mirror of
https://github.com/zerotier/ZeroTierOne.git
synced 2024-12-24 07:06:39 +00:00
2848 lines
223 KiB
C++
2848 lines
223 KiB
C++
/*
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Matthew Dempsky
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Public domain.
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Derived from public domain code by D. J. Bernstein.
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*/
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// Modified very slightly for ZeroTier One by Adam Ierymenko
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// This code remains in the public domain.
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#include <stdint.h>
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#include <stdlib.h>
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#include <string.h>
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#include "Constants.hpp"
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#include "C25519.hpp"
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#include "SHA512.hpp"
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#include "Buffer.hpp"
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#include "Hashtable.hpp"
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#include "Mutex.hpp"
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#ifdef __WINDOWS__
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#pragma warning(disable: 4146)
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#endif
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namespace {
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#define crypto_int32 int32_t
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#define crypto_uint32 uint32_t
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#define crypto_int64 int64_t
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#define crypto_uint64 uint64_t
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#define crypto_hash_sha512_BYTES 64
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//////////////////////////////////////////////////////////////////////////////
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//////////////////////////////////////////////////////////////////////////////
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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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static inline 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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static inline 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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static inline 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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static inline 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]) +
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((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]) +
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((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]) +
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((limb) ((s32) in2[2])) * ((s32) in[7]) +
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((limb) ((s32) in2[7])) * ((s32) in[2]) +
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((limb) ((s32) in2[1])) * ((s32) in[8]) +
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((limb) ((s32) in2[8])) * ((s32) in[1]) +
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((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]) +
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((limb) ((s32) in2[7])) * ((s32) in[3]) +
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((limb) ((s32) in2[1])) * ((s32) in[9]) +
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((limb) ((s32) in2[9])) * ((s32) in[1])) +
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((limb) ((s32) in2[4])) * ((s32) in[6]) +
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((limb) ((s32) in2[6])) * ((s32) in[4]) +
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((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]) +
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((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])) +
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((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]) +
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((limb) ((s32) in2[9])) * ((s32) in[7]));
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output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
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((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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static inline void freduce_degree(limb *output) {
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output[8] += output[18] << 4;
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output[8] += output[18] << 1;
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output[8] += output[18];
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output[7] += output[17] << 4;
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output[7] += output[17] << 1;
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output[7] += output[17];
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output[6] += output[16] << 4;
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output[6] += output[16] << 1;
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output[6] += output[16];
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output[5] += output[15] << 4;
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output[5] += output[15] << 1;
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output[5] += output[15];
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output[4] += output[14] << 4;
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output[4] += output[14] << 1;
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output[4] += output[14];
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output[3] += output[13] << 4;
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output[3] += output[13] << 1;
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output[3] += output[13];
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output[2] += output[12] << 4;
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output[2] += output[12] << 1;
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output[2] += output[12];
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output[1] += output[11] << 4;
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output[1] += output[11] << 1;
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output[1] += output[11];
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output[0] += output[10] << 4;
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output[0] += output[10] << 1;
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output[0] += output[10];
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}
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#if (-1 & 3) != 3
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#error "This code only works on a two's complement system"
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#endif
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static inline limb div_by_2_26(const limb v)
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{
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/* High word of v; no shift needed. */
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const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
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/* Set to all 1s if v was negative; else set to 0s. */
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const int32_t sign = ((int32_t) highword) >> 31;
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/* Set to 0x3ffffff if v was negative; else set to 0. */
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const int32_t roundoff = ((uint32_t) sign) >> 6;
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/* Should return v / (1<<26) */
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return (v + roundoff) >> 26;
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}
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static inline limb div_by_2_25(const limb v)
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{
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/* High word of v; no shift needed*/
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const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
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/* Set to all 1s if v was negative; else set to 0s. */
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const int32_t sign = ((int32_t) highword) >> 31;
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/* Set to 0x1ffffff if v was negative; else set to 0. */
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const int32_t roundoff = ((uint32_t) sign) >> 7;
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/* Should return v / (1<<25) */
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return (v + roundoff) >> 25;
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}
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static inline void freduce_coefficients(limb *output) {
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unsigned i;
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output[10] = 0;
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for (i = 0; i < 10; i += 2) {
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limb over = div_by_2_26(output[i]);
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/* The entry condition (that |output[i]| < 280*2^54) means that over is, at
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* most, 280*2^28 in the first iteration of this loop. This is added to the
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* next limb and we can approximate the resulting bound of that limb by
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* 281*2^54. */
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output[i] -= over << 26;
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output[i+1] += over;
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/* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
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* 281*2^29. When this is added to the next limb, the resulting bound can
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* be approximated as 281*2^54.
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*
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* For subsequent iterations of the loop, 281*2^54 remains a conservative
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* bound and no overflow occurs. */
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over = div_by_2_25(output[i+1]);
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output[i+1] -= over << 25;
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output[i+2] += over;
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}
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/* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
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output[0] += output[10] << 4;
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output[0] += output[10] << 1;
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output[0] += output[10];
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output[10] = 0;
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/* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
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* So |over| will be no more than 2^16. */
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{
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limb over = div_by_2_26(output[0]);
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output[0] -= over << 26;
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output[1] += over;
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}
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/* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
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* bound on |output[1]| is sufficient to meet our needs. */
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}
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static inline void fmul(limb *output, const limb *in, const limb *in2) {
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limb t[19];
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fproduct(t, in, in2);
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/* |t[i]| < 14*2^54 */
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freduce_degree(t);
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freduce_coefficients(t);
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/* |t[i]| < 2^26 */
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memcpy(output, t, sizeof(limb) * 10);
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}
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static inline void fsquare_inner(limb *output, const limb *in) {
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output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
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output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
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output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
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((limb) ((s32) in[0])) * ((s32) in[2]));
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output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
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((limb) ((s32) in[0])) * ((s32) in[3]));
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output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
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4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
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2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
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output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
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((limb) ((s32) in[1])) * ((s32) in[4]) +
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((limb) ((s32) in[0])) * ((s32) in[5]));
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output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
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((limb) ((s32) in[2])) * ((s32) in[4]) +
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((limb) ((s32) in[0])) * ((s32) in[6]) +
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2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
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output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
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((limb) ((s32) in[2])) * ((s32) in[5]) +
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((limb) ((s32) in[1])) * ((s32) in[6]) +
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((limb) ((s32) in[0])) * ((s32) in[7]));
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output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
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2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
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((limb) ((s32) in[0])) * ((s32) in[8]) +
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2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
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((limb) ((s32) in[3])) * ((s32) in[5])));
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output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
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((limb) ((s32) in[3])) * ((s32) in[6]) +
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((limb) ((s32) in[2])) * ((s32) in[7]) +
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((limb) ((s32) in[1])) * ((s32) in[8]) +
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((limb) ((s32) in[0])) * ((s32) in[9]));
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output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
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((limb) ((s32) in[4])) * ((s32) in[6]) +
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((limb) ((s32) in[2])) * ((s32) in[8]) +
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2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
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((limb) ((s32) in[1])) * ((s32) in[9])));
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output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
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((limb) ((s32) in[4])) * ((s32) in[7]) +
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((limb) ((s32) in[3])) * ((s32) in[8]) +
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((limb) ((s32) in[2])) * ((s32) in[9]));
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output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
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2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
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2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
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((limb) ((s32) in[3])) * ((s32) in[9])));
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output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
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((limb) ((s32) in[5])) * ((s32) in[8]) +
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((limb) ((s32) in[4])) * ((s32) in[9]));
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output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
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((limb) ((s32) in[6])) * ((s32) in[8]) +
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2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
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output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
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((limb) ((s32) in[6])) * ((s32) in[9]));
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output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
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4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
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output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
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output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]);
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}
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static void fsquare(limb *output, const limb *in) {
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limb t[19];
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fsquare_inner(t, in);
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/* |t[i]| < 14*2^54 because the largest product of two limbs will be <
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* 2^(27+27) and fsquare_inner adds together, at most, 14 of those
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* products. */
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freduce_degree(t);
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freduce_coefficients(t);
|
|
/* |t[i]| < 2^26 */
|
|
memcpy(output, t, sizeof(limb) * 10);
|
|
}
|
|
|
|
static inline 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
|
|
|
|
static inline 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;
|
|
}
|
|
|
|
static inline s32 s32_gte(s32 a, s32 b) {
|
|
a -= b;
|
|
/* a >= 0 iff a >= b. */
|
|
return ~(a >> 31);
|
|
}
|
|
|
|
static inline 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
|
|
}
|
|
|
|
static inline 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 */
|
|
}
|
|
|
|
static inline 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;
|
|
}
|
|
}
|
|
|
|
static inline 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);
|
|
}
|
|
|
|
static inline 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);
|
|
}
|
|
|
|
static void crypto_scalarmult(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);
|
|
}
|
|
|
|
#if 0
|
|
void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
|
|
{
|
|
unsigned int j;
|
|
unsigned int u;
|
|
u = 0;
|
|
for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; }
|
|
u += a[31] + b[31]; out[31] = u;
|
|
}
|
|
|
|
void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
|
|
{
|
|
unsigned int j;
|
|
unsigned int u;
|
|
u = 218;
|
|
for (j = 0;j < 31;++j) {
|
|
u += a[j] + 65280 - b[j];
|
|
out[j] = u & 255;
|
|
u >>= 8;
|
|
}
|
|
u += a[31] - b[31];
|
|
out[31] = u;
|
|
}
|
|
|
|
void squeeze(unsigned int a[32])
|
|
{
|
|
unsigned int j;
|
|
unsigned int u;
|
|
u = 0;
|
|
for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
|
|
u += a[31]; a[31] = u & 127;
|
|
u = 19 * (u >> 7);
|
|
for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
|
|
u += a[31]; a[31] = u;
|
|
}
|
|
|
|
static const unsigned int minusp[32] = {
|
|
19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128
|
|
} ;
|
|
|
|
void freeze(unsigned int a[32])
|
|
{
|
|
unsigned int aorig[32];
|
|
unsigned int j;
|
|
unsigned int negative;
|
|
|
|
for (j = 0;j < 32;++j) aorig[j] = a[j];
|
|
add(a,a,minusp);
|
|
negative = -((a[31] >> 7) & 1);
|
|
for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]);
|
|
}
|
|
|
|
void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
|
|
{
|
|
unsigned int i;
|
|
unsigned int j;
|
|
unsigned int u;
|
|
|
|
for (i = 0;i < 32;++i) {
|
|
u = 0;
|
|
for (j = 0;j <= i;++j) u += a[j] * b[i - j];
|
|
for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j];
|
|
out[i] = u;
|
|
}
|
|
squeeze(out);
|
|
}
|
|
|
|
void mult121665(unsigned int out[32],const unsigned int a[32])
|
|
{
|
|
unsigned int j;
|
|
unsigned int u;
|
|
|
|
u = 0;
|
|
for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; }
|
|
u += 121665 * a[31]; out[31] = u & 127;
|
|
u = 19 * (u >> 7);
|
|
for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; }
|
|
u += out[j]; out[j] = u;
|
|
}
|
|
|
|
void square(unsigned int out[32],const unsigned int a[32])
|
|
{
|
|
unsigned int i;
|
|
unsigned int j;
|
|
unsigned int u;
|
|
|
|
for (i = 0;i < 32;++i) {
|
|
u = 0;
|
|
for (j = 0;j < i - j;++j) u += a[j] * a[i - j];
|
|
for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j];
|
|
u *= 2;
|
|
if ((i & 1) == 0) {
|
|
u += a[i / 2] * a[i / 2];
|
|
u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
|
|
}
|
|
out[i] = u;
|
|
}
|
|
squeeze(out);
|
|
}
|
|
|
|
void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b)
|
|
{
|
|
unsigned int j;
|
|
unsigned int t;
|
|
unsigned int bminus1;
|
|
|
|
bminus1 = b - 1;
|
|
for (j = 0;j < 64;++j) {
|
|
t = bminus1 & (r[j] ^ s[j]);
|
|
p[j] = s[j] ^ t;
|
|
q[j] = r[j] ^ t;
|
|
}
|
|
}
|
|
|
|
static void mainloop(unsigned int work[64],const unsigned char e[32])
|
|
{
|
|
unsigned int xzm1[64];
|
|
unsigned int xzm[64];
|
|
unsigned int xzmb[64];
|
|
unsigned int xzm1b[64];
|
|
unsigned int xznb[64];
|
|
unsigned int xzn1b[64];
|
|
unsigned int a0[64];
|
|
unsigned int a1[64];
|
|
unsigned int b0[64];
|
|
unsigned int b1[64];
|
|
unsigned int c1[64];
|
|
unsigned int r[32];
|
|
unsigned int s[32];
|
|
unsigned int t[32];
|
|
unsigned int u[32];
|
|
//unsigned int i;
|
|
unsigned int j;
|
|
unsigned int b;
|
|
int pos;
|
|
|
|
for (j = 0;j < 32;++j) xzm1[j] = work[j];
|
|
xzm1[32] = 1;
|
|
for (j = 33;j < 64;++j) xzm1[j] = 0;
|
|
|
|
xzm[0] = 1;
|
|
for (j = 1;j < 64;++j) xzm[j] = 0;
|
|
|
|
for (pos = 254;pos >= 0;--pos) {
|
|
b = e[pos / 8] >> (pos & 7);
|
|
b &= 1;
|
|
select(xzmb,xzm1b,xzm,xzm1,b);
|
|
add(a0,xzmb,xzmb + 32);
|
|
sub(a0 + 32,xzmb,xzmb + 32);
|
|
add(a1,xzm1b,xzm1b + 32);
|
|
sub(a1 + 32,xzm1b,xzm1b + 32);
|
|
square(b0,a0);
|
|
square(b0 + 32,a0 + 32);
|
|
mult(b1,a1,a0 + 32);
|
|
mult(b1 + 32,a1 + 32,a0);
|
|
add(c1,b1,b1 + 32);
|
|
sub(c1 + 32,b1,b1 + 32);
|
|
square(r,c1 + 32);
|
|
sub(s,b0,b0 + 32);
|
|
mult121665(t,s);
|
|
add(u,t,b0);
|
|
mult(xznb,b0,b0 + 32);
|
|
mult(xznb + 32,s,u);
|
|
square(xzn1b,c1);
|
|
mult(xzn1b + 32,r,work);
|
|
select(xzm,xzm1,xznb,xzn1b,b);
|
|
}
|
|
|
|
for (j = 0;j < 64;++j) work[j] = xzm[j];
|
|
}
|
|
|
|
static void recip(unsigned int out[32],const unsigned int z[32])
|
|
{
|
|
unsigned int z2[32];
|
|
unsigned int z9[32];
|
|
unsigned int z11[32];
|
|
unsigned int z2_5_0[32];
|
|
unsigned int z2_10_0[32];
|
|
unsigned int z2_20_0[32];
|
|
unsigned int z2_50_0[32];
|
|
unsigned int z2_100_0[32];
|
|
unsigned int t0[32];
|
|
unsigned int t1[32];
|
|
int i;
|
|
|
|
/* 2 */ square(z2,z);
|
|
/* 4 */ square(t1,z2);
|
|
/* 8 */ square(t0,t1);
|
|
/* 9 */ mult(z9,t0,z);
|
|
/* 11 */ mult(z11,z9,z2);
|
|
/* 22 */ square(t0,z11);
|
|
/* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9);
|
|
|
|
/* 2^6 - 2^1 */ square(t0,z2_5_0);
|
|
/* 2^7 - 2^2 */ square(t1,t0);
|
|
/* 2^8 - 2^3 */ square(t0,t1);
|
|
/* 2^9 - 2^4 */ square(t1,t0);
|
|
/* 2^10 - 2^5 */ square(t0,t1);
|
|
/* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0);
|
|
|
|
/* 2^11 - 2^1 */ square(t0,z2_10_0);
|
|
/* 2^12 - 2^2 */ square(t1,t0);
|
|
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); }
|
|
/* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0);
|
|
|
|
/* 2^21 - 2^1 */ square(t0,z2_20_0);
|
|
/* 2^22 - 2^2 */ square(t1,t0);
|
|
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); }
|
|
/* 2^40 - 2^0 */ mult(t0,t1,z2_20_0);
|
|
|
|
/* 2^41 - 2^1 */ square(t1,t0);
|
|
/* 2^42 - 2^2 */ square(t0,t1);
|
|
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); }
|
|
/* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0);
|
|
|
|
/* 2^51 - 2^1 */ square(t0,z2_50_0);
|
|
/* 2^52 - 2^2 */ square(t1,t0);
|
|
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
|
|
/* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0);
|
|
|
|
/* 2^101 - 2^1 */ square(t1,z2_100_0);
|
|
/* 2^102 - 2^2 */ square(t0,t1);
|
|
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); }
|
|
/* 2^200 - 2^0 */ mult(t1,t0,z2_100_0);
|
|
|
|
/* 2^201 - 2^1 */ square(t0,t1);
|
|
/* 2^202 - 2^2 */ square(t1,t0);
|
|
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
|
|
/* 2^250 - 2^0 */ mult(t0,t1,z2_50_0);
|
|
|
|
/* 2^251 - 2^1 */ square(t1,t0);
|
|
/* 2^252 - 2^2 */ square(t0,t1);
|
|
/* 2^253 - 2^3 */ square(t1,t0);
|
|
/* 2^254 - 2^4 */ square(t0,t1);
|
|
/* 2^255 - 2^5 */ square(t1,t0);
|
|
/* 2^255 - 21 */ mult(out,t1,z11);
|
|
}
|
|
|
|
int crypto_scalarmult(unsigned char *q,const unsigned char *n,const unsigned char *p)
|
|
{
|
|
unsigned int work[96];
|
|
unsigned char e[32];
|
|
unsigned int i;
|
|
for (i = 0;i < 32;++i) e[i] = n[i];
|
|
e[0] &= 248;
|
|
e[31] &= 127;
|
|
e[31] |= 64;
|
|
for (i = 0;i < 32;++i) work[i] = p[i];
|
|
mainloop(work,e);
|
|
recip(work + 32,work + 32);
|
|
mult(work + 64,work,work + 32);
|
|
freeze(work + 64);
|
|
for (i = 0;i < 32;++i) q[i] = work[64 + i];
|
|
return 0;
|
|
}
|
|
#endif
|
|
|
|
static const unsigned char base[32] = {9};
|
|
static inline void crypto_scalarmult_base(unsigned char *q,const unsigned char *n)
|
|
{
|
|
crypto_scalarmult(q,n,base);
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////////
|
|
//////////////////////////////////////////////////////////////////////////////
|
|
|
|
// Ed25519 ref from: http://bench.cr.yp.to/supercop.html
|
|
|
|
typedef struct
|
|
{
|
|
crypto_uint32 v[32];
|
|
}
|
|
fe25519;
|
|
|
|
typedef struct
|
|
{
|
|
crypto_uint32 v[32];
|
|
}
|
|
sc25519;
|
|
|
|
typedef struct
|
|
{
|
|
crypto_uint32 v[16];
|
|
}
|
|
shortsc25519;
|
|
|
|
typedef struct
|
|
{
|
|
fe25519 x;
|
|
fe25519 y;
|
|
fe25519 z;
|
|
fe25519 t;
|
|
} ge25519;
|
|
|
|
#define ge25519_p3 ge25519
|
|
|
|
typedef struct
|
|
{
|
|
fe25519 x;
|
|
fe25519 z;
|
|
fe25519 y;
|
|
fe25519 t;
|
|
} ge25519_p1p1;
|
|
|
|
typedef struct
|
|
{
|
|
fe25519 x;
|
|
fe25519 y;
|
|
fe25519 z;
|
|
} ge25519_p2;
|
|
|
|
typedef struct
|
|
{
|
|
fe25519 x;
|
|
fe25519 y;
|
|
} ge25519_aff;
|
|
|
|
static void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y);
|
|
|
|
crypto_uint32 equal(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
|
|
{
|
|
crypto_uint32 x = a ^ b; /* 0: yes; 1..65535: no */
|
|
x -= 1; /* 4294967295: yes; 0..65534: no */
|
|
x >>= 31; /* 1: yes; 0: no */
|
|
return x;
|
|
}
|
|
|
|
crypto_uint32 ge(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
|
|
{
|
|
unsigned int x = a;
|
|
x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */
|
|
x >>= 31; /* 0: yes; 1: no */
|
|
x ^= 1; /* 1: yes; 0: no */
|
|
return x;
|
|
}
|
|
|
|
crypto_uint32 times19(crypto_uint32 a)
|
|
{
|
|
return (a << 4) + (a << 1) + a;
|
|
}
|
|
|
|
crypto_uint32 times38(crypto_uint32 a)
|
|
{
|
|
return (a << 5) + (a << 2) + (a << 1);
|
|
}
|
|
|
|
void reduce_add_sub(fe25519 *r)
|
|
{
|
|
crypto_uint32 t;
|
|
int i,rep;
|
|
|
|
for(rep=0;rep<4;rep++)
|
|
{
|
|
t = r->v[31] >> 7;
|
|
r->v[31] &= 127;
|
|
t = times19(t);
|
|
r->v[0] += t;
|
|
for(i=0;i<31;i++)
|
|
{
|
|
t = r->v[i] >> 8;
|
|
r->v[i+1] += t;
|
|
r->v[i] &= 255;
|
|
}
|
|
}
|
|
}
|
|
|
|
void reduce_mul(fe25519 *r)
|
|
{
|
|
crypto_uint32 t;
|
|
int i,rep;
|
|
|
|
for(rep=0;rep<2;rep++)
|
|
{
|
|
t = r->v[31] >> 7;
|
|
r->v[31] &= 127;
|
|
t = times19(t);
|
|
r->v[0] += t;
|
|
for(i=0;i<31;i++)
|
|
{
|
|
t = r->v[i] >> 8;
|
|
r->v[i+1] += t;
|
|
r->v[i] &= 255;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* reduction modulo 2^255-19 */
|
|
void fe25519_freeze(fe25519 *r)
|
|
{
|
|
int i;
|
|
crypto_uint32 m = equal(r->v[31],127);
|
|
for(i=30;i>0;i--)
|
|
m &= equal(r->v[i],255);
|
|
m &= ge(r->v[0],237);
|
|
|
|
m = -m;
|
|
|
|
r->v[31] -= m&127;
|
|
for(i=30;i>0;i--)
|
|
r->v[i] -= m&255;
|
|
r->v[0] -= m&237;
|
|
}
|
|
|
|
void fe25519_unpack(fe25519 *r, const unsigned char x[32])
|
|
{
|
|
int i;
|
|
for(i=0;i<32;i++) r->v[i] = x[i];
|
|
r->v[31] &= 127;
|
|
}
|
|
|
|
/* Assumes input x being reduced below 2^255 */
|
|
void fe25519_pack(unsigned char r[32], const fe25519 *x)
|
|
{
|
|
int i;
|
|
fe25519 y = *x;
|
|
fe25519_freeze(&y);
|
|
for(i=0;i<32;i++)
|
|
r[i] = y.v[i];
|
|
}
|
|
|
|
int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y)
|
|
{
|
|
int i;
|
|
fe25519 t1 = *x;
|
|
fe25519 t2 = *y;
|
|
fe25519_freeze(&t1);
|
|
fe25519_freeze(&t2);
|
|
for(i=0;i<32;i++)
|
|
if(t1.v[i] != t2.v[i]) return 0;
|
|
return 1;
|
|
}
|
|
|
|
void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b)
|
|
{
|
|
int i;
|
|
crypto_uint32 mask = b;
|
|
mask = -mask;
|
|
for(i=0;i<32;i++) r->v[i] ^= mask & (x->v[i] ^ r->v[i]);
|
|
}
|
|
|
|
unsigned char fe25519_getparity(const fe25519 *x)
|
|
{
|
|
fe25519 t = *x;
|
|
fe25519_freeze(&t);
|
|
return t.v[0] & 1;
|
|
}
|
|
|
|
void fe25519_setone(fe25519 *r)
|
|
{
|
|
int i;
|
|
r->v[0] = 1;
|
|
for(i=1;i<32;i++) r->v[i]=0;
|
|
}
|
|
|
|
void fe25519_setzero(fe25519 *r)
|
|
{
|
|
int i;
|
|
for(i=0;i<32;i++) r->v[i]=0;
|
|
}
|
|
|
|
void fe25519_neg(fe25519 *r, const fe25519 *x)
|
|
{
|
|
fe25519 t;
|
|
int i;
|
|
for(i=0;i<32;i++) t.v[i]=x->v[i];
|
|
fe25519_setzero(r);
|
|
fe25519_sub(r, r, &t);
|
|
}
|
|
|
|
void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y)
|
|
{
|
|
int i;
|
|
for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i];
|
|
reduce_add_sub(r);
|
|
}
|
|
|
|
void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y)
|
|
{
|
|
int i;
|
|
crypto_uint32 t[32];
|
|
t[0] = x->v[0] + 0x1da;
|
|
t[31] = x->v[31] + 0xfe;
|
|
for(i=1;i<31;i++) t[i] = x->v[i] + 0x1fe;
|
|
for(i=0;i<32;i++) r->v[i] = t[i] - y->v[i];
|
|
reduce_add_sub(r);
|
|
}
|
|
|
|
void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y)
|
|
{
|
|
int i,j;
|
|
crypto_uint32 t[63];
|
|
for(i=0;i<63;i++)t[i] = 0;
|
|
|
|
for(i=0;i<32;i++)
|
|
for(j=0;j<32;j++)
|
|
t[i+j] += x->v[i] * y->v[j];
|
|
|
|
for(i=32;i<63;i++)
|
|
r->v[i-32] = t[i-32] + times38(t[i]);
|
|
r->v[31] = t[31]; /* result now in r[0]...r[31] */
|
|
|
|
reduce_mul(r);
|
|
}
|
|
|
|
void fe25519_square(fe25519 *r, const fe25519 *x)
|
|
{
|
|
fe25519_mul(r, x, x);
|
|
}
|
|
|
|
void fe25519_invert(fe25519 *r, const fe25519 *x)
|
|
{
|
|
fe25519 z2;
|
|
fe25519 z9;
|
|
fe25519 z11;
|
|
fe25519 z2_5_0;
|
|
fe25519 z2_10_0;
|
|
fe25519 z2_20_0;
|
|
fe25519 z2_50_0;
|
|
fe25519 z2_100_0;
|
|
fe25519 t0;
|
|
fe25519 t1;
|
|
int i;
|
|
|
|
/* 2 */ fe25519_square(&z2,x);
|
|
/* 4 */ fe25519_square(&t1,&z2);
|
|
/* 8 */ fe25519_square(&t0,&t1);
|
|
/* 9 */ fe25519_mul(&z9,&t0,x);
|
|
/* 11 */ fe25519_mul(&z11,&z9,&z2);
|
|
/* 22 */ fe25519_square(&t0,&z11);
|
|
/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t0,&z9);
|
|
|
|
/* 2^6 - 2^1 */ fe25519_square(&t0,&z2_5_0);
|
|
/* 2^7 - 2^2 */ fe25519_square(&t1,&t0);
|
|
/* 2^8 - 2^3 */ fe25519_square(&t0,&t1);
|
|
/* 2^9 - 2^4 */ fe25519_square(&t1,&t0);
|
|
/* 2^10 - 2^5 */ fe25519_square(&t0,&t1);
|
|
/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t0,&z2_5_0);
|
|
|
|
/* 2^11 - 2^1 */ fe25519_square(&t0,&z2_10_0);
|
|
/* 2^12 - 2^2 */ fe25519_square(&t1,&t0);
|
|
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
|
|
/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t1,&z2_10_0);
|
|
|
|
/* 2^21 - 2^1 */ fe25519_square(&t0,&z2_20_0);
|
|
/* 2^22 - 2^2 */ fe25519_square(&t1,&t0);
|
|
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
|
|
/* 2^40 - 2^0 */ fe25519_mul(&t0,&t1,&z2_20_0);
|
|
|
|
/* 2^41 - 2^1 */ fe25519_square(&t1,&t0);
|
|
/* 2^42 - 2^2 */ fe25519_square(&t0,&t1);
|
|
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); }
|
|
/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0);
|
|
|
|
/* 2^51 - 2^1 */ fe25519_square(&t0,&z2_50_0);
|
|
/* 2^52 - 2^2 */ fe25519_square(&t1,&t0);
|
|
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
|
|
/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t1,&z2_50_0);
|
|
|
|
/* 2^101 - 2^1 */ fe25519_square(&t1,&z2_100_0);
|
|
/* 2^102 - 2^2 */ fe25519_square(&t0,&t1);
|
|
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); }
|
|
/* 2^200 - 2^0 */ fe25519_mul(&t1,&t0,&z2_100_0);
|
|
|
|
/* 2^201 - 2^1 */ fe25519_square(&t0,&t1);
|
|
/* 2^202 - 2^2 */ fe25519_square(&t1,&t0);
|
|
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
|
|
/* 2^250 - 2^0 */ fe25519_mul(&t0,&t1,&z2_50_0);
|
|
|
|
/* 2^251 - 2^1 */ fe25519_square(&t1,&t0);
|
|
/* 2^252 - 2^2 */ fe25519_square(&t0,&t1);
|
|
/* 2^253 - 2^3 */ fe25519_square(&t1,&t0);
|
|
/* 2^254 - 2^4 */ fe25519_square(&t0,&t1);
|
|
/* 2^255 - 2^5 */ fe25519_square(&t1,&t0);
|
|
/* 2^255 - 21 */ fe25519_mul(r,&t1,&z11);
|
|
}
|
|
|
|
void fe25519_pow2523(fe25519 *r, const fe25519 *x)
|
|
{
|
|
fe25519 z2;
|
|
fe25519 z9;
|
|
fe25519 z11;
|
|
fe25519 z2_5_0;
|
|
fe25519 z2_10_0;
|
|
fe25519 z2_20_0;
|
|
fe25519 z2_50_0;
|
|
fe25519 z2_100_0;
|
|
fe25519 t;
|
|
int i;
|
|
|
|
/* 2 */ fe25519_square(&z2,x);
|
|
/* 4 */ fe25519_square(&t,&z2);
|
|
/* 8 */ fe25519_square(&t,&t);
|
|
/* 9 */ fe25519_mul(&z9,&t,x);
|
|
/* 11 */ fe25519_mul(&z11,&z9,&z2);
|
|
/* 22 */ fe25519_square(&t,&z11);
|
|
/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t,&z9);
|
|
|
|
/* 2^6 - 2^1 */ fe25519_square(&t,&z2_5_0);
|
|
/* 2^10 - 2^5 */ for (i = 1;i < 5;i++) { fe25519_square(&t,&t); }
|
|
/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t,&z2_5_0);
|
|
|
|
/* 2^11 - 2^1 */ fe25519_square(&t,&z2_10_0);
|
|
/* 2^20 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); }
|
|
/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t,&z2_10_0);
|
|
|
|
/* 2^21 - 2^1 */ fe25519_square(&t,&z2_20_0);
|
|
/* 2^40 - 2^20 */ for (i = 1;i < 20;i++) { fe25519_square(&t,&t); }
|
|
/* 2^40 - 2^0 */ fe25519_mul(&t,&t,&z2_20_0);
|
|
|
|
/* 2^41 - 2^1 */ fe25519_square(&t,&t);
|
|
/* 2^50 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); }
|
|
/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t,&z2_10_0);
|
|
|
|
/* 2^51 - 2^1 */ fe25519_square(&t,&z2_50_0);
|
|
/* 2^100 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); }
|
|
/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t,&z2_50_0);
|
|
|
|
/* 2^101 - 2^1 */ fe25519_square(&t,&z2_100_0);
|
|
/* 2^200 - 2^100 */ for (i = 1;i < 100;i++) { fe25519_square(&t,&t); }
|
|
/* 2^200 - 2^0 */ fe25519_mul(&t,&t,&z2_100_0);
|
|
|
|
/* 2^201 - 2^1 */ fe25519_square(&t,&t);
|
|
/* 2^250 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); }
|
|
/* 2^250 - 2^0 */ fe25519_mul(&t,&t,&z2_50_0);
|
|
|
|
/* 2^251 - 2^1 */ fe25519_square(&t,&t);
|
|
/* 2^252 - 2^2 */ fe25519_square(&t,&t);
|
|
/* 2^252 - 3 */ fe25519_mul(r,&t,x);
|
|
}
|
|
|
|
static const crypto_uint32 m[32] = {0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, 0xDE, 0xF9, 0xDE, 0x14,
|
|
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10};
|
|
|
|
static const crypto_uint32 mu[33] = {0x1B, 0x13, 0x2C, 0x0A, 0xA3, 0xE5, 0x9C, 0xED, 0xA7, 0x29, 0x63, 0x08, 0x5D, 0x21, 0x06, 0x21,
|
|
0xEB, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0F};
|
|
|
|
crypto_uint32 lt(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
|
|
{
|
|
unsigned int x = a;
|
|
x -= (unsigned int) b; /* 0..65535: no; 4294901761..4294967295: yes */
|
|
x >>= 31; /* 0: no; 1: yes */
|
|
return x;
|
|
}
|
|
|
|
/* Reduce coefficients of r before calling reduce_add_sub */
|
|
void reduce_add_sub(sc25519 *r)
|
|
{
|
|
crypto_uint32 pb = 0;
|
|
crypto_uint32 b;
|
|
crypto_uint32 mask;
|
|
int i;
|
|
unsigned char t[32];
|
|
|
|
for(i=0;i<32;i++)
|
|
{
|
|
pb += m[i];
|
|
b = lt(r->v[i],pb);
|
|
t[i] = r->v[i]-pb+(b<<8);
|
|
pb = b;
|
|
}
|
|
mask = b - 1;
|
|
for(i=0;i<32;i++)
|
|
r->v[i] ^= mask & (r->v[i] ^ t[i]);
|
|
}
|
|
|
|
/* Reduce coefficients of x before calling barrett_reduce */
|
|
void barrett_reduce(sc25519 *r, const crypto_uint32 x[64])
|
|
{
|
|
/* See HAC, Alg. 14.42 */
|
|
int i,j;
|
|
crypto_uint32 q2[66];
|
|
crypto_uint32 *q3 = q2 + 33;
|
|
crypto_uint32 r1[33];
|
|
crypto_uint32 r2[33];
|
|
crypto_uint32 carry;
|
|
crypto_uint32 pb = 0;
|
|
crypto_uint32 b;
|
|
|
|
for (i = 0;i < 66;++i) q2[i] = 0;
|
|
for (i = 0;i < 33;++i) r2[i] = 0;
|
|
|
|
for(i=0;i<33;i++)
|
|
for(j=0;j<33;j++)
|
|
if(i+j >= 31) q2[i+j] += mu[i]*x[j+31];
|
|
carry = q2[31] >> 8;
|
|
q2[32] += carry;
|
|
carry = q2[32] >> 8;
|
|
q2[33] += carry;
|
|
|
|
for(i=0;i<33;i++)r1[i] = x[i];
|
|
for(i=0;i<32;i++)
|
|
for(j=0;j<33;j++)
|
|
if(i+j < 33) r2[i+j] += m[i]*q3[j];
|
|
|
|
for(i=0;i<32;i++)
|
|
{
|
|
carry = r2[i] >> 8;
|
|
r2[i+1] += carry;
|
|
r2[i] &= 0xff;
|
|
}
|
|
|
|
for(i=0;i<32;i++)
|
|
{
|
|
pb += r2[i];
|
|
b = lt(r1[i],pb);
|
|
r->v[i] = r1[i]-pb+(b<<8);
|
|
pb = b;
|
|
}
|
|
|
|
/* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3
|
|
* If so: Handle it here!
|
|
*/
|
|
|
|
reduce_add_sub(r);
|
|
reduce_add_sub(r);
|
|
}
|
|
|
|
void sc25519_from32bytes(sc25519 *r, const unsigned char x[32])
|
|
{
|
|
int i;
|
|
crypto_uint32 t[64];
|
|
for(i=0;i<32;i++) t[i] = x[i];
|
|
for(i=32;i<64;++i) t[i] = 0;
|
|
barrett_reduce(r, t);
|
|
}
|
|
|
|
void sc25519_from64bytes(sc25519 *r, const unsigned char x[64])
|
|
{
|
|
int i;
|
|
crypto_uint32 t[64];
|
|
for(i=0;i<64;i++) t[i] = x[i];
|
|
barrett_reduce(r, t);
|
|
}
|
|
|
|
void sc25519_to32bytes(unsigned char r[32], const sc25519 *x)
|
|
{
|
|
int i;
|
|
for(i=0;i<32;i++) r[i] = x->v[i];
|
|
}
|
|
|
|
void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y)
|
|
{
|
|
int i, carry;
|
|
for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i];
|
|
for(i=0;i<31;i++)
|
|
{
|
|
carry = r->v[i] >> 8;
|
|
r->v[i+1] += carry;
|
|
r->v[i] &= 0xff;
|
|
}
|
|
reduce_add_sub(r);
|
|
}
|
|
|
|
void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y)
|
|
{
|
|
int i,j,carry;
|
|
crypto_uint32 t[64];
|
|
for(i=0;i<64;i++)t[i] = 0;
|
|
|
|
for(i=0;i<32;i++)
|
|
for(j=0;j<32;j++)
|
|
t[i+j] += x->v[i] * y->v[j];
|
|
|
|
for(i=0;i<63;i++)
|
|
{
|
|
carry = t[i] >> 8;
|
|
t[i+1] += carry;
|
|
t[i] &= 0xff;
|
|
}
|
|
|
|
barrett_reduce(r, t);
|
|
}
|
|
|
|
void sc25519_window3(signed char r[85], const sc25519 *s)
|
|
{
|
|
char carry;
|
|
int i;
|
|
for(i=0;i<10;i++)
|
|
{
|
|
r[8*i+0] = s->v[3*i+0] & 7;
|
|
r[8*i+1] = (s->v[3*i+0] >> 3) & 7;
|
|
r[8*i+2] = (s->v[3*i+0] >> 6) & 7;
|
|
r[8*i+2] ^= (s->v[3*i+1] << 2) & 7;
|
|
r[8*i+3] = (s->v[3*i+1] >> 1) & 7;
|
|
r[8*i+4] = (s->v[3*i+1] >> 4) & 7;
|
|
r[8*i+5] = (s->v[3*i+1] >> 7) & 7;
|
|
r[8*i+5] ^= (s->v[3*i+2] << 1) & 7;
|
|
r[8*i+6] = (s->v[3*i+2] >> 2) & 7;
|
|
r[8*i+7] = (s->v[3*i+2] >> 5) & 7;
|
|
}
|
|
r[8*i+0] = s->v[3*i+0] & 7;
|
|
r[8*i+1] = (s->v[3*i+0] >> 3) & 7;
|
|
r[8*i+2] = (s->v[3*i+0] >> 6) & 7;
|
|
r[8*i+2] ^= (s->v[3*i+1] << 2) & 7;
|
|
r[8*i+3] = (s->v[3*i+1] >> 1) & 7;
|
|
r[8*i+4] = (s->v[3*i+1] >> 4) & 7;
|
|
|
|
/* Making it signed */
|
|
carry = 0;
|
|
for(i=0;i<84;i++)
|
|
{
|
|
r[i] += carry;
|
|
r[i+1] += r[i] >> 3;
|
|
r[i] &= 7;
|
|
carry = r[i] >> 2;
|
|
r[i] -= carry<<3;
|
|
}
|
|
r[84] += carry;
|
|
}
|
|
|
|
void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2)
|
|
{
|
|
int i;
|
|
for(i=0;i<31;i++)
|
|
{
|
|
r[4*i] = ( s1->v[i] & 3) ^ (( s2->v[i] & 3) << 2);
|
|
r[4*i+1] = ((s1->v[i] >> 2) & 3) ^ (((s2->v[i] >> 2) & 3) << 2);
|
|
r[4*i+2] = ((s1->v[i] >> 4) & 3) ^ (((s2->v[i] >> 4) & 3) << 2);
|
|
r[4*i+3] = ((s1->v[i] >> 6) & 3) ^ (((s2->v[i] >> 6) & 3) << 2);
|
|
}
|
|
r[124] = ( s1->v[31] & 3) ^ (( s2->v[31] & 3) << 2);
|
|
r[125] = ((s1->v[31] >> 2) & 3) ^ (((s2->v[31] >> 2) & 3) << 2);
|
|
r[126] = ((s1->v[31] >> 4) & 3) ^ (((s2->v[31] >> 4) & 3) << 2);
|
|
}
|
|
|
|
/* d */
|
|
static const fe25519 ge25519_ecd = {{0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00,
|
|
0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}};
|
|
/* 2*d */
|
|
static const fe25519 ge25519_ec2d = {{0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB, 0x56, 0xB1, 0x83, 0x82, 0x9A, 0x14, 0xE0, 0x00,
|
|
0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80, 0x8E, 0x19, 0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24}};
|
|
/* sqrt(-1) */
|
|
static const fe25519 ge25519_sqrtm1 = {{0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4, 0x78, 0xE4, 0x2F, 0xAD, 0x06, 0x18, 0x43, 0x2F,
|
|
0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00, 0x4D, 0x2B, 0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B}};
|
|
|
|
/* Packed coordinates of the base point */
|
|
static const ge25519 ge25519_base = {{{0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69,
|
|
0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}},
|
|
{{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
|
|
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}},
|
|
{{0x01, 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}},
|
|
{{0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20,
|
|
0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}}};
|
|
|
|
/* Multiples of the base point in affine representation */
|
|
static const ge25519_aff ge25519_base_multiples_affine[425] = {
|
|
{{{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, 0x00}},
|
|
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{{{0x87, 0xdd, 0xcf, 0xf0, 0x5b, 0x49, 0xa2, 0x5d, 0x40, 0x7a, 0x23, 0x26, 0xa4, 0x7a, 0x83, 0x8a, 0xb7, 0x8b, 0xd2, 0x1a, 0xbf, 0xea, 0x02, 0x24, 0x08, 0x5f, 0x7b, 0xa9, 0xb1, 0xbe, 0x9d, 0x37}} ,
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{{{0x0a, 0x34, 0xcd, 0x82, 0x3c, 0x33, 0x09, 0x54, 0xd2, 0x61, 0x39, 0x30, 0x9b, 0xfd, 0xef, 0x21, 0x26, 0xd4, 0x70, 0xfa, 0xee, 0xf9, 0x31, 0x33, 0x73, 0x84, 0xd0, 0xb3, 0x81, 0xbf, 0xec, 0x2e}} ,
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{{{0x68, 0x2b, 0x4a, 0x5b, 0xd5, 0xc7, 0x51, 0x91, 0x1d, 0xe1, 0x2a, 0x4b, 0xc4, 0x47, 0xf1, 0xbc, 0x7a, 0xb3, 0xcb, 0xc8, 0xb6, 0x7c, 0xac, 0x90, 0x05, 0xfd, 0xf3, 0xf9, 0x52, 0x3a, 0x11, 0x6b}} ,
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{{{0xf7, 0x17, 0x13, 0xbd, 0xfb, 0xbc, 0xd2, 0xec, 0x45, 0xb3, 0x15, 0x31, 0xe9, 0xaf, 0x82, 0x84, 0x3d, 0x28, 0xc6, 0xfc, 0x11, 0xf5, 0x41, 0xb5, 0x8b, 0xd3, 0x12, 0x76, 0x52, 0xe7, 0x1a, 0x3c}} ,
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{{{0xde, 0xc9, 0xb1, 0x31, 0x10, 0x16, 0xaa, 0x35, 0x14, 0x6a, 0xd4, 0xb5, 0x34, 0x82, 0x71, 0xd2, 0x4a, 0x5d, 0x9a, 0x1f, 0x53, 0x26, 0x3c, 0xe5, 0x8e, 0x8d, 0x33, 0x7f, 0xff, 0xa9, 0xd5, 0x17}} ,
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{{{0x64, 0x1d, 0x49, 0x13, 0x2f, 0x71, 0xec, 0x69, 0x87, 0xd0, 0x42, 0xee, 0x13, 0xec, 0xe3, 0xed, 0x56, 0x7b, 0xbf, 0xbd, 0x8c, 0x2f, 0x7d, 0x7b, 0x9d, 0x28, 0xec, 0x8e, 0x76, 0x2f, 0x6f, 0x08}} ,
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{{{0x8a, 0x4b, 0xe7, 0x38, 0xbc, 0xda, 0xc2, 0xb0, 0x85, 0xe1, 0x4a, 0xfe, 0x2d, 0x44, 0x84, 0xcb, 0x20, 0x6b, 0x2d, 0xbf, 0x11, 0x9c, 0xd7, 0xbe, 0xd3, 0x3e, 0x5f, 0xbf, 0x68, 0xbc, 0xa8, 0x07}} ,
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{{{0x02, 0xff, 0x32, 0x2b, 0x5c, 0x93, 0x54, 0x32, 0xe8, 0x57, 0x54, 0x1a, 0x8b, 0x33, 0x60, 0x65, 0xd3, 0x67, 0xa4, 0xc1, 0x26, 0xc4, 0xa4, 0x34, 0x1f, 0x9b, 0xa7, 0xa9, 0xf4, 0xd9, 0x4f, 0x5b}} ,
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{{{0x65, 0xa5, 0x11, 0x84, 0x8a, 0x67, 0x9d, 0x9e, 0xd1, 0x44, 0x68, 0x7a, 0x34, 0xe1, 0x9f, 0xa3, 0x54, 0xcd, 0x07, 0xca, 0x79, 0x1f, 0x54, 0x2f, 0x13, 0x70, 0x4e, 0xee, 0xa2, 0xfa, 0xe7, 0x5d}} ,
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{{{0xa7, 0xd6, 0x2e, 0xd5, 0xcc, 0xd4, 0xcb, 0x5a, 0x3b, 0xa7, 0xf9, 0x46, 0x03, 0x1d, 0xad, 0x2b, 0x34, 0x31, 0x90, 0x00, 0x46, 0x08, 0x82, 0x14, 0xc4, 0xe0, 0x9c, 0xf0, 0xe3, 0x55, 0x43, 0x31}} ,
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{{{0x87, 0xee, 0xa6, 0x56, 0x9e, 0xc2, 0x9a, 0x56, 0x24, 0x42, 0x85, 0x4d, 0x98, 0x31, 0x1e, 0x60, 0x4d, 0x87, 0x85, 0x04, 0xae, 0x46, 0x12, 0xf9, 0x8e, 0x7f, 0xe4, 0x7f, 0xf6, 0x1c, 0x37, 0x01}} ,
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{{{0x72, 0xd3, 0xae, 0xa6, 0xca, 0x8f, 0xcd, 0xcc, 0x78, 0x8e, 0x19, 0x4d, 0xa7, 0xd2, 0x27, 0xe9, 0xa4, 0x3c, 0x16, 0x5b, 0x84, 0x80, 0xf9, 0xd0, 0xcc, 0x6a, 0x1e, 0xca, 0x1e, 0x67, 0xbd, 0x63}} ,
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{{{0x3f, 0x75, 0x8e, 0xb4, 0xff, 0xd8, 0xdd, 0xd6, 0x37, 0x57, 0x9d, 0x6d, 0x3b, 0xbd, 0xd5, 0x60, 0x88, 0x65, 0x9a, 0xb9, 0x4a, 0x68, 0x84, 0xa2, 0x67, 0xdd, 0x17, 0x25, 0x97, 0x04, 0x8b, 0x5e}} ,
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{{{0x20, 0xa8, 0x88, 0xe3, 0x91, 0xc0, 0x6e, 0xbb, 0x8a, 0x27, 0x82, 0x51, 0x83, 0xb2, 0x28, 0xa9, 0x83, 0xeb, 0xa6, 0xa9, 0x4d, 0x17, 0x59, 0x22, 0x54, 0x00, 0x50, 0x45, 0xcb, 0x48, 0x4b, 0x18}} ,
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{{{0x34, 0x5c, 0x13, 0xfb, 0xc0, 0xe3, 0x78, 0x2b, 0x54, 0x58, 0x22, 0x9b, 0x76, 0x81, 0x7f, 0x93, 0x9c, 0x25, 0x3c, 0xd2, 0xe9, 0x96, 0x21, 0x26, 0x08, 0xf5, 0xed, 0x95, 0x11, 0xae, 0x04, 0x5a}} ,
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{{{0xb3, 0x40, 0x29, 0xd1, 0xcb, 0x1b, 0x08, 0x9e, 0x9c, 0xb7, 0x53, 0xb9, 0x3b, 0x71, 0x08, 0x95, 0x12, 0x1a, 0x58, 0xaf, 0x7e, 0x82, 0x52, 0x43, 0x4f, 0x11, 0x39, 0xf4, 0x93, 0x1a, 0x26, 0x05}} ,
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{{{0x3e, 0xa8, 0x38, 0xc2, 0x57, 0x56, 0x42, 0x9a, 0xb1, 0xe2, 0xf8, 0x45, 0xaa, 0x11, 0x48, 0x5f, 0x17, 0xc4, 0x54, 0x27, 0xdc, 0x5d, 0xaa, 0xdd, 0x41, 0xbc, 0xdf, 0x81, 0xb9, 0x53, 0xee, 0x52}} ,
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{{{0x25, 0x24, 0x1d, 0x8a, 0x67, 0x20, 0xee, 0x42, 0xeb, 0x38, 0xed, 0x0b, 0x8b, 0xcd, 0x46, 0x9d, 0x5e, 0x6b, 0x1e, 0x24, 0x9d, 0x12, 0x05, 0x1a, 0xcc, 0x05, 0x4e, 0x92, 0x38, 0xe1, 0x1f, 0x50}} ,
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{{0x4e, 0xee, 0x1c, 0x91, 0xe6, 0x11, 0xbd, 0x8e, 0x55, 0x1a, 0x18, 0x75, 0x66, 0xaf, 0x4d, 0x7b, 0x0f, 0xae, 0x6d, 0x85, 0xca, 0x82, 0x58, 0x21, 0x9c, 0x18, 0xe0, 0xed, 0xec, 0x22, 0x80, 0x2f}}},
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{{{0x68, 0x3b, 0x0a, 0x39, 0x1d, 0x6a, 0x15, 0x57, 0xfc, 0xf0, 0x63, 0x54, 0xdb, 0x39, 0xdb, 0xe8, 0x5c, 0x64, 0xff, 0xa0, 0x09, 0x4f, 0x3b, 0xb7, 0x32, 0x60, 0x99, 0x94, 0xfd, 0x94, 0x82, 0x2d}} ,
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{{{0x78, 0x52, 0x87, 0xc9, 0x97, 0x63, 0xb1, 0xdd, 0x54, 0x5f, 0xc1, 0xf8, 0xf1, 0x06, 0xa6, 0xa8, 0xa3, 0x88, 0x82, 0xd4, 0xcb, 0xa6, 0x19, 0xdd, 0xd1, 0x11, 0x87, 0x08, 0x17, 0x4c, 0x37, 0x2a}} ,
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{{{0x1d, 0xda, 0xe4, 0x61, 0x03, 0x50, 0xa9, 0x8b, 0x68, 0x18, 0xef, 0xb2, 0x1c, 0x84, 0x3b, 0xa2, 0x44, 0x95, 0xa3, 0x04, 0x3b, 0xd6, 0x99, 0x00, 0xaf, 0x76, 0x42, 0x67, 0x02, 0x7d, 0x85, 0x56}} ,
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{{{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, 0x00}},
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{{{0x52, 0xfd, 0x04, 0xc5, 0xfb, 0x99, 0xe7, 0xe8, 0xfb, 0x8c, 0xe1, 0x42, 0x03, 0xef, 0x9d, 0xd9, 0x9e, 0x4d, 0xf7, 0x80, 0xcf, 0x2e, 0xcc, 0x9b, 0x45, 0xc9, 0x7b, 0x7a, 0xbc, 0x37, 0xa8, 0x52}} ,
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{{{0x53, 0xcd, 0xf3, 0x86, 0x40, 0xe6, 0x39, 0x42, 0x95, 0xd6, 0xcb, 0x45, 0x1a, 0x20, 0xc8, 0x45, 0x4b, 0x32, 0x69, 0x04, 0xb1, 0xaf, 0x20, 0x46, 0xc7, 0x6b, 0x23, 0x5b, 0x69, 0xee, 0x30, 0x3f}} ,
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{{{0xca, 0xfc, 0x88, 0x6b, 0x96, 0x78, 0x0a, 0x8b, 0x83, 0xdc, 0xbc, 0xaf, 0x40, 0xb6, 0x8d, 0x7f, 0xef, 0xb4, 0xd1, 0x3f, 0xcc, 0xa2, 0x74, 0xc9, 0xc2, 0x92, 0x55, 0x00, 0xab, 0xdb, 0xbf, 0x4f}} ,
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{{0x93, 0x1c, 0x06, 0x2d, 0x66, 0x65, 0x02, 0xa4, 0x97, 0x18, 0xfd, 0x00, 0xe7, 0xab, 0x03, 0xec, 0xce, 0xc1, 0xbf, 0x37, 0xf8, 0x13, 0x53, 0xa5, 0xe5, 0x0c, 0x3a, 0xa8, 0x55, 0xb9, 0xff, 0x68}}},
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{{{0xe4, 0xe6, 0x6d, 0x30, 0x7d, 0x30, 0x35, 0xc2, 0x78, 0x87, 0xf9, 0xfc, 0x6b, 0x5a, 0xc3, 0xb7, 0x65, 0xd8, 0x2e, 0xc7, 0xa5, 0x0c, 0xc6, 0xdc, 0x12, 0xaa, 0xd6, 0x4f, 0xc5, 0x38, 0xbc, 0x0e}} ,
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{{{0xa9, 0x62, 0x93, 0x85, 0xbe, 0xe8, 0x73, 0x4a, 0x0e, 0xb0, 0xb5, 0x2d, 0x94, 0x50, 0xaa, 0xd3, 0xb2, 0xea, 0x9d, 0x62, 0x76, 0x3b, 0x07, 0x34, 0x4e, 0x2d, 0x70, 0xc8, 0x9a, 0x15, 0x66, 0x6b}} ,
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{{{0x22, 0xd6, 0xb5, 0x17, 0x84, 0xbf, 0x12, 0xcc, 0x23, 0x14, 0x4a, 0xdf, 0x14, 0x31, 0xbc, 0xa1, 0xac, 0x6e, 0xab, 0xfa, 0x57, 0x11, 0x53, 0xb3, 0x27, 0xe6, 0xf9, 0x47, 0x33, 0x44, 0x34, 0x1e}} ,
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{{{0x56, 0xe1, 0xf5, 0xf1, 0xd5, 0xab, 0xa8, 0x2b, 0xae, 0x89, 0xf3, 0xcf, 0x56, 0x9f, 0xf2, 0x4b, 0x31, 0xbc, 0x18, 0xa9, 0x06, 0x5b, 0xbe, 0xb4, 0x61, 0xf8, 0xb2, 0x06, 0x9c, 0x81, 0xab, 0x4c}} ,
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{{{0x41, 0x97, 0xbf, 0x71, 0x6a, 0x9b, 0x72, 0xec, 0xf3, 0xf8, 0x6b, 0xe6, 0x0e, 0x6c, 0x69, 0xa5, 0x2f, 0x68, 0x52, 0xd8, 0x61, 0x81, 0xc0, 0x63, 0x3f, 0xa6, 0x3c, 0x13, 0x90, 0xe6, 0x8d, 0x56}} ,
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{{{0x85, 0x57, 0x9f, 0xb5, 0xc8, 0x06, 0xb2, 0x9f, 0x47, 0x3f, 0xf0, 0xfa, 0xe6, 0xa9, 0xb1, 0x9b, 0x6f, 0x96, 0x7d, 0xf9, 0xa4, 0x65, 0x09, 0x75, 0x32, 0xa6, 0x6c, 0x7f, 0x47, 0x4b, 0x2f, 0x4f}} ,
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{{{0xda, 0x03, 0x34, 0x66, 0xc4, 0x0c, 0x73, 0x6e, 0xbc, 0x24, 0xb5, 0xf9, 0x70, 0x81, 0x52, 0xe9, 0xf4, 0x7c, 0x23, 0xdd, 0x9f, 0xb8, 0x46, 0xef, 0x1d, 0x22, 0x55, 0x7d, 0x71, 0xc4, 0x42, 0x33}} ,
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{{{0x9a, 0x4d, 0x42, 0x29, 0x5d, 0xa4, 0x6b, 0x6f, 0xa8, 0x8a, 0x4d, 0x91, 0x7b, 0xd2, 0xdf, 0x36, 0xef, 0x01, 0x22, 0xc5, 0xcc, 0x8d, 0xeb, 0x58, 0x3d, 0xb3, 0x50, 0xfc, 0x8b, 0x97, 0x96, 0x33}} ,
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{{{0x45, 0xb8, 0x41, 0xd7, 0xab, 0x07, 0x15, 0x00, 0x8e, 0xce, 0xdf, 0xb2, 0x43, 0x5c, 0x01, 0xdc, 0xf4, 0x01, 0x51, 0x95, 0x10, 0x5a, 0xf6, 0x24, 0x24, 0xa0, 0x19, 0x3a, 0x09, 0x2a, 0xaa, 0x3f}} ,
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{{{0x89, 0xef, 0xbf, 0x03, 0x75, 0xd0, 0x29, 0x50, 0xcb, 0x7d, 0xd6, 0xbe, 0xad, 0x5f, 0x7b, 0x00, 0x32, 0xaa, 0x98, 0xed, 0x3f, 0x8f, 0x92, 0xcb, 0x81, 0x56, 0x01, 0x63, 0x64, 0xa3, 0x38, 0x39}} ,
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{{{0xc0, 0xd7, 0x56, 0x97, 0x58, 0x91, 0xde, 0x09, 0x4f, 0x9f, 0xbe, 0x63, 0xb0, 0x83, 0x86, 0x43, 0x5d, 0xbc, 0xe0, 0xf3, 0xc0, 0x75, 0xbf, 0x8b, 0x8e, 0xaa, 0xf7, 0x8b, 0x64, 0x6e, 0xb0, 0x63}} ,
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{{{0xbd, 0xaa, 0x13, 0xe6, 0xcd, 0x45, 0x4a, 0xa4, 0x59, 0x0a, 0x64, 0xb1, 0x98, 0xd6, 0x34, 0x13, 0x04, 0xe6, 0x97, 0x94, 0x06, 0xcb, 0xd4, 0x4e, 0xbb, 0x96, 0xcd, 0xd1, 0x57, 0xd1, 0xe3, 0x06}} ,
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{{{0x93, 0x03, 0x36, 0x81, 0xac, 0xe4, 0x20, 0x09, 0x35, 0x4c, 0x45, 0xb2, 0x1e, 0x4c, 0x14, 0x21, 0xe6, 0xe9, 0x8a, 0x7b, 0x8d, 0xfe, 0x1e, 0xc6, 0x3e, 0xc1, 0x35, 0xfa, 0xe7, 0x70, 0x4e, 0x1d}} ,
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{{{0x85, 0xe0, 0x24, 0x32, 0xb4, 0xd1, 0xef, 0xfc, 0x69, 0xa2, 0xbf, 0x8f, 0x72, 0x2c, 0x95, 0xf6, 0xe4, 0x6e, 0x7d, 0x90, 0xf7, 0x57, 0x81, 0xa0, 0xf7, 0xda, 0xef, 0x33, 0x07, 0xe3, 0x6b, 0x78}} ,
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{{{0x13, 0xaa, 0x2e, 0x4c, 0xf0, 0x22, 0xb8, 0x6c, 0xb3, 0x19, 0x4d, 0xeb, 0x6b, 0xd0, 0xa4, 0xc6, 0x9c, 0xdd, 0xc8, 0x5b, 0x81, 0x57, 0x89, 0xdf, 0x33, 0xa9, 0x68, 0x49, 0x80, 0xe4, 0xfe, 0x21}} ,
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{{{0x34, 0x75, 0x37, 0x1f, 0x34, 0x4e, 0xa9, 0x1d, 0x68, 0x67, 0xf8, 0x49, 0x98, 0x96, 0xfc, 0x4c, 0x65, 0x97, 0xf7, 0x02, 0x4a, 0x52, 0x6c, 0x01, 0xbd, 0x48, 0xbb, 0x1b, 0xed, 0xa4, 0xe2, 0x53}} ,
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{{0x59, 0xd5, 0x9b, 0x5a, 0xa2, 0x90, 0xd3, 0xb8, 0x37, 0x4c, 0x55, 0x82, 0x28, 0x08, 0x0f, 0x7f, 0xaa, 0x81, 0x65, 0xe0, 0x0c, 0x52, 0xc9, 0xa3, 0x32, 0x27, 0x64, 0xda, 0xfd, 0x34, 0x23, 0x5a}}},
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{{{0xb5, 0xb0, 0x0c, 0x4d, 0xb3, 0x7b, 0x23, 0xc8, 0x1f, 0x8a, 0x39, 0x66, 0xe6, 0xba, 0x4c, 0x10, 0x37, 0xca, 0x9c, 0x7c, 0x05, 0x9e, 0xff, 0xc0, 0xf8, 0x8e, 0xb1, 0x8f, 0x6f, 0x67, 0x18, 0x26}} ,
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{{{0xa4, 0x29, 0x47, 0x86, 0x2e, 0x92, 0x4f, 0x11, 0x4f, 0xf3, 0xb2, 0x5c, 0xd5, 0x3e, 0xa6, 0xb9, 0xc8, 0xe2, 0x33, 0x11, 0x1f, 0x01, 0x8f, 0xb0, 0x9b, 0xc7, 0xa5, 0xff, 0x83, 0x0f, 0x1e, 0x28}} ,
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{{{0x0a, 0x6c, 0x4f, 0xbc, 0x3e, 0x32, 0xe7, 0x4a, 0x1a, 0x13, 0xc1, 0x49, 0x38, 0xbf, 0xf7, 0xc2, 0xd3, 0x8f, 0x6b, 0xad, 0x52, 0xf7, 0xcf, 0xbc, 0x27, 0xcb, 0x40, 0x67, 0x76, 0xcd, 0x6d, 0x56}} ,
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{{{0xe7, 0xc4, 0x43, 0x4d, 0xc9, 0x2b, 0x69, 0x5d, 0x1d, 0x3c, 0xaf, 0xbb, 0x43, 0x38, 0x4e, 0x98, 0x3d, 0xed, 0x0d, 0x21, 0x03, 0xfd, 0xf0, 0x99, 0x47, 0x04, 0xb0, 0x98, 0x69, 0x55, 0x72, 0x0f}} ,
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{{{0x1b, 0x37, 0x47, 0xe3, 0xf5, 0x9e, 0xea, 0x2c, 0x2a, 0xe7, 0x82, 0x36, 0xf4, 0x1f, 0x81, 0x47, 0x92, 0x4b, 0x69, 0x0e, 0x11, 0x8c, 0x5d, 0x53, 0x5b, 0x81, 0x27, 0x08, 0xbc, 0xa0, 0xae, 0x25}} ,
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{{{0xfc, 0xf9, 0x21, 0x4f, 0x2e, 0x76, 0x9b, 0x1f, 0x28, 0x60, 0x77, 0x43, 0x32, 0x9d, 0xbe, 0x17, 0x30, 0x2a, 0xc6, 0x18, 0x92, 0x66, 0x62, 0x30, 0x98, 0x40, 0x11, 0xa6, 0x7f, 0x18, 0x84, 0x28}} ,
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{{{0xe9, 0x9f, 0xdc, 0x3f, 0xc1, 0x89, 0x44, 0x74, 0x27, 0xe4, 0xc1, 0x90, 0xff, 0x4a, 0xa7, 0x3c, 0xee, 0xcd, 0xf4, 0x1d, 0x25, 0x94, 0x7f, 0x63, 0x16, 0x48, 0xbc, 0x64, 0xfe, 0x95, 0xc4, 0x0c}} ,
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{{{0xfa, 0x94, 0xf7, 0x40, 0xd0, 0xd7, 0xeb, 0xa9, 0x82, 0x36, 0xd5, 0x15, 0xb9, 0x33, 0x7a, 0xbf, 0x8a, 0xf2, 0x63, 0xaa, 0x37, 0xf5, 0x59, 0xac, 0xbd, 0xbb, 0x32, 0x36, 0xbe, 0x73, 0x99, 0x38}} ,
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{{0x2c, 0xb3, 0xda, 0x7a, 0xd8, 0x3d, 0x99, 0xca, 0xd2, 0xf4, 0xda, 0x99, 0x8e, 0x4f, 0x98, 0xb7, 0xf4, 0xae, 0x3e, 0x9f, 0x8e, 0x35, 0x60, 0xa4, 0x33, 0x75, 0xa4, 0x04, 0x93, 0xb1, 0x6b, 0x4d}}},
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{{{0x97, 0x9d, 0xa8, 0xcd, 0x97, 0x7b, 0x9d, 0xb9, 0xe7, 0xa5, 0xef, 0xfd, 0xa8, 0x42, 0x6b, 0xc3, 0x62, 0x64, 0x7d, 0xa5, 0x1b, 0xc9, 0x9e, 0xd2, 0x45, 0xb9, 0xee, 0x03, 0xb0, 0xbf, 0xc0, 0x68}} ,
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{{{0x54, 0x83, 0x02, 0x18, 0x82, 0x93, 0x99, 0x07, 0xd0, 0xa7, 0xda, 0xd8, 0x75, 0x89, 0xfa, 0xf2, 0xd9, 0xa3, 0xb8, 0x6b, 0x5a, 0x35, 0x28, 0xd2, 0x6b, 0x59, 0xc2, 0xf8, 0x45, 0xe2, 0xbc, 0x06}} ,
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{{{0xf7, 0xd4, 0x16, 0x6c, 0x4e, 0x95, 0x9d, 0x5d, 0x0f, 0x91, 0x2b, 0x52, 0xfe, 0x5c, 0x34, 0xe5, 0x30, 0xe6, 0xa4, 0x3b, 0xf3, 0xf3, 0x34, 0x08, 0xa9, 0x4a, 0xa0, 0xb5, 0x6e, 0xb3, 0x09, 0x0a}} ,
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{{{0x4d, 0x4a, 0xd7, 0x98, 0x71, 0x57, 0xac, 0x7d, 0x8b, 0x37, 0xbd, 0x63, 0xff, 0x87, 0xb1, 0x49, 0x95, 0x20, 0x7c, 0xcf, 0x7c, 0x59, 0xc4, 0x91, 0x9c, 0xef, 0xd0, 0xdb, 0x60, 0x09, 0x9d, 0x46}} ,
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{{{0x2a, 0x36, 0x68, 0xfc, 0x5f, 0xb6, 0x4f, 0xa5, 0xe3, 0x9d, 0x24, 0x2f, 0xc0, 0x93, 0x61, 0xcf, 0xf8, 0x0a, 0xed, 0xe1, 0xdb, 0x27, 0xec, 0x0e, 0x14, 0x32, 0x5f, 0x8e, 0xa1, 0x62, 0x41, 0x16}} ,
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{{{0x92, 0x67, 0x77, 0x56, 0xa1, 0xff, 0xc4, 0xc5, 0x95, 0xf0, 0xe3, 0x3a, 0x0a, 0xca, 0x94, 0x4d, 0x9e, 0x7e, 0x3d, 0xb9, 0x6e, 0xb6, 0xb0, 0xce, 0xa4, 0x30, 0x89, 0x99, 0xe9, 0xad, 0x11, 0x59}} ,
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{{{0x32, 0x99, 0x93, 0xd1, 0x9a, 0x72, 0xf3, 0xa9, 0x16, 0xbd, 0xb4, 0x4c, 0xdd, 0xf9, 0xd4, 0xb2, 0x64, 0x9a, 0xd3, 0x05, 0xe4, 0xa3, 0x73, 0x1c, 0xcb, 0x7e, 0x57, 0x67, 0xff, 0x04, 0xb3, 0x10}} ,
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{{0xb9, 0x4b, 0xa4, 0xad, 0xd0, 0x6d, 0x61, 0x23, 0xb4, 0xaf, 0x34, 0xa9, 0xaa, 0x65, 0xec, 0xd9, 0x69, 0xe3, 0x85, 0xcd, 0xcc, 0xe7, 0xb0, 0x9b, 0x41, 0xc1, 0x1c, 0xf9, 0xa0, 0xfa, 0xb7, 0x13}}},
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{{{0x04, 0xfd, 0x88, 0x3c, 0x0c, 0xd0, 0x09, 0x52, 0x51, 0x4f, 0x06, 0x19, 0xcc, 0xc3, 0xbb, 0xde, 0x80, 0xc5, 0x33, 0xbc, 0xf9, 0xf3, 0x17, 0x36, 0xdd, 0xc6, 0xde, 0xe8, 0x9b, 0x5d, 0x79, 0x1b}} ,
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{{{0x4f, 0x00, 0xb2, 0x66, 0x55, 0xed, 0x4a, 0xed, 0x8d, 0xe1, 0x66, 0x18, 0xb2, 0x14, 0x74, 0x8d, 0xfd, 0x1a, 0x36, 0x0f, 0x26, 0x5c, 0x8b, 0x89, 0xf3, 0xab, 0xf2, 0xf3, 0x24, 0x67, 0xfd, 0x70}} ,
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{{{0xeb, 0xcb, 0xc5, 0x70, 0x91, 0x31, 0x10, 0x93, 0x0d, 0xc8, 0xd0, 0xef, 0x62, 0xe8, 0x6f, 0x82, 0xe3, 0x69, 0x3d, 0x91, 0x7f, 0x31, 0xe1, 0x26, 0x35, 0x3c, 0x4a, 0x2f, 0xab, 0xc4, 0x9a, 0x5e}} ,
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{{{0xf6, 0xdb, 0x0d, 0x22, 0x3d, 0xb5, 0x14, 0x75, 0x31, 0xf0, 0x81, 0xe2, 0xb9, 0x37, 0xa2, 0xa9, 0x84, 0x11, 0x9a, 0x07, 0xb5, 0x53, 0x89, 0x78, 0xa9, 0x30, 0x27, 0xa1, 0xf1, 0x4e, 0x5c, 0x2e}} ,
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{{{0xe9, 0xc3, 0xbc, 0x7b, 0x5c, 0xfc, 0xb2, 0xf9, 0xc9, 0x2f, 0xe5, 0xba, 0x3a, 0x0b, 0xab, 0x64, 0x38, 0x6f, 0x5b, 0x4b, 0x93, 0xda, 0x64, 0xec, 0x4d, 0x3d, 0xa0, 0xf5, 0xbb, 0xba, 0x47, 0x48}} ,
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{{{0x96, 0x88, 0xa6, 0xab, 0x8f, 0xe3, 0x3a, 0x49, 0xf8, 0xfe, 0x34, 0xe7, 0x6a, 0xb2, 0xfe, 0x40, 0x26, 0x74, 0x57, 0x4c, 0xf6, 0xd4, 0x99, 0xce, 0x5d, 0x7b, 0x2f, 0x67, 0xd6, 0x5a, 0xe4, 0x4e}} ,
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{{{0xdb, 0xfa, 0x9b, 0x2c, 0xd4, 0x23, 0x67, 0x2c, 0x8a, 0x63, 0x6c, 0x07, 0x26, 0x48, 0x4f, 0xc2, 0x03, 0xd2, 0x53, 0x20, 0x28, 0xed, 0x65, 0x71, 0x47, 0xa9, 0x16, 0x16, 0x12, 0xbc, 0x28, 0x33}} ,
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{{{0x86, 0xe6, 0x8c, 0x1d, 0xdf, 0xca, 0xfc, 0xd5, 0xf8, 0x3a, 0xc3, 0x44, 0x72, 0xe6, 0x78, 0x9d, 0x2b, 0x97, 0xf8, 0x28, 0x45, 0xb4, 0x20, 0xc9, 0x2a, 0x8c, 0x67, 0xaa, 0x11, 0xc5, 0x5b, 0x2f}} ,
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{{{0x33, 0xa7, 0x90, 0x7c, 0xc3, 0x6f, 0x17, 0xa5, 0xa0, 0x67, 0x72, 0x17, 0xea, 0x7e, 0x63, 0x14, 0x83, 0xde, 0xc1, 0x71, 0x2d, 0x41, 0x32, 0x7a, 0xf3, 0xd1, 0x2b, 0xd8, 0x2a, 0xa6, 0x46, 0x36}} ,
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{{{0x9c, 0xb2, 0x61, 0x0a, 0x98, 0x2a, 0xa5, 0xd7, 0xee, 0xa9, 0xac, 0x65, 0xcb, 0x0a, 0x1e, 0xe2, 0xbe, 0xdc, 0x85, 0x59, 0x0f, 0x9c, 0xa6, 0x57, 0x34, 0xa5, 0x87, 0xeb, 0x7b, 0x1e, 0x0c, 0x3c}} ,
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{{{0x0a, 0x67, 0x90, 0x6d, 0x0c, 0x4c, 0xcc, 0xc0, 0xe6, 0xbd, 0xa7, 0x5e, 0x55, 0x8c, 0xcd, 0x58, 0x9b, 0x11, 0xa2, 0xbb, 0x4b, 0xb1, 0x43, 0x04, 0x3c, 0x55, 0xed, 0x23, 0xfe, 0xcd, 0xb1, 0x53}} ,
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{{{0x0d, 0x88, 0x1a, 0x90, 0x7e, 0xdc, 0xd8, 0xfe, 0xc1, 0x2f, 0x5d, 0x67, 0xee, 0x67, 0x2f, 0xed, 0x6f, 0x55, 0x43, 0x5f, 0x87, 0x14, 0x35, 0x42, 0xd3, 0x75, 0xae, 0xd5, 0xd3, 0x85, 0x1a, 0x76}} ,
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{{{0x98, 0x83, 0xc2, 0x37, 0xa0, 0x41, 0xa8, 0x48, 0x5c, 0x5f, 0xbf, 0xc8, 0xfa, 0x24, 0xe0, 0x59, 0x2c, 0xbd, 0xf6, 0x81, 0x7e, 0x88, 0xe6, 0xca, 0x04, 0xd8, 0x5d, 0x60, 0xbb, 0x74, 0xa7, 0x0b}} ,
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{{{0x48, 0xd5, 0x39, 0x4a, 0x0b, 0x20, 0x6a, 0x43, 0xa0, 0x07, 0x82, 0x5e, 0x49, 0x7c, 0xc9, 0x47, 0xf1, 0x7c, 0x37, 0xb9, 0x23, 0xef, 0x6b, 0x46, 0x45, 0x8c, 0x45, 0x76, 0xdf, 0x14, 0x6b, 0x6e}} ,
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{{{0x4c, 0x6f, 0xfe, 0x6b, 0x0c, 0x62, 0xd7, 0x48, 0x71, 0xef, 0xb1, 0x85, 0x79, 0xc0, 0xed, 0x24, 0xb1, 0x08, 0x93, 0x76, 0x8e, 0xf7, 0x38, 0x8e, 0xeb, 0xfe, 0x80, 0x40, 0xaf, 0x90, 0x64, 0x49}} ,
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{{{0x3d, 0x81, 0xf0, 0xeb, 0x16, 0xfd, 0x58, 0x33, 0x8d, 0x7c, 0x1a, 0xfb, 0x20, 0x2c, 0x8a, 0xee, 0x90, 0xbb, 0x33, 0x6d, 0x45, 0xe9, 0x8e, 0x99, 0x85, 0xe1, 0x08, 0x1f, 0xc5, 0xf1, 0xb5, 0x46}} ,
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{{{0xe0, 0x67, 0xe9, 0x7b, 0xdb, 0x96, 0x5c, 0xb0, 0x32, 0xd0, 0x59, 0x31, 0x90, 0xdc, 0x92, 0x97, 0xac, 0x09, 0x38, 0x31, 0x0f, 0x7e, 0xd6, 0x5d, 0xd0, 0x06, 0xb6, 0x1f, 0xea, 0xf0, 0x5b, 0x07}} ,
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{{{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, 0x00}},
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{{{0x4c, 0xb6, 0x69, 0xc8, 0x81, 0x95, 0x94, 0x33, 0x92, 0x34, 0xe9, 0x3c, 0x84, 0x0d, 0x3d, 0x5a, 0x37, 0x9c, 0x22, 0xa0, 0xaa, 0x65, 0xce, 0xb4, 0xc2, 0x2d, 0x66, 0x67, 0x02, 0xff, 0x74, 0x10}} ,
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{{0x22, 0xb0, 0xd5, 0xe6, 0xc7, 0xef, 0xb1, 0xa7, 0x13, 0xda, 0x60, 0xb4, 0x80, 0xc1, 0x42, 0x7d, 0x10, 0x70, 0x97, 0x04, 0x4d, 0xda, 0x23, 0x89, 0xc2, 0x0e, 0x68, 0xcb, 0xde, 0xe0, 0x9b, 0x29}}},
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{{{0x33, 0xfe, 0x42, 0x2a, 0x36, 0x2b, 0x2e, 0x36, 0x64, 0x5c, 0x8b, 0xcc, 0x81, 0x6a, 0x15, 0x08, 0xa1, 0x27, 0xe8, 0x57, 0xe5, 0x78, 0x8e, 0xf2, 0x58, 0x19, 0x12, 0x42, 0xae, 0xc4, 0x63, 0x3e}} ,
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{{0x78, 0x96, 0x9c, 0xa7, 0xca, 0x80, 0xae, 0x02, 0x85, 0xb1, 0x7c, 0x04, 0x5c, 0xc1, 0x5b, 0x26, 0xc1, 0xba, 0xed, 0xa5, 0x59, 0x70, 0x85, 0x8c, 0x8c, 0xe8, 0x87, 0xac, 0x6a, 0x28, 0x99, 0x35}}},
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{{{0x9f, 0x04, 0x08, 0x28, 0xbe, 0x87, 0xda, 0x80, 0x28, 0x38, 0xde, 0x9f, 0xcd, 0xe4, 0xe3, 0x62, 0xfb, 0x2e, 0x46, 0x8d, 0x01, 0xb3, 0x06, 0x51, 0xd4, 0x19, 0x3b, 0x11, 0xfa, 0xe2, 0xad, 0x1e}} ,
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{{{0x91, 0x4a, 0x07, 0xad, 0x08, 0x75, 0xc1, 0x4f, 0xa4, 0xb2, 0xc3, 0x6f, 0x46, 0x3e, 0xb1, 0xce, 0x52, 0xab, 0x67, 0x09, 0x54, 0x48, 0x6b, 0x6c, 0xd7, 0x1d, 0x71, 0x76, 0xcb, 0xff, 0xdd, 0x31}} ,
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{{{0xc2, 0x5b, 0x9b, 0x78, 0x23, 0x1b, 0x3a, 0x88, 0x94, 0x5f, 0x0a, 0x9b, 0x98, 0x2b, 0x6e, 0x53, 0x11, 0xf6, 0xff, 0xc6, 0x7d, 0x42, 0xcc, 0x02, 0x80, 0x40, 0x0d, 0x1e, 0xfb, 0xaf, 0x61, 0x07}} ,
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{{{0x2b, 0x06, 0xd9, 0xa1, 0x5d, 0xe1, 0xf4, 0xd1, 0x1e, 0x3c, 0x9a, 0xc6, 0x29, 0x2b, 0x13, 0x13, 0x78, 0xc0, 0xd8, 0x16, 0x17, 0x2d, 0x9e, 0xa9, 0xc9, 0x79, 0x57, 0xab, 0x24, 0x91, 0x92, 0x19}} ,
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|
|
{{0x01, 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}}},
|
|
{{{0xec, 0xd3, 0xff, 0x57, 0x0b, 0xb0, 0xb2, 0xdc, 0xf8, 0x4f, 0xe2, 0x12, 0xd5, 0x36, 0xbe, 0x6b, 0x09, 0x43, 0x6d, 0xa3, 0x4d, 0x90, 0x2d, 0xb8, 0x74, 0xe8, 0x71, 0x45, 0x19, 0x8b, 0x0c, 0x6a}} ,
|
|
{{0xb8, 0x42, 0x1c, 0x03, 0xad, 0x2c, 0x03, 0x8e, 0xac, 0xd7, 0x98, 0x29, 0x13, 0xc6, 0x02, 0x29, 0xb5, 0xd4, 0xe7, 0xcf, 0xcc, 0x8b, 0x83, 0xec, 0x35, 0xc7, 0x9c, 0x74, 0xb7, 0xad, 0x85, 0x5f}}},
|
|
{{{0x78, 0x84, 0xe1, 0x56, 0x45, 0x69, 0x68, 0x5a, 0x4f, 0xb8, 0xb1, 0x29, 0xff, 0x33, 0x03, 0x31, 0xb7, 0xcb, 0x96, 0x25, 0xe6, 0xe6, 0x41, 0x98, 0x1a, 0xbb, 0x03, 0x56, 0xf2, 0xb2, 0x91, 0x34}} ,
|
|
{{0x2c, 0x6c, 0xf7, 0x66, 0xa4, 0x62, 0x6b, 0x39, 0xb3, 0xba, 0x65, 0xd3, 0x1c, 0xf8, 0x11, 0xaa, 0xbe, 0xdc, 0x80, 0x59, 0x87, 0xf5, 0x7b, 0xe5, 0xe3, 0xb3, 0x3e, 0x39, 0xda, 0xbe, 0x88, 0x09}}},
|
|
{{{0x8b, 0xf1, 0xa0, 0xf5, 0xdc, 0x29, 0xb4, 0xe2, 0x07, 0xc6, 0x7a, 0x00, 0xd0, 0x89, 0x17, 0x51, 0xd4, 0xbb, 0xd4, 0x22, 0xea, 0x7e, 0x7d, 0x7c, 0x24, 0xea, 0xf2, 0xe8, 0x22, 0x12, 0x95, 0x06}} ,
|
|
{{0xda, 0x7c, 0xa4, 0x0c, 0xf4, 0xba, 0x6e, 0xe1, 0x89, 0xb5, 0x59, 0xca, 0xf1, 0xc0, 0x29, 0x36, 0x09, 0x44, 0xe2, 0x7f, 0xd1, 0x63, 0x15, 0x99, 0xea, 0x25, 0xcf, 0x0c, 0x9d, 0xc0, 0x44, 0x6f}}},
|
|
{{{0x1d, 0x86, 0x4e, 0xcf, 0xf7, 0x37, 0x10, 0x25, 0x8f, 0x12, 0xfb, 0x19, 0xfb, 0xe0, 0xed, 0x10, 0xc8, 0xe2, 0xf5, 0x75, 0xb1, 0x33, 0xc0, 0x96, 0x0d, 0xfb, 0x15, 0x6c, 0x0d, 0x07, 0x5f, 0x05}} ,
|
|
{{0x69, 0x3e, 0x47, 0x97, 0x2c, 0xaf, 0x52, 0x7c, 0x78, 0x83, 0xad, 0x1b, 0x39, 0x82, 0x2f, 0x02, 0x6f, 0x47, 0xdb, 0x2a, 0xb0, 0xe1, 0x91, 0x99, 0x55, 0xb8, 0x99, 0x3a, 0xa0, 0x44, 0x11, 0x51}}}
|
|
};
|
|
|
|
void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)
|
|
{
|
|
fe25519_mul(&r->x, &p->x, &p->t);
|
|
fe25519_mul(&r->y, &p->y, &p->z);
|
|
fe25519_mul(&r->z, &p->z, &p->t);
|
|
}
|
|
|
|
void p1p1_to_p2_2(ge25519_p3 *r, const ge25519_p1p1 *p)
|
|
{
|
|
fe25519_mul(&r->x, &p->x, &p->t);
|
|
fe25519_mul(&r->y, &p->y, &p->z);
|
|
fe25519_mul(&r->z, &p->z, &p->t);
|
|
}
|
|
|
|
void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)
|
|
{
|
|
p1p1_to_p2_2(r, p);
|
|
fe25519_mul(&r->t, &p->x, &p->y);
|
|
}
|
|
|
|
void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q)
|
|
{
|
|
fe25519 a,b,t1,t2,c,d,e,f,g,h,qt;
|
|
fe25519_mul(&qt, &q->x, &q->y);
|
|
fe25519_sub(&a, &r->y, &r->x); /* A = (Y1-X1)*(Y2-X2) */
|
|
fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)*(Y2+X2) */
|
|
fe25519_sub(&t1, &q->y, &q->x);
|
|
fe25519_add(&t2, &q->y, &q->x);
|
|
fe25519_mul(&a, &a, &t1);
|
|
fe25519_mul(&b, &b, &t2);
|
|
fe25519_sub(&e, &b, &a); /* E = B-A */
|
|
fe25519_add(&h, &b, &a); /* H = B+A */
|
|
fe25519_mul(&c, &r->t, &qt); /* C = T1*k*T2 */
|
|
fe25519_mul(&c, &c, &ge25519_ec2d);
|
|
fe25519_add(&d, &r->z, &r->z); /* D = Z1*2 */
|
|
fe25519_sub(&f, &d, &c); /* F = D-C */
|
|
fe25519_add(&g, &d, &c); /* G = D+C */
|
|
fe25519_mul(&r->x, &e, &f);
|
|
fe25519_mul(&r->y, &h, &g);
|
|
fe25519_mul(&r->z, &g, &f);
|
|
fe25519_mul(&r->t, &e, &h);
|
|
}
|
|
|
|
void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q)
|
|
{
|
|
fe25519 a, b, c, d, t;
|
|
|
|
fe25519_sub(&a, &p->y, &p->x); /* A = (Y1-X1)*(Y2-X2) */
|
|
fe25519_sub(&t, &q->y, &q->x);
|
|
fe25519_mul(&a, &a, &t);
|
|
fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)*(Y2+X2) */
|
|
fe25519_add(&t, &q->x, &q->y);
|
|
fe25519_mul(&b, &b, &t);
|
|
fe25519_mul(&c, &p->t, &q->t); /* C = T1*k*T2 */
|
|
fe25519_mul(&c, &c, &ge25519_ec2d);
|
|
fe25519_mul(&d, &p->z, &q->z); /* D = Z1*2*Z2 */
|
|
fe25519_add(&d, &d, &d);
|
|
fe25519_sub(&r->x, &b, &a); /* E = B-A */
|
|
fe25519_sub(&r->t, &d, &c); /* F = D-C */
|
|
fe25519_add(&r->z, &d, &c); /* G = D+C */
|
|
fe25519_add(&r->y, &b, &a); /* H = B+A */
|
|
}
|
|
|
|
/* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */
|
|
void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p)
|
|
{
|
|
fe25519 a,b,c,d;
|
|
fe25519_square(&a, &p->x);
|
|
fe25519_square(&b, &p->y);
|
|
fe25519_square(&c, &p->z);
|
|
fe25519_add(&c, &c, &c);
|
|
fe25519_neg(&d, &a);
|
|
|
|
fe25519_add(&r->x, &p->x, &p->y);
|
|
fe25519_square(&r->x, &r->x);
|
|
fe25519_sub(&r->x, &r->x, &a);
|
|
fe25519_sub(&r->x, &r->x, &b);
|
|
fe25519_add(&r->z, &d, &b);
|
|
fe25519_sub(&r->t, &r->z, &c);
|
|
fe25519_sub(&r->y, &d, &b);
|
|
}
|
|
|
|
/* Constant-time version of: if(b) r = p */
|
|
void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b)
|
|
{
|
|
fe25519_cmov(&r->x, &p->x, b);
|
|
fe25519_cmov(&r->y, &p->y, b);
|
|
}
|
|
|
|
unsigned char equal(signed char b,signed char c)
|
|
{
|
|
unsigned char ub = b;
|
|
unsigned char uc = c;
|
|
unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
|
|
crypto_uint32 y = x; /* 0: yes; 1..255: no */
|
|
y -= 1; /* 4294967295: yes; 0..254: no */
|
|
y >>= 31; /* 1: yes; 0: no */
|
|
return (unsigned char)y;
|
|
}
|
|
|
|
unsigned char negative(signed char b)
|
|
{
|
|
unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
|
|
x >>= 63; /* 1: yes; 0: no */
|
|
return (unsigned char)x;
|
|
}
|
|
|
|
void choose_t(ge25519_aff *t, unsigned long long pos, signed char b)
|
|
{
|
|
/* constant time */
|
|
fe25519 v;
|
|
*t = ge25519_base_multiples_affine[5*pos+0];
|
|
cmov_aff(t, &ge25519_base_multiples_affine[5*pos+1],equal(b,1) | equal(b,-1));
|
|
cmov_aff(t, &ge25519_base_multiples_affine[5*pos+2],equal(b,2) | equal(b,-2));
|
|
cmov_aff(t, &ge25519_base_multiples_affine[5*pos+3],equal(b,3) | equal(b,-3));
|
|
cmov_aff(t, &ge25519_base_multiples_affine[5*pos+4],equal(b,-4));
|
|
fe25519_neg(&v, &t->x);
|
|
fe25519_cmov(&t->x, &v, negative(b));
|
|
}
|
|
|
|
void setneutral(ge25519 *r)
|
|
{
|
|
fe25519_setzero(&r->x);
|
|
fe25519_setone(&r->y);
|
|
fe25519_setone(&r->z);
|
|
fe25519_setzero(&r->t);
|
|
}
|
|
|
|
/* return 0 on success, -1 otherwise */
|
|
int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32])
|
|
{
|
|
unsigned char par;
|
|
fe25519 t, chk, num, den, den2, den4, den6;
|
|
fe25519_setone(&r->z);
|
|
par = p[31] >> 7;
|
|
fe25519_unpack(&r->y, p);
|
|
fe25519_square(&num, &r->y); /* x = y^2 */
|
|
fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */
|
|
fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */
|
|
fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */
|
|
|
|
/* Computation of sqrt(num/den) */
|
|
/* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
|
|
fe25519_square(&den2, &den);
|
|
fe25519_square(&den4, &den2);
|
|
fe25519_mul(&den6, &den4, &den2);
|
|
fe25519_mul(&t, &den6, &num);
|
|
fe25519_mul(&t, &t, &den);
|
|
|
|
fe25519_pow2523(&t, &t);
|
|
/* 2. computation of r->x = t * num * den^3 */
|
|
fe25519_mul(&t, &t, &num);
|
|
fe25519_mul(&t, &t, &den);
|
|
fe25519_mul(&t, &t, &den);
|
|
fe25519_mul(&r->x, &t, &den);
|
|
|
|
/* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */
|
|
fe25519_square(&chk, &r->x);
|
|
fe25519_mul(&chk, &chk, &den);
|
|
if (!fe25519_iseq_vartime(&chk, &num))
|
|
fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
|
|
|
|
/* 4. Now we have one of the two square roots, except if input was not a square */
|
|
fe25519_square(&chk, &r->x);
|
|
fe25519_mul(&chk, &chk, &den);
|
|
if (!fe25519_iseq_vartime(&chk, &num))
|
|
return -1;
|
|
|
|
/* 5. Choose the desired square root according to parity: */
|
|
if(fe25519_getparity(&r->x) != (1-par))
|
|
fe25519_neg(&r->x, &r->x);
|
|
|
|
fe25519_mul(&r->t, &r->x, &r->y);
|
|
return 0;
|
|
}
|
|
|
|
void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)
|
|
{
|
|
fe25519 tx, ty, zi;
|
|
fe25519_invert(&zi, &p->z);
|
|
fe25519_mul(&tx, &p->x, &zi);
|
|
fe25519_mul(&ty, &p->y, &zi);
|
|
fe25519_pack(r, &ty);
|
|
r[31] ^= fe25519_getparity(&tx) << 7;
|
|
}
|
|
|
|
/* computes [s1]p1 + [s2]p2 */
|
|
void ge25519_double_scalarmult_vartime(ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2)
|
|
{
|
|
ge25519_p1p1 tp1p1;
|
|
ge25519_p3 pre[16];
|
|
char *pre5 = (char *)(&(pre[5])); // eliminate type punning warning
|
|
unsigned char b[127];
|
|
int i;
|
|
|
|
/* precomputation s2 s1 */
|
|
setneutral(pre); /* 00 00 */
|
|
pre[1] = *p1; /* 00 01 */
|
|
dbl_p1p1(&tp1p1,(ge25519_p2 *)p1); p1p1_to_p3( &pre[2], &tp1p1); /* 00 10 */
|
|
add_p1p1(&tp1p1,&pre[1], &pre[2]); p1p1_to_p3( &pre[3], &tp1p1); /* 00 11 */
|
|
pre[4] = *p2; /* 01 00 */
|
|
add_p1p1(&tp1p1,&pre[1], &pre[4]); p1p1_to_p3( &pre[5], &tp1p1); /* 01 01 */
|
|
add_p1p1(&tp1p1,&pre[2], &pre[4]); p1p1_to_p3( &pre[6], &tp1p1); /* 01 10 */
|
|
add_p1p1(&tp1p1,&pre[3], &pre[4]); p1p1_to_p3( &pre[7], &tp1p1); /* 01 11 */
|
|
dbl_p1p1(&tp1p1,(ge25519_p2 *)p2); p1p1_to_p3( &pre[8], &tp1p1); /* 10 00 */
|
|
add_p1p1(&tp1p1,&pre[1], &pre[8]); p1p1_to_p3( &pre[9], &tp1p1); /* 10 01 */
|
|
dbl_p1p1(&tp1p1,(ge25519_p2 *)pre5); p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */
|
|
add_p1p1(&tp1p1,&pre[3], &pre[8]); p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */
|
|
add_p1p1(&tp1p1,&pre[4], &pre[8]); p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */
|
|
add_p1p1(&tp1p1,&pre[1],&pre[12]); p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */
|
|
add_p1p1(&tp1p1,&pre[2],&pre[12]); p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */
|
|
add_p1p1(&tp1p1,&pre[3],&pre[12]); p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */
|
|
|
|
sc25519_2interleave2(b,s1,s2);
|
|
|
|
/* scalar multiplication */
|
|
*r = pre[b[126]];
|
|
for(i=125;i>=0;i--)
|
|
{
|
|
dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
|
|
p1p1_to_p2((ge25519_p2 *) r, &tp1p1);
|
|
dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
|
|
if(b[i]!=0)
|
|
{
|
|
p1p1_to_p3(r, &tp1p1);
|
|
add_p1p1(&tp1p1, r, &pre[b[i]]);
|
|
}
|
|
if(i != 0) p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
|
|
else p1p1_to_p3(r, &tp1p1);
|
|
}
|
|
}
|
|
|
|
void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)
|
|
{
|
|
signed char b[85];
|
|
int i;
|
|
ge25519_aff t;
|
|
sc25519_window3(b,s);
|
|
|
|
choose_t((ge25519_aff *)r, 0, b[0]);
|
|
fe25519_setone(&r->z);
|
|
fe25519_mul(&r->t, &r->x, &r->y);
|
|
for(i=1;i<85;i++)
|
|
{
|
|
choose_t(&t, (unsigned long long) i, b[i]);
|
|
ge25519_mixadd2(r, &t);
|
|
}
|
|
}
|
|
|
|
void get_hram(unsigned char *hram, const unsigned char *sm, const unsigned char *pk, unsigned char *playground, unsigned long smlen)
|
|
{
|
|
unsigned long long i;
|
|
|
|
for (i = 0;i < 32;++i) playground[i] = sm[i];
|
|
for (i = 32;i < 64;++i) playground[i] = pk[i-32];
|
|
for (i = 64;i < smlen;++i) playground[i] = sm[i];
|
|
|
|
//crypto_hash_sha512(hram,playground,smlen);
|
|
ZeroTier::SHA512::hash(hram,playground,(unsigned int)smlen);
|
|
}
|
|
|
|
//////////////////////////////////////////////////////////////////////////////
|
|
//////////////////////////////////////////////////////////////////////////////
|
|
|
|
} // anonymous namespace
|
|
|
|
#ifdef ZT_USE_FAST_X64_ED25519
|
|
extern "C" void ed25519_amd64_asm_sign(const unsigned char *sk,const unsigned char *pk,const unsigned char *digest,unsigned char *sig);
|
|
#endif
|
|
|
|
namespace ZeroTier {
|
|
|
|
void C25519::agree(const C25519::Private &mine,const C25519::Public &their,void *keybuf,unsigned int keylen)
|
|
{
|
|
unsigned char rawkey[32];
|
|
unsigned char digest[64];
|
|
|
|
crypto_scalarmult(rawkey,mine.data,their.data);
|
|
SHA512::hash(digest,rawkey,32);
|
|
for(unsigned int i=0,k=0;i<keylen;) {
|
|
if (k == 64) {
|
|
k = 0;
|
|
SHA512::hash(digest,digest,64);
|
|
}
|
|
((unsigned char *)keybuf)[i++] = digest[k++];
|
|
}
|
|
}
|
|
|
|
void C25519::sign(const C25519::Private &myPrivate,const C25519::Public &myPublic,const void *msg,unsigned int len,void *signature)
|
|
{
|
|
unsigned char digest[64]; // we sign the first 32 bytes of SHA-512(msg)
|
|
SHA512::hash(digest,msg,len);
|
|
|
|
#ifdef ZT_USE_FAST_X64_ED25519
|
|
ed25519_amd64_asm_sign(myPrivate.data + 32,myPublic.data + 32,digest,(unsigned char *)signature);
|
|
#else
|
|
sc25519 sck, scs, scsk;
|
|
ge25519 ger;
|
|
unsigned char r[32];
|
|
unsigned char s[32];
|
|
unsigned char extsk[64];
|
|
unsigned char hmg[crypto_hash_sha512_BYTES];
|
|
unsigned char hram[crypto_hash_sha512_BYTES];
|
|
unsigned char *sig = (unsigned char *)signature;
|
|
|
|
SHA512::hash(extsk,myPrivate.data + 32,32);
|
|
extsk[0] &= 248;
|
|
extsk[31] &= 127;
|
|
extsk[31] |= 64;
|
|
|
|
for(unsigned int i=0;i<32;i++)
|
|
sig[32 + i] = extsk[32 + i];
|
|
for(unsigned int i=0;i<32;i++)
|
|
sig[64 + i] = digest[i];
|
|
|
|
SHA512::hash(hmg,sig + 32,64);
|
|
|
|
/* Computation of R */
|
|
sc25519_from64bytes(&sck, hmg);
|
|
ge25519_scalarmult_base(&ger, &sck);
|
|
ge25519_pack(r, &ger);
|
|
|
|
/* Computation of s */
|
|
for(unsigned int i=0;i<32;i++)
|
|
sig[i] = r[i];
|
|
|
|
get_hram(hram,sig,myPublic.data + 32,sig,96);
|
|
|
|
sc25519_from64bytes(&scs, hram);
|
|
sc25519_from32bytes(&scsk, extsk);
|
|
sc25519_mul(&scs, &scs, &scsk);
|
|
|
|
sc25519_add(&scs, &scs, &sck);
|
|
|
|
sc25519_to32bytes(s,&scs); /* cat s */
|
|
for(unsigned int i=0;i<32;i++)
|
|
sig[32 + i] = s[i];
|
|
#endif
|
|
}
|
|
|
|
bool C25519::verify(const C25519::Public &their,const void *msg,unsigned int len,const void *signature,const unsigned int siglen)
|
|
{
|
|
if (siglen < 64) return false;
|
|
|
|
const unsigned char *sig = (const unsigned char *)signature;
|
|
unsigned char digest[64]; // we sign the first 32 bytes of SHA-512(msg)
|
|
unsigned char sigtmp[96];
|
|
SHA512::hash(digest,msg,len);
|
|
|
|
if ((siglen == 96)&&(!Utils::secureEq(sig+64,digest,32))) {
|
|
return false;
|
|
} else if (siglen == 64) {
|
|
memcpy(sigtmp,sig,64);
|
|
memcpy(sigtmp+64,digest,32);
|
|
sig = sigtmp;
|
|
}
|
|
|
|
unsigned char t2[32];
|
|
ge25519 get1, get2;
|
|
sc25519 schram, scs;
|
|
unsigned char hram[crypto_hash_sha512_BYTES];
|
|
unsigned char m[96];
|
|
|
|
if (ge25519_unpackneg_vartime(&get1,their.data + 32))
|
|
return false;
|
|
|
|
get_hram(hram,sig,their.data + 32,m,96);
|
|
|
|
sc25519_from64bytes(&schram, hram);
|
|
|
|
sc25519_from32bytes(&scs, sig+32);
|
|
|
|
ge25519_double_scalarmult_vartime(&get2, &get1, &schram, &ge25519_base, &scs);
|
|
ge25519_pack(t2, &get2);
|
|
|
|
return Utils::secureEq(sig,t2,32);
|
|
}
|
|
|
|
void C25519::_calcPubDH(C25519::Pair &kp)
|
|
{
|
|
// First 32 bytes of pub and priv are the keys for ECDH key
|
|
// agreement. This generates the public portion from the private.
|
|
crypto_scalarmult_base(kp.pub.data,kp.priv.data);
|
|
}
|
|
|
|
void C25519::_calcPubED(C25519::Pair &kp)
|
|
{
|
|
unsigned char extsk[64];
|
|
sc25519 scsk;
|
|
ge25519 gepk;
|
|
|
|
// Second 32 bytes of pub and priv are the keys for ed25519
|
|
// signing and verification.
|
|
SHA512::hash(extsk,kp.priv.data + 32,32);
|
|
extsk[0] &= 248;
|
|
extsk[31] &= 127;
|
|
extsk[31] |= 64;
|
|
sc25519_from32bytes(&scsk,extsk);
|
|
ge25519_scalarmult_base(&gepk,&scsk);
|
|
ge25519_pack(kp.pub.data + 32,&gepk);
|
|
// In NaCl, the public key is crammed into the next 32 bytes
|
|
// of the private key for signing since both keys are required
|
|
// to sign. In this version we just get it from kp.pub, so we
|
|
// leave that out of private.
|
|
}
|
|
|
|
} // namespace ZeroTier
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