Added Curve25519-donna changes.
Added a wrapper class that implements the following API calls which for
Curve25519.
+ ScalarMult to compute the shared key.
+ ScalarBaseMult to get public key.
+ ConvertToPrivateKey returns a private key from random bytes.
Per agl/wtc, grabbed the rev 234205ff from the git repo
(234205ff1e
)
and checked it in to crypto/ because that version has pure Google copyright.
R=wtc@chromium.org,agl@chromium.org,rsleevi@chromium.org
TEST=crypto unit tests
Review URL: https://chromiumcodereview.appspot.com/12457004
git-svn-id: svn://svn.chromium.org/chrome/trunk/src@187074 0039d316-1c4b-4281-b951-d872f2087c98
This commit is contained in:
@ -186,6 +186,9 @@
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'crypto_module_blocking_password_delegate.h',
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'cssm_init.cc',
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'cssm_init.h',
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'curve25519.cc',
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'curve25519.h',
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'curve25519-donna.c',
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'ghash.cc',
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'ghash.h',
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'ec_private_key.h',
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@ -262,6 +265,7 @@
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'run_all_unittests.cc',
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# Tests.
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'curve25519_unittest.cc',
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'ec_private_key_unittest.cc',
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'ec_signature_creator_unittest.cc',
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'encryptor_unittest.cc',
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|
592
crypto/curve25519-donna.c
Normal file
592
crypto/curve25519-donna.c
Normal file
@ -0,0 +1,592 @@
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// Copyright (c) 2013 The Chromium Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style license that can be
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// found in the LICENSE file.
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/*
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* curve25519-donna: Curve25519 elliptic curve, public key function
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*
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* http://code.google.com/p/curve25519-donna/
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*
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* Adam Langley <agl@imperialviolet.org>
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*
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* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
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*
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* More information about curve25519 can be found here
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* http://cr.yp.to/ecdh.html
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*
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* djb's sample implementation of curve25519 is written in a special assembly
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* language called qhasm and uses the floating point registers.
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*
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* This is, almost, a clean room reimplementation from the curve25519 paper. It
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* uses many of the tricks described therein. Only the crecip function is taken
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* from the sample implementation.
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*/
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#include <string.h>
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#include <stdint.h>
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typedef uint8_t u8;
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typedef int32_t s32;
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typedef int64_t limb;
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/* Field element representation:
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*
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* Field elements are written as an array of signed, 64-bit limbs, least
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* significant first. The value of the field element is:
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* x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
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*
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* i.e. the limbs are 26, 25, 26, 25, ... bits wide.
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*/
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/* Sum two numbers: output += in */
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static void fsum(limb *output, const limb *in) {
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unsigned i;
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for (i = 0; i < 10; i += 2) {
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output[0+i] = (output[0+i] + in[0+i]);
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output[1+i] = (output[1+i] + in[1+i]);
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}
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}
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/* Find the difference of two numbers: output = in - output
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* (note the order of the arguments!)
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*/
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static void fdifference(limb *output, const limb *in) {
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unsigned i;
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for (i = 0; i < 10; ++i) {
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output[i] = (in[i] - output[i]);
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}
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}
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/* Multiply a number my a scalar: output = in * scalar */
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static void fscalar_product(limb *output, const limb *in, const limb scalar) {
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unsigned i;
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for (i = 0; i < 10; ++i) {
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output[i] = in[i] * scalar;
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}
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}
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/* Multiply two numbers: output = in2 * in
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*
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* output must be distinct to both inputs. The inputs are reduced coefficient
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* form, the output is not.
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*/
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static void fproduct(limb *output, const limb *in2, const limb *in) {
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output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]);
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output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
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((limb) ((s32) in2[1])) * ((s32) in[0]);
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output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
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((limb) ((s32) in2[0])) * ((s32) in[2]) +
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((limb) ((s32) in2[2])) * ((s32) in[0]);
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output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
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((limb) ((s32) in2[2])) * ((s32) in[1]) +
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((limb) ((s32) in2[0])) * ((s32) in[3]) +
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((limb) ((s32) in2[3])) * ((s32) in[0]);
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output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
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2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
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((limb) ((s32) in2[3])) * ((s32) in[1])) +
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((limb) ((s32) in2[0])) * ((s32) in[4]) +
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((limb) ((s32) in2[4])) * ((s32) in[0]);
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output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
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((limb) ((s32) in2[3])) * ((s32) in[2]) +
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((limb) ((s32) in2[1])) * ((s32) in[4]) +
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((limb) ((s32) in2[4])) * ((s32) in[1]) +
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((limb) ((s32) in2[0])) * ((s32) in[5]) +
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((limb) ((s32) in2[5])) * ((s32) in[0]);
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output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
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((limb) ((s32) in2[1])) * ((s32) in[5]) +
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((limb) ((s32) in2[5])) * ((s32) in[1])) +
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((limb) ((s32) in2[2])) * ((s32) in[4]) +
|
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((limb) ((s32) in2[4])) * ((s32) in[2]) +
|
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((limb) ((s32) in2[0])) * ((s32) in[6]) +
|
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((limb) ((s32) in2[6])) * ((s32) in[0]);
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output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
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((limb) ((s32) in2[4])) * ((s32) in[3]) +
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((limb) ((s32) in2[2])) * ((s32) in[5]) +
|
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((limb) ((s32) in2[5])) * ((s32) in[2]) +
|
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((limb) ((s32) in2[1])) * ((s32) in[6]) +
|
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((limb) ((s32) in2[6])) * ((s32) in[1]) +
|
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((limb) ((s32) in2[0])) * ((s32) in[7]) +
|
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((limb) ((s32) in2[7])) * ((s32) in[0]);
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output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
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2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
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((limb) ((s32) in2[5])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[1])) * ((s32) in[7]) +
|
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((limb) ((s32) in2[7])) * ((s32) in[1])) +
|
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((limb) ((s32) in2[2])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[2]) +
|
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((limb) ((s32) in2[0])) * ((s32) in[8]) +
|
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((limb) ((s32) in2[8])) * ((s32) in[0]);
|
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output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
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((limb) ((s32) in2[5])) * ((s32) in[4]) +
|
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((limb) ((s32) in2[3])) * ((s32) in[6]) +
|
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((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]) +
|
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((limb) ((s32) in2[9])) * ((s32) in[0]);
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output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
|
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((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]) +
|
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((limb) ((s32) in2[8])) * ((s32) in[2]);
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output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
|
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((limb) ((s32) in2[6])) * ((s32) in[5]) +
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((limb) ((s32) in2[4])) * ((s32) in[7]) +
|
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((limb) ((s32) in2[7])) * ((s32) in[4]) +
|
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((limb) ((s32) in2[3])) * ((s32) in[8]) +
|
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((limb) ((s32) in2[8])) * ((s32) in[3]) +
|
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((limb) ((s32) in2[2])) * ((s32) in[9]) +
|
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((limb) ((s32) in2[9])) * ((s32) in[2]);
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output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
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2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
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((limb) ((s32) in2[7])) * ((s32) in[5]) +
|
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((limb) ((s32) in2[3])) * ((s32) in[9]) +
|
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((limb) ((s32) in2[9])) * ((s32) in[3])) +
|
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((limb) ((s32) in2[4])) * ((s32) in[8]) +
|
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((limb) ((s32) in2[8])) * ((s32) in[4]);
|
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output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
|
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((limb) ((s32) in2[7])) * ((s32) in[6]) +
|
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((limb) ((s32) in2[5])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[5]) +
|
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((limb) ((s32) in2[4])) * ((s32) in[9]) +
|
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((limb) ((s32) in2[9])) * ((s32) in[4]);
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output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
|
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((limb) ((s32) in2[5])) * ((s32) in[9]) +
|
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((limb) ((s32) in2[9])) * ((s32) in[5])) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[8]) +
|
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((limb) ((s32) in2[8])) * ((s32) in[6]);
|
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output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
|
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((limb) ((s32) in2[8])) * ((s32) in[7]) +
|
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((limb) ((s32) in2[6])) * ((s32) in[9]) +
|
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((limb) ((s32) in2[9])) * ((s32) in[6]);
|
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output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
|
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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]);
|
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output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]);
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}
|
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/* Reduce a long form to a short form by taking the input mod 2^255 - 19. */
|
||||
static void freduce_degree(limb *output) {
|
||||
/* Each of these shifts and adds ends up multiplying the value by 19. */
|
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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];
|
||||
}
|
||||
|
||||
/* Reduce all coefficients of the short form input so that |x| < 2^26.
|
||||
*
|
||||
* On entry: |output[i]| < 2^62
|
||||
*/
|
||||
static void freduce_coefficients(limb *output) {
|
||||
unsigned i;
|
||||
do {
|
||||
output[10] = 0;
|
||||
|
||||
for (i = 0; i < 10; i += 2) {
|
||||
limb over = output[i] / 0x4000000l;
|
||||
output[i+1] += over;
|
||||
output[i] -= over * 0x4000000l;
|
||||
|
||||
over = output[i+1] / 0x2000000;
|
||||
output[i+2] += over;
|
||||
output[i+1] -= over * 0x2000000;
|
||||
}
|
||||
output[0] += 19 * output[10];
|
||||
} while (output[10]);
|
||||
}
|
||||
|
||||
/* A helpful wrapper around fproduct: output = in * in2.
|
||||
*
|
||||
* output must be distinct to both inputs. The output is reduced degree and
|
||||
* reduced coefficient.
|
||||
*/
|
||||
static void
|
||||
fmul(limb *output, const limb *in, const limb *in2) {
|
||||
limb t[19];
|
||||
fproduct(t, in, in2);
|
||||
freduce_degree(t);
|
||||
freduce_coefficients(t);
|
||||
memcpy(output, t, sizeof(limb) * 10);
|
||||
}
|
||||
|
||||
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]);
|
||||
}
|
||||
|
||||
static void
|
||||
fsquare(limb *output, const limb *in) {
|
||||
limb t[19];
|
||||
fsquare_inner(t, in);
|
||||
freduce_degree(t);
|
||||
freduce_coefficients(t);
|
||||
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
|
||||
}
|
||||
|
||||
/* Take a fully reduced polynomial form number and contract it into a
|
||||
* little-endian, 32-byte array
|
||||
*/
|
||||
static void
|
||||
fcontract(u8 *output, limb *input) {
|
||||
int i;
|
||||
|
||||
do {
|
||||
for (i = 0; i < 9; ++i) {
|
||||
if ((i & 1) == 1) {
|
||||
while (input[i] < 0) {
|
||||
input[i] += 0x2000000;
|
||||
input[i + 1]--;
|
||||
}
|
||||
} else {
|
||||
while (input[i] < 0) {
|
||||
input[i] += 0x4000000;
|
||||
input[i + 1]--;
|
||||
}
|
||||
}
|
||||
}
|
||||
while (input[9] < 0) {
|
||||
input[9] += 0x2000000;
|
||||
input[0] -= 19;
|
||||
}
|
||||
} while (input[0] < 0);
|
||||
|
||||
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
|
||||
*/
|
||||
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);
|
||||
fdifference(z, origx); // does x - z
|
||||
|
||||
memcpy(origxprime, xprime, sizeof(limb) * 10);
|
||||
fsum(xprime, zprime);
|
||||
fdifference(zprime, origxprime);
|
||||
fproduct(xxprime, xprime, z);
|
||||
fproduct(zzprime, x, zprime);
|
||||
freduce_degree(xxprime);
|
||||
freduce_coefficients(xxprime);
|
||||
freduce_degree(zzprime);
|
||||
freduce_coefficients(zzprime);
|
||||
memcpy(origxprime, xxprime, sizeof(limb) * 10);
|
||||
fsum(xxprime, zzprime);
|
||||
fdifference(zzprime, origxprime);
|
||||
fsquare(xxxprime, xxprime);
|
||||
fsquare(zzzprime, zzprime);
|
||||
fproduct(zzprime, zzzprime, qmqp);
|
||||
freduce_degree(zzprime);
|
||||
freduce_coefficients(zzprime);
|
||||
memcpy(x3, xxxprime, sizeof(limb) * 10);
|
||||
memcpy(z3, zzprime, sizeof(limb) * 10);
|
||||
|
||||
fsquare(xx, x);
|
||||
fsquare(zz, z);
|
||||
fproduct(x2, xx, zz);
|
||||
freduce_degree(x2);
|
||||
freduce_coefficients(x2);
|
||||
fdifference(zz, xx); // does zz = xx - zz
|
||||
memset(zzz + 10, 0, sizeof(limb) * 9);
|
||||
fscalar_product(zzz, zz, 121665);
|
||||
freduce_degree(zzz);
|
||||
freduce_coefficients(zzz);
|
||||
fsum(zzz, xx);
|
||||
fproduct(z2, zz, zzz);
|
||||
freduce_degree(z2);
|
||||
freduce_coefficients(z2);
|
||||
}
|
||||
|
||||
/* 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) {
|
||||
if (byte & 0x80) {
|
||||
fmonty(nqpqx2, nqpqz2,
|
||||
nqx2, nqz2,
|
||||
nqpqx, nqpqz,
|
||||
nqx, nqz,
|
||||
q);
|
||||
} else {
|
||||
fmonty(nqx2, nqz2,
|
||||
nqpqx2, nqpqz2,
|
||||
nqx, nqz,
|
||||
nqpqx, nqpqz,
|
||||
q);
|
||||
}
|
||||
|
||||
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[10], 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;
|
||||
}
|
36
crypto/curve25519.cc
Normal file
36
crypto/curve25519.cc
Normal file
@ -0,0 +1,36 @@
|
||||
// Copyright (c) 2013 The Chromium Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style license that can be
|
||||
// found in the LICENSE file.
|
||||
|
||||
#include "crypto/curve25519.h"
|
||||
|
||||
// Curve25519 is specified in terms of byte strings, not numbers, so all
|
||||
// implementations take and return the same sequence of bits. So the byte
|
||||
// order is implicitly specified as in, say, SHA1.
|
||||
//
|
||||
// Prototype for |curve25519_donna| function in
|
||||
// third_party/curve25519-donna/curve25519-donna.c
|
||||
extern "C" int curve25519_donna(uint8*, const uint8*, const uint8*);
|
||||
|
||||
namespace crypto {
|
||||
|
||||
namespace curve25519 {
|
||||
|
||||
void ScalarMult(const uint8* private_key,
|
||||
const uint8* peer_public_key,
|
||||
uint8* shared_key) {
|
||||
curve25519_donna(shared_key, private_key, peer_public_key);
|
||||
}
|
||||
|
||||
// kBasePoint is the base point (generator) of the elliptic curve group.
|
||||
// It is little-endian version of '9' followed by 31 zeros.
|
||||
// See "Computing public keys" section of http://cr.yp.to/ecdh.html.
|
||||
static const unsigned char kBasePoint[32] = {9};
|
||||
|
||||
void ScalarBaseMult(const uint8* private_key, uint8* public_key) {
|
||||
curve25519_donna(public_key, private_key, kBasePoint);
|
||||
}
|
||||
|
||||
} // namespace curve25519
|
||||
|
||||
} // namespace crypto
|
48
crypto/curve25519.h
Normal file
48
crypto/curve25519.h
Normal file
@ -0,0 +1,48 @@
|
||||
// Copyright (c) 2013 The Chromium Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style license that can be
|
||||
// found in the LICENSE file.
|
||||
|
||||
#ifndef CRYPTO_CURVE25519_H
|
||||
#define CRYPTO_CURVE25519_H
|
||||
|
||||
#include "base/basictypes.h"
|
||||
#include "crypto/crypto_export.h"
|
||||
|
||||
namespace crypto {
|
||||
|
||||
// Curve25519 implements the elliptic curve group known as Curve25519, as
|
||||
// described in "Curve 25519: new Diffie-Hellman Speed Records",
|
||||
// by D.J. Bernstein. Additional information is available at
|
||||
// http://cr.yp.to/ecdh.html.
|
||||
namespace curve25519 {
|
||||
|
||||
// kBytes is the number of bytes in the result of the Diffie-Hellman operation,
|
||||
// which is an element of GF(2^255-19).
|
||||
static const size_t kBytes = 32;
|
||||
|
||||
// kScalarBytes is the number of bytes in an element of the scalar field:
|
||||
// GF(2^252 + 27742317777372353535851937790883648493).
|
||||
static const size_t kScalarBytes = 32;
|
||||
|
||||
// ScalarMult computes the |shared_key| from |private_key| and
|
||||
// |peer_public_key|. This method is a wrapper for |curve25519_donna()|. It
|
||||
// calls that function with |private_key| as |secret| and |peer_public_key| as
|
||||
// basepoint. |private_key| should be of length |kScalarBytes| and
|
||||
// |peer_public_key| should be of length |kBytes|.
|
||||
// See "Computing shared secrets" section of/ http://cr.yp.to/ecdh.html.
|
||||
CRYPTO_EXPORT void ScalarMult(const uint8* private_key,
|
||||
const uint8* peer_public_key,
|
||||
uint8* shared_key);
|
||||
|
||||
// ScalarBaseMult computes the |public_key| from |private_key|. This method is a
|
||||
// wrapper for |curve25519_donna()|. It calls that function with |private_key|
|
||||
// as |secret| and |kBasePoint| as basepoint. |private_key| should be of length
|
||||
// |kScalarBytes|. See "Computing public keys" section of
|
||||
// http://cr.yp.to/ecdh.html.
|
||||
CRYPTO_EXPORT void ScalarBaseMult(const uint8* private_key, uint8* public_key);
|
||||
|
||||
} // namespace curve25519
|
||||
|
||||
} // namespace crypto
|
||||
|
||||
#endif // CRYPTO_CURVE25519_H
|
44
crypto/curve25519_unittest.cc
Normal file
44
crypto/curve25519_unittest.cc
Normal file
@ -0,0 +1,44 @@
|
||||
// Copyright (c) 2013 The Chromium Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style license that can be
|
||||
// found in the LICENSE file.
|
||||
|
||||
#include "crypto/curve25519.h"
|
||||
|
||||
#include <string>
|
||||
|
||||
#include "crypto/random.h"
|
||||
#include "testing/gtest/include/gtest/gtest.h"
|
||||
|
||||
namespace crypto {
|
||||
|
||||
// Test that the basic shared key exchange identity holds: that both parties end
|
||||
// up with the same shared key. This test starts with a fixed private key for
|
||||
// two parties: alice and bob. Runs ScalarBaseMult and ScalarMult to compute
|
||||
// public key and shared key for alice and bob. It asserts that alice and bob
|
||||
// have the same shared key.
|
||||
TEST(Curve25519, SharedKeyIdentity) {
|
||||
uint8 alice_private_key[curve25519::kScalarBytes] = {3};
|
||||
uint8 bob_private_key[curve25519::kScalarBytes] = {5};
|
||||
|
||||
// Get public key for alice and bob.
|
||||
uint8 alice_public_key[curve25519::kBytes];
|
||||
curve25519::ScalarBaseMult(alice_private_key, alice_public_key);
|
||||
|
||||
uint8 bob_public_key[curve25519::kBytes];
|
||||
curve25519::ScalarBaseMult(bob_private_key, bob_public_key);
|
||||
|
||||
// Get the shared key for alice, by using alice's private key and bob's
|
||||
// public key.
|
||||
uint8 alice_shared_key[curve25519::kBytes];
|
||||
curve25519::ScalarMult(alice_private_key, bob_public_key, alice_shared_key);
|
||||
|
||||
// Get the shared key for bob, by using bob's private key and alice's public
|
||||
// key.
|
||||
uint8 bob_shared_key[curve25519::kBytes];
|
||||
curve25519::ScalarMult(bob_private_key, alice_public_key, bob_shared_key);
|
||||
|
||||
// Computed shared key of alice and bob should be the same.
|
||||
ASSERT_EQ(0, memcmp(alice_shared_key, bob_shared_key, curve25519::kBytes));
|
||||
}
|
||||
|
||||
} // namespace crypto
|
Reference in New Issue
Block a user