve25519-donna.podspec
@@ -0,0 +1,13 @@
+Pod::Spec.new do |s|
+ s.name = "curve25519-donna"
+ s.version = "1.2.1"
+ s.summary = "Implementations of a fast elliptic-curve, Diffie-Hellman primitive"
+ s.description = <<-DESC
+ Curve25519 is a state-of-the-art Diffie-Hellman function suitable for a wide variety of applications.
+ DESC
+ s.homepage = "http://code.google.com/p/curve25519-donna"
+ s.license = 'BSD 3-Clause'
+ s.author = 'Dan Bernstein'
+ s.source = { :git => "https://github.com/agl/curve25519-donna.git", :tag => "1.2.1" }
+ s.source_files = 'curve25519-donna.c'
+end
diff --git a/python-src/curve25519/__init__.py b/python-src/curve25519/__init__.py
new file mode 100644
index 0000000..873ff57
--- /dev/null
+++ b/python-src/curve25519/__init__.py
@@ -0,0 +1,4 @@
+
+from .keys import Private, Public
+
+hush_pyflakes = [Private, Public]; del hush_pyflakes
diff --git a/python-src/curve25519/curve25519module.c b/python-src/curve25519/curve25519module.c
new file mode 100644
index 0000000..e309ec0
--- /dev/null
+++ b/python-src/curve25519/curve25519module.c
@@ -0,0 +1,105 @@
+/* tell python that PyArg_ParseTuple(t#) means Py_ssize_t, not int */
+#define PY_SSIZE_T_CLEAN
+#include <Python.h>
+#if (PY_VERSION_HEX < 0x02050000)
+ typedef int Py_ssize_t;
+#endif
+
+/* This is required for compatibility with Python 2. */
+#if PY_MAJOR_VERSION >= 3
+ #include <bytesobject.h>
+ #define y "y"
+#else
+ #define PyBytes_FromStringAndSize PyString_FromStringAndSize
+ #define y "t"
+#endif
+
+int curve25519_donna(char *mypublic,
+ const char *secret, const char *basepoint);
+
+static PyObject *
+pycurve25519_makeprivate(PyObject *self, PyObject *args)
+{
+ char *in1;
+ Py_ssize_t in1len;
+ if (!PyArg_ParseTuple(args, y"#:clamp", &in1, &in1len))
+ return NULL;
+ if (in1len != 32) {
+ PyErr_SetString(PyExc_ValueError, "input must be 32-byte string");
+ return NULL;
+ }
+ in1[0] &= 248;
+ in1[31] &= 127;
+ in1[31] |= 64;
+ return PyBytes_FromStringAndSize((char *)in1, 32);
+}
+
+static PyObject *
+pycurve25519_makepublic(PyObject *self, PyObject *args)
+{
+ const char *private;
+ char mypublic[32];
+ char basepoint[32] = {9};
+ Py_ssize_t privatelen;
+ if (!PyArg_ParseTuple(args, y"#:makepublic", &private, &privatelen))
+ return NULL;
+ if (privatelen != 32) {
+ PyErr_SetString(PyExc_ValueError, "input must be 32-byte string");
+ return NULL;
+ }
+ curve25519_donna(mypublic, private, basepoint);
+ return PyBytes_FromStringAndSize((char *)mypublic, 32);
+}
+
+static PyObject *
+pycurve25519_makeshared(PyObject *self, PyObject *args)
+{
+ const char *myprivate, *theirpublic;
+ char shared_key[32];
+ Py_ssize_t myprivatelen, theirpubliclen;
+ if (!PyArg_ParseTuple(args, y"#"y"#:generate",
+ &myprivate, &myprivatelen, &theirpublic, &theirpubliclen))
+ return NULL;
+ if (myprivatelen != 32) {
+ PyErr_SetString(PyExc_ValueError, "input must be 32-byte string");
+ return NULL;
+ }
+ if (theirpubliclen != 32) {
+ PyErr_SetString(PyExc_ValueError, "input must be 32-byte string");
+ return NULL;
+ }
+ curve25519_donna(shared_key, myprivate, theirpublic);
+ return PyBytes_FromStringAndSize((char *)shared_key, 32);
+}
+
+
+static PyMethodDef
+curve25519_functions[] = {
+ {"make_private", pycurve25519_makeprivate, METH_VARARGS, "data->private"},
+ {"make_public", pycurve25519_makepublic, METH_VARARGS, "private->public"},
+ {"make_shared", pycurve25519_makeshared, METH_VARARGS, "private+public->shared"},
+ {NULL, NULL, 0, NULL},
+};
+
+#if PY_MAJOR_VERSION >= 3
+ static struct PyModuleDef
+ curve25519_module = {
+ PyModuleDef_HEAD_INIT,
+ "_curve25519",
+ NULL,
+ NULL,
+ curve25519_functions,
+ };
+
+ PyObject *
+ PyInit__curve25519(void)
+ {
+ return PyModule_Create(&curve25519_module);
+ }
+#else
+ PyMODINIT_FUNC
+ init_curve25519(void)
+ {
+ (void)Py_InitModule("_curve25519", curve25519_functions);
+ }
+#endif \ No newline at end of file
diff --git a/python-src/curve25519/keys.py b/python-src/curve25519/keys.py
new file mode 100644
index 0000000..e131dac
--- /dev/null
+++ b/python-src/curve25519/keys.py
@@ -0,0 +1,46 @@
+from . import _curve25519
+from hashlib import sha256
+import os
+
+# the curve25519 functions are really simple, and could be used without an
+# OOP layer, but it's a bit too easy to accidentally swap the private and
+# public keys that way.
+
+def _hash_shared(shared):
+ return sha256(b"curve25519-shared:"+shared).digest()
+
+class Private:
+ def __init__(self, secret=None, seed=None):
+ if secret is None:
+ if seed is None:
+ secret = os.urandom(32)
+ else:
+ secret = sha256(b"curve25519-private:"+seed).digest()
+ else:
+ assert seed is None, "provide secret, seed, or neither, not both"
+ if not isinstance(secret, bytes) or len(secret) != 32:
+ raise TypeError("secret= must be 32-byte string")
+ self.private = _curve25519.make_private(secret)
+
+ def serialize(self):
+ return self.private
+
+ def get_public(self):
+ return Public(_curve25519.make_public(self.private))
+
+ def get_shared_key(self, public, hashfunc=None):
+ if not isinstance(public, Public):
+ raise ValueError("'public' must be an instance of Public")
+ if hashfunc is None:
+ hashfunc = _hash_shared
+ shared = _curve25519.make_shared(self.private, public.public)
+ return hashfunc(shared)
+
+class Public:
+ def __init__(self, public):
+ assert isinstance(public, bytes)
+ assert len(public) == 32
+ self.public = public
+
+ def serialize(self):
+ return self.public
diff --git a/python-src/curve25519/test/__init__.py b/python-src/curve25519/test/__init__.py
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/python-src/curve25519/test/__init__.py
diff --git a/python-src/curve25519/test/test_curve25519.py b/python-src/curve25519/test/test_curve25519.py
new file mode 100755
index 0000000..2ecbd47
--- /dev/null
+++ b/python-src/curve25519/test/test_curve25519.py
@@ -0,0 +1,99 @@
+#! /usr/bin/python
+
+import unittest
+
+from curve25519 import Private, Public
+from hashlib import sha1, sha256
+from binascii import hexlify
+
+class Basic(unittest.TestCase):
+ def test_basic(self):
+ secret1 = b"abcdefghijklmnopqrstuvwxyz123456"
+ self.assertEqual(len(secret1), 32)
+
+ secret2 = b"654321zyxwvutsrqponmlkjihgfedcba"
+ self.assertEqual(len(secret2), 32)
+ priv1 = Private(secret=secret1)
+ pub1 = priv1.get_public()
+ priv2 = Private(secret=secret2)
+ pub2 = priv2.get_public()
+ shared12 = priv1.get_shared_key(pub2)
+ e = b"b0818125eab42a8ac1af5e8b9b9c15ed2605c2bbe9675de89e5e6e7f442b9598"
+ self.assertEqual(hexlify(shared12), e)
+ shared21 = priv2.get_shared_key(pub1)
+ self.assertEqual(shared12, shared21)
+
+ pub2a = Public(pub2.serialize())
+ shared12a = priv1.get_shared_key(pub2a)
+ self.assertEqual(hexlify(shared12a), e)
+
+ def test_errors(self):
+ priv1 = Private()
+ self.assertRaises(ValueError, priv1.get_shared_key, priv1)
+
+ def test_seed(self):
+ # use 32-byte secret
+ self.assertRaises(TypeError, Private, secret=123)
+ self.assertRaises(TypeError, Private, secret=b"too short")
+ secret1 = b"abcdefghijklmnopqrstuvwxyz123456"
+ assert len(secret1) == 32
+ priv1 = Private(secret=secret1)
+ priv1a = Private(secret=secret1)
+ priv1b = Private(priv1.serialize())
+ self.assertEqual(priv1.serialize(), priv1a.serialize())
+ self.assertEqual(priv1.serialize(), priv1b.serialize())
+ e = b"6062636465666768696a6b6c6d6e6f707172737475767778797a313233343576"
+ self.assertEqual(hexlify(priv1.serialize()), e)
+
+ # the private key is a clamped form of the secret, so they won't
+ # quite be the same
+ p = Private(secret=b"\x00"*32)
+ self.assertEqual(hexlify(p.serialize()), b"00"*31+b"40")
+ p = Private(secret=b"\xff"*32)
+ self.assertEqual(hexlify(p.serialize()), b"f8"+b"ff"*30+b"7f")
+
+ # use arbitrary-length seed
+ self.assertRaises(TypeError, Private, seed=123)
+ priv1 = Private(seed=b"abc")
+ priv1a = Private(seed=b"abc")
+ priv1b = Private(priv1.serialize())
+ self.assertEqual(priv1.serialize(), priv1a.serialize())
+ self.assertEqual(priv1.serialize(), priv1b.serialize())
+ self.assertRaises(AssertionError, Private, seed=b"abc", secret=b"no")
+
+ priv1 = Private(seed=b"abc")
+ priv1a = Private(priv1.serialize())
+ self.assertEqual(priv1.serialize(), priv1a.serialize())
+ self.assertRaises(AssertionError, Private, seed=b"abc", secret=b"no")
+
+ # use built-in os.urandom
+ priv2 = Private()
+ priv2a = Private(priv2.private)
+ self.assertEqual(priv2.serialize(), priv2a.serialize())
+
+ # attempt to use both secret= and seed=, not allowed
+ self.assertRaises(AssertionError, Private, seed=b"abc", secret=b"no")
+
+ def test_hashfunc(self):
+ priv1 = Private(seed=b"abc")
+ priv2 = Private(seed=b"def")
+ shared_sha256 = priv1.get_shared_key(priv2.get_public())
+ e = b"da959ffe77ebeb4757fe5ba310e28ede425ae0d0ff5ec9c884e2d08f311cf5e5"
+ self.assertEqual(hexlify(shared_sha256), e)
+
+ # confirm the hash function remains what we think it is
+ def myhash(shared_key):
+ return sha256(b"curve25519-shared:"+shared_key).digest()
+ shared_myhash = priv1.get_shared_key(priv2.get_public(), myhash)
+ self.assertEqual(hexlify(shared_myhash), e)
+
+ def hexhash(shared_key):
+ return sha1(shared_key).hexdigest().encode()
+ shared_hexhash = priv1.get_shared_key(priv2.get_public(), hexhash)
+ self.assertEqual(shared_hexhash,
+ b"80eec98222c8edc4324fb9477a3c775ce7c6c93a")
+
+
+if __name__ == "__main__":
+ unittest.main()
+
diff --git a/python-src/curve25519/test/test_speed.py b/python-src/curve25519/test/test_speed.py
new file mode 100755
index 0000000..87952fa
--- /dev/null
+++ b/python-src/curve25519/test/test_speed.py
@@ -0,0 +1,46 @@
+#! /usr/bin/python
+
+from time import time
+from curve25519 import Private
+
+count = 10000
+elapsed_get_public = 0.0
+elapsed_get_shared = 0.0
+
+def abbreviate_time(data):
+ # 1.23s, 790ms, 132us
+ if data is None:
+ return ""
+ s = float(data)
+ if s >= 10:
+ #return abbreviate.abbreviate_time(data)
+ return "%d" % s
+ if s >= 1.0:
+ return "%.2fs" % s
+ if s >= 0.01:
+ return "%dms" % (1000*s)
+ if s >= 0.001:
+ return "%.1fms" % (1000*s)
+ if s >= 0.000001:
+ return "%.1fus" % (1000000*s)
+ return "%dns" % (1000000000*s)
+
+def nohash(key): return key
+
+for i in range(count):
+ p = Private()
+ start = time()
+ pub = p.get_public()
+ elapsed_get_public += time() - start
+ pub2 = Private().get_public()
+ start = time()
+ shared = p.get_shared_key(pub2) #, hashfunc=nohash)
+ elapsed_get_shared += time() - start
+
+print("get_public: %s" % abbreviate_time(elapsed_get_public / count))
+print("get_shared: %s" % abbreviate_time(elapsed_get_shared / count))
+
+# these take about 560us-570us each (with the default compiler settings, -Os)
+# on my laptop, same with -O2
+# of which the python overhead is about 5us
+# and the get_shared_key() hash step adds about 5us
diff --git a/setup.py b/setup.py
new file mode 100755
index 0000000..dc1b8eb
--- /dev/null
+++ b/setup.py
@@ -0,0 +1,38 @@
+#! /usr/bin/python
+
+from subprocess import Popen, PIPE
+from distutils.core import setup, Extension
+
+version = Popen(["git", "describe", "--tags"], stdout=PIPE).communicate()[0]\
+ .strip().decode("utf8")
+
+ext_modules = [Extension("curve25519._curve25519",
+ ["python-src/curve25519/curve25519module.c",
+ "curve25519-donna.c"],
+ )]
+
+short_description="Python wrapper for the Curve25519 cryptographic library"
+long_description="""\
+Curve25519 is a fast elliptic-curve key-agreement protocol, in which two
+parties Alice and Bob each generate a (public,private) keypair, exchange
+public keys, and can then compute the same shared key. Specifically, Alice
+computes F(Aprivate, Bpublic), Bob computes F(Bprivate, Apublic), and both
+get the same value (and nobody else can guess that shared value, even if they
+know Apublic and Bpublic).
+
+This is a Python wrapper for the portable 'curve25519-donna' implementation
+of this algorithm, written by Adam Langley, hosted at
+http://code.google.com/p/curve25519-donna/
+"""
+
+setup(name="curve25519-donna",
+ version=version,
+ description=short_description,
+ long_description=long_description,
+ author="Brian Warner",
+ author_email="warner-pycurve25519-donna@lothar.com",
+ license="BSD",
+ packages=["curve25519", "curve25519.test"],
+ package_dir={"curve25519": "python-src/curve25519"},
+ ext_modules=ext_modules,
+ )
diff --git a/speed-curve25519.c b/speed-curve25519.c
new file mode 100644
index 0000000..d945d48
--- /dev/null
+++ b/speed-curve25519.c
@@ -0,0 +1,50 @@
+#include <stdio.h>
+#include <string.h>
+#include <sys/time.h>
+#include <time.h>
+#include <stdint.h>
+
+typedef uint8_t u8;
+
+extern void curve25519_donna(u8 *output, const u8 *secret, const u8 *bp);
+
+static uint64_t
+time_now() {
+ struct timeval tv;
+ uint64_t ret;
+
+ gettimeofday(&tv, NULL);
+ ret = tv.tv_sec;
+ ret *= 1000000;
+ ret += tv.tv_usec;
+
+ return ret;
+}
+
+int
+main() {
+ static const unsigned char basepoint[32] = {9};
+ unsigned char mysecret[32], mypublic[32];
+ unsigned i;
+ uint64_t start, end;
+
+ memset(mysecret, 42, 32);
+ mysecret[0] &= 248;
+ mysecret[31] &= 127;
+ mysecret[31] |= 64;
+
+ // Load the caches
+ for (i = 0; i < 1000; ++i) {
+ curve25519_donna(mypublic, mysecret, basepoint);
+ }
+
+ start = time_now();
+ for (i = 0; i < 30000; ++i) {
+ curve25519_donna(mypublic, mysecret, basepoint);
+ }
+ end = time_now();
+
+ printf("%luus\n", (unsigned long) ((end - start) / 30000));
+
+ return 0;
+}
diff --git a/test-curve25519.c b/test-curve25519.c
new file mode 100644
index 0000000..591d871
--- /dev/null
+++ b/test-curve25519.c
@@ -0,0 +1,54 @@
+/*
+test-curve25519 version 20050915
+D. J. Bernstein
+Public domain.
+
+Tiny modifications by agl
+*/
+
+#include <stdio.h>
+
+extern void curve25519_donna(unsigned char *output, const unsigned char *a,
+ const unsigned char *b);
+void doit(unsigned char *ek,unsigned char *e,unsigned char *k);
+
+void doit(unsigned char *ek,unsigned char *e,unsigned char *k)
+{
+ int i;
+
+ for (i = 0;i < 32;++i) printf("%02x",(unsigned int) e[i]); printf(" ");
+ for (i = 0;i < 32;++i) printf("%02x",(unsigned int) k[i]); printf(" ");
+ curve25519_donna(ek,e,k);
+ for (i = 0;i < 32;++i) printf("%02x",(unsigned int) ek[i]); printf("\n");
+}
+
+unsigned char e1k[32];
+unsigned char e2k[32];
+unsigned char e1e2k[32];
+unsigned char e2e1k[32];
+unsigned char e1[32] = {3};
+unsigned char e2[32] = {5};
+unsigned char k[32] = {9};
+
+int
+main()
+{
+ int loop;
+ int i;
+
+ for (loop = 0;loop < 10000;++loop) {
+ doit(e1k,e1,k);
+ doit(e2e1k,e2,e1k);
+ doit(e2k,e2,k);
+ doit(e1e2k,e1,e2k);
+ for (i = 0;i < 32;++i) if (e1e2k[i] != e2e1k[i]) {
+ printf("fail\n");
+ return 1;
+ }
+ for (i = 0;i < 32;++i) e1[i] ^= e2k[i];
+ for (i = 0;i < 32;++i) e2[i] ^= e1k[i];
+ for (i = 0;i < 32;++i) k[i] ^= e1e2k[i];
+ }
+
+ return 0;
+}
diff --git a/test-noncanon.c b/test-noncanon.c
new file mode 100644
index 0000000..6de4e8d
--- /dev/null
+++ b/test-noncanon.c
@@ -0,0 +1,39 @@
+/* This file can be used to test whether the code handles non-canonical curve
+ * points (i.e. points with the 256th bit set) in the same way as the reference
+ * implementation. */
+
+#include <stdint.h>
+#include <stdio.h>
+#include <string.h>
+
+extern void curve25519_donna(unsigned char *output, const unsigned char *a,
+ const unsigned char *b);
+int
+main()
+{
+ static const uint8_t point1[32] = {
+ 0x25,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+ 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+ 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+ 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+ };
+ static const uint8_t point2[32] = {
+ 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
+ 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
+ 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
+ 0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
+ };
+ static const uint8_t scalar[32] = { 1 };
+ uint8_t out1[32], out2[32];
+
+ curve25519_donna(out1, scalar, point1);
+ curve25519_donna(out2, scalar, point2);
+
+ if (0 == memcmp(out1, out2, sizeof(out1))) {
+ fprintf(stderr, "Top bit not ignored.\n");
+ return 1;
+ }
+
+ fprintf(stderr, "Top bit correctly ignored.\n");
+ return 0;
+}
diff --git a/test-sc-curve25519.c b/test-sc-curve25519.c
new file mode 100644
index 0000000..14a7e3c
--- /dev/null
+++ b/test-sc-curve25519.c
@@ -0,0 +1,72 @@
+#define _GNU_SOURCE
+
+#include <stdio.h>
+#include <string.h>
+#include <stdint.h>
+#include <math.h>
+
+extern void curve25519_donna(uint8_t *, const uint8_t *, const uint8_t *);
+extern uint64_t tsc_read();
+
+int
+main(int argc, char **argv) {
+ uint8_t private_key[32], public[32], peer1[32], peer2[32], output[32];
+ static const uint8_t basepoint[32] = {9};
+ unsigned i;
+ uint64_t sum = 0, sum_squares = 0, skipped = 0, mean;
+ static const unsigned count = 200000;
+
+ memset(private_key, 42, sizeof(private_key));
+
+ private_key[0] &= 248;
+ private_key[31] &= 127;
+ private_key[31] |= 64;
+
+ curve25519_donna(public, private_key, basepoint);
+ memset(peer1, 0, sizeof(peer1));
+ memset(peer2, 255, sizeof(peer2));
+
+ for (i = 0; i < count; ++i) {
+ const uint64_t start = tsc_read();
+ curve25519_donna(output, peer1, public);
+ const uint64_t end = tsc_read();
+ const uint64_t delta = end - start;
+ if (delta > 650000) {
+ // something terrible happened (task switch etc)
+ skipped++;
+ continue;
+ }
+ sum += delta;
+ sum_squares += (delta * delta);
+ }
+
+ mean = sum / ((uint64_t) count);
+ printf("all 0: mean:%lu sd:%f skipped:%lu\n",
+ mean,
+ sqrt((double)(sum_squares/((uint64_t) count) - mean*mean)),
+ skipped);
+
+ sum = sum_squares = skipped = 0;
+
+ for (i = 0; i < count; ++i) {
+ const uint64_t start = tsc_read();
+ curve25519_donna(output, peer2, public);
+ const uint64_t end = tsc_read();
+ const uint64_t delta = end - start;
+ if (delta > 650000) {
+ // something terrible happened (task switch etc)
+ skipped++;
+ continue;
+ }
+ sum += delta;
+ sum_squares += (delta * delta);
+ }
+
+ mean = sum / ((uint64_t) count);
+ printf("all 1: mean:%lu sd:%f skipped:%lu\n",
+ mean,
+ sqrt((double)(sum_squares/((uint64_t) count) - mean*mean)),
+ skipped);
+
+ return 0;
+}
diff --git a/test-sc-curve25519.s b/test-sc-curve25519.s
new file mode 100644
index 0000000..1da4f68
--- /dev/null
+++ b/test-sc-curve25519.s
@@ -0,0 +1,8 @@
+.text
+.globl tsc_read
+
+tsc_read:
+rdtsc
+shl $32,%rdx
+or %rdx,%rax
+ret
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-09 15:17:20 +0000