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donna_32.cpp
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// donna_32.cpp - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Andrew
// Moon's public domain curve25519-donna and ed25519-donna,
// https://github.com/floodyberry/curve25519-donna and
// https://github.com/floodyberry/ed25519-donna.
// The curve25519 and ed25519 source files multiplex different repos and
// architectures using namespaces. The repos are Andrew Moon's
// curve25519-donna and ed25519-donna. The architectures are 32-bit, 64-bit
// and SSE. For example, 32-bit x25519 uses symbols from Donna::X25519 and
// Donna::Arch32.
// A fair amount of duplication happens below, but we could not directly
// use curve25519 for both x25519 and ed25519. A close examination reveals
// slight differences in the implementation. For example, look at the
// two curve25519_sub functions.
// If needed, see Moon's commit "Go back to ignoring 256th bit [sic]",
// https://github.com/floodyberry/curve25519-donna/commit/57a683d18721a658
#include "pch.h"
#include "config.h"
#include "donna.h"
#include "secblock.h"
#include "sha.h"
#include "misc.h"
#include "cpu.h"
#include <istream>
#include <sstream>
#if CRYPTOPP_GCC_DIAGNOSTIC_AVAILABLE
# pragma GCC diagnostic ignored "-Wunused-function"
#endif
#if CRYPTOPP_MSC_VERSION
# pragma warning(disable: 4244)
#endif
// Squash MS LNK4221 and libtool warnings
extern const char DONNA32_FNAME[] = __FILE__;
ANONYMOUS_NAMESPACE_BEGIN
// Can't use GetAlignmentOf<word32>() because of C++11 and constexpr
// Can use 'const unsigned int' because of MSVC 2013
#if (CRYPTOPP_BOOL_X86 || CRYPTOPP_BOOL_X32 || CRYPTOPP_BOOL_X64)
# define ALIGN_SPEC 16
#else
# define ALIGN_SPEC 4
#endif
ANONYMOUS_NAMESPACE_END
#if defined(CRYPTOPP_CURVE25519_32BIT)
#include "donna_32.h"
ANONYMOUS_NAMESPACE_BEGIN
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::GetWord;
using CryptoPP::PutWord;
using CryptoPP::LITTLE_ENDIAN_ORDER;
inline word32 U8TO32_LE(const byte* p)
{
return GetWord<word32>(false, LITTLE_ENDIAN_ORDER, p);
}
inline void U32TO8_LE(byte* p, word32 w)
{
PutWord(false, LITTLE_ENDIAN_ORDER, p, w);
}
ANONYMOUS_NAMESPACE_END
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
NAMESPACE_BEGIN(X25519)
ANONYMOUS_NAMESPACE_BEGIN
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::sword32;
using CryptoPP::word64;
using CryptoPP::sword64;
using CryptoPP::GetBlock;
using CryptoPP::LittleEndian;
// Bring in all the symbols from the 32-bit header
using namespace CryptoPP::Donna::Arch32;
/* out = in */
inline void
curve25519_copy(bignum25519 out, const bignum25519 in) {
out[0] = in[0]; out[1] = in[1];
out[2] = in[2]; out[3] = in[3];
out[4] = in[4]; out[5] = in[5];
out[6] = in[6]; out[7] = in[7];
out[8] = in[8]; out[9] = in[9];
}
/* out = a + b */
inline void
curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
out[4] = a[4] + b[4]; out[5] = a[5] + b[5];
out[6] = a[6] + b[6]; out[7] = a[7] + b[7];
out[8] = a[8] + b[8]; out[9] = a[9] + b[9];
}
/* out = a - b */
inline void
curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word32 c;
out[0] = 0x7ffffda + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
out[1] = 0x3fffffe + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
out[2] = 0x7fffffe + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
out[3] = 0x3fffffe + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
out[4] = 0x7fffffe + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
out[5] = 0x3fffffe + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
out[6] = 0x7fffffe + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
out[7] = 0x3fffffe + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
out[8] = 0x7fffffe + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
out[9] = 0x3fffffe + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
out[0] += 19 * c;
}
/* out = in * scalar */
inline void
curve25519_scalar_product(bignum25519 out, const bignum25519 in, const word32 scalar) {
word64 a;
word32 c;
a = mul32x32_64(in[0], scalar); out[0] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
a = mul32x32_64(in[1], scalar) + c; out[1] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
a = mul32x32_64(in[2], scalar) + c; out[2] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
a = mul32x32_64(in[3], scalar) + c; out[3] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
a = mul32x32_64(in[4], scalar) + c; out[4] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
a = mul32x32_64(in[5], scalar) + c; out[5] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
a = mul32x32_64(in[6], scalar) + c; out[6] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
a = mul32x32_64(in[7], scalar) + c; out[7] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
a = mul32x32_64(in[8], scalar) + c; out[8] = (word32)a & reduce_mask_26; c = (word32)(a >> 26);
a = mul32x32_64(in[9], scalar) + c; out[9] = (word32)a & reduce_mask_25; c = (word32)(a >> 25);
out[0] += c * 19;
}
/* out = a * b */
inline void
curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
word32 s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
word32 p;
r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4];
r5 = b[5]; r6 = b[6]; r7 = b[7]; r8 = b[8]; r9 = b[9];
s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4];
s5 = a[5]; s6 = a[6]; s7 = a[7]; s8 = a[8]; s9 = a[9];
m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0);
m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0);
m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0);
r1 *= 2; r3 *= 2; r5 *= 2; r7 *= 2;
m0 = mul32x32_64(r0, s0);
m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0);
m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0);
r1 *= 19; r2 *= 19;
r3 = (r3 / 2) * 19;
r4 *= 19;
r5 = (r5 / 2) * 19;
r6 *= 19;
r7 = (r7 / 2) * 19;
r8 *= 19; r9 *= 19;
m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9));
m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9));
m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
r3 *= 2; r5 *= 2; r7 *= 2; r9 *= 2;
m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9));
m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9));
m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
m8 += (mul32x32_64(r9, s9));
r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
r1 += p;
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
}
/* out = in * in */
inline void
curve25519_square(bignum25519 out, const bignum25519 in) {
word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
word32 d6,d7,d8,d9;
word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
word32 p;
r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9];
m0 = mul32x32_64(r0, r0);
r0 *= 2;
m1 = mul32x32_64(r0, r1);
m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
r1 *= 2;
m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
r2 *= 2;
m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
r3 *= 2;
m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
d6 = r6 * 19; d7 = r7 * 2 * 19;
d8 = r8 * 19; d9 = r9 * 2 * 19;
m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
m7 += (mul32x32_64(d9, r8 ));
m8 += (mul32x32_64(d9, r9 ));
r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
r1 += p;
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
}
/* out = in^(2 * count) */
void
curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
word32 d6,d7,d8,d9;
word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
word32 p;
r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
r5 = in[5]; r6 = in[6]; r7 = in[7]; r8 = in[8]; r9 = in[9];
do {
m0 = mul32x32_64(r0, r0);
r0 *= 2;
m1 = mul32x32_64(r0, r1);
m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
r1 *= 2;
m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
r2 *= 2;
m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
r3 *= 2;
m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
d6 = r6 * 19; d7 = r7 * 2 * 19;
d8 = r8 * 19; d9 = r9 * 2 * 19;
m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
m7 += (mul32x32_64(d9, r8 ));
m8 += (mul32x32_64(d9, r9 ));
r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
r1 += p;
} while (--count);
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
out[5] = r5; out[6] = r6; out[7] = r7; out[8] = r8; out[9] = r9;
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
void
curve25519_expand(bignum25519 out, const byte in[32]) {
word32 x0,x1,x2,x3,x4,x5,x6,x7;
GetBlock<word32, LittleEndian> block(in);
block(x0)(x1)(x2)(x3)(x4)(x5)(x6)(x7);
out[0] = ( x0 ) & reduce_mask_26;
out[1] = ((((word64)x1 << 32) | x0) >> 26) & reduce_mask_25;
out[2] = ((((word64)x2 << 32) | x1) >> 19) & reduce_mask_26;
out[3] = ((((word64)x3 << 32) | x2) >> 13) & reduce_mask_25;
out[4] = (( x3) >> 6) & reduce_mask_26;
out[5] = ( x4 ) & reduce_mask_25;
out[6] = ((((word64)x5 << 32) | x4) >> 25) & reduce_mask_26;
out[7] = ((((word64)x6 << 32) | x5) >> 19) & reduce_mask_25;
out[8] = ((((word64)x7 << 32) | x6) >> 12) & reduce_mask_26;
out[9] = (( x7) >> 6) & reduce_mask_25; /* ignore the top bit */
}
/* Take a fully reduced polynomial form number and contract it into a little-endian, 32-byte array */
void
curve25519_contract(byte out[32], const bignum25519 in) {
bignum25519 f;
curve25519_copy(f, in);
#define carry_pass() \
f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
#define carry_pass_full() \
carry_pass() \
f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
#define carry_pass_final() \
carry_pass() \
f[9] &= reduce_mask_25;
carry_pass_full()
carry_pass_full()
/* now t is between 0 and 2^255-1, properly carried. */
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
f[0] += 19;
carry_pass_full()
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
f[0] += (1 << 26) - 19;
f[1] += (1 << 25) - 1;
f[2] += (1 << 26) - 1;
f[3] += (1 << 25) - 1;
f[4] += (1 << 26) - 1;
f[5] += (1 << 25) - 1;
f[6] += (1 << 26) - 1;
f[7] += (1 << 25) - 1;
f[8] += (1 << 26) - 1;
f[9] += (1 << 25) - 1;
/* now between 2^255 and 2^256-20, and offset by 2^255. */
carry_pass_final()
#undef carry_pass
#undef carry_full
#undef carry_final
f[1] <<= 2;
f[2] <<= 3;
f[3] <<= 5;
f[4] <<= 6;
f[6] <<= 1;
f[7] <<= 3;
f[8] <<= 4;
f[9] <<= 6;
#define F(i, s) \
out[s+0] |= (byte)( f[i] & 0xff); \
out[s+1] = (byte)((f[i] >> 8) & 0xff); \
out[s+2] = (byte)((f[i] >> 16) & 0xff); \
out[s+3] = (byte)((f[i] >> 24) & 0xff);
out[0] = out[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
}
inline void
curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, word32 iswap) {
const word32 swap = (word32)(-(sword32)iswap);
word32 x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
x5 = swap & (x[5] ^ qpx[5]); x[5] ^= x5; qpx[5] ^= x5;
x6 = swap & (x[6] ^ qpx[6]); x[6] ^= x6; qpx[6] ^= x6;
x7 = swap & (x[7] ^ qpx[7]); x[7] ^= x7; qpx[7] ^= x7;
x8 = swap & (x[8] ^ qpx[8]); x[8] ^= x8; qpx[8] ^= x8;
x9 = swap & (x[9] ^ qpx[9]); x[9] ^= x9; qpx[9] ^= x9;
}
/*
* In: b = 2^5 - 2^0
* Out: b = 2^250 - 2^0
*/
void
curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
ALIGN(ALIGN_SPEC) bignum25519 t0,c;
/* 2^5 - 2^0 */ /* b */
/* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
/* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
/* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
/* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
/* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
/* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
/* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
/* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
/* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
/* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
/* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
/* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
/* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
/* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
}
/*
* z^(p - 2) = z(2^255 - 21)
*/
void
curve25519_recip(bignum25519 out, const bignum25519 z) {
ALIGN(ALIGN_SPEC) bignum25519 a, t0, b;
/* 2 */ curve25519_square(a, z); /* a = 2 */
/* 8 */ curve25519_square_times(t0, a, 2);
/* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
/* 11 */ curve25519_mul(a, b, a); /* a = 11 */
/* 22 */ curve25519_square(t0, a);
/* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
/* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
/* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
/* 2^255 - 21 */ curve25519_mul(out, b, a);
}
ANONYMOUS_NAMESPACE_END
NAMESPACE_END // X25519
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
//******************************* ed25519 *******************************//
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
NAMESPACE_BEGIN(Ed25519)
ANONYMOUS_NAMESPACE_BEGIN
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::sword32;
using CryptoPP::word64;
using CryptoPP::sword64;
using CryptoPP::GetBlock;
using CryptoPP::LittleEndian;
using CryptoPP::SHA512;
// Bring in all the symbols from the 32-bit header
using namespace CryptoPP::Donna::Arch32;
/* out = in */
inline void
curve25519_copy(bignum25519 out, const bignum25519 in) {
out[0] = in[0]; out[1] = in[1];
out[2] = in[2]; out[3] = in[3];
out[4] = in[4]; out[5] = in[5];
out[6] = in[6]; out[7] = in[7];
out[8] = in[8]; out[9] = in[9];
}
/* out = a + b */
inline void
curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
out[4] = a[4] + b[4]; out[5] = a[5] + b[5];
out[6] = a[6] + b[6]; out[7] = a[7] + b[7];
out[8] = a[8] + b[8]; out[9] = a[9] + b[9];
}
inline void
curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word32 c;
out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
out[0] += 19 * c;
}
inline void
curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word32 c;
out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
out[0] += 19 * c;
}
/* out = a - b */
inline void
curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word32 c;
out[0] = twoP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
out[2] = twoP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
out[4] = twoP2468 + a[4] - b[4] + c;
out[5] = twoP13579 + a[5] - b[5] ;
out[6] = twoP2468 + a[6] - b[6] ;
out[7] = twoP13579 + a[7] - b[7] ;
out[8] = twoP2468 + a[8] - b[8] ;
out[9] = twoP13579 + a[9] - b[9] ;
}
/* out = a - b, where a is the result of a basic op (add,sub) */
inline void
curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word32 c;
out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
out[0] += 19 * c;
}
inline void
curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word32 c;
out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
out[0] += 19 * c;
}
/* out = -a */
inline void
curve25519_neg(bignum25519 out, const bignum25519 a) {
word32 c;
out[0] = twoP0 - a[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
out[2] = twoP2468 - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
out[4] = twoP2468 - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
out[6] = twoP2468 - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
out[8] = twoP2468 - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
out[0] += 19 * c;
}
/* out = a * b */
void
curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
word32 s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
word32 p;
r0 = b[0]; r1 = b[1];
r2 = b[2]; r3 = b[3];
r4 = b[4]; r5 = b[5];
r6 = b[6]; r7 = b[7];
r8 = b[8]; r9 = b[9];
s0 = a[0]; s1 = a[1];
s2 = a[2]; s3 = a[3];
s4 = a[4]; s5 = a[5];
s6 = a[6]; s7 = a[7];
s8 = a[8]; s9 = a[9];
m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0);
m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0);
m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0);
r1 *= 2; r3 *= 2;
r5 *= 2; r7 *= 2;
m0 = mul32x32_64(r0, s0);
m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0);
m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0);
r1 *= 19; r2 *= 19;
r3 = (r3 / 2) * 19;
r4 *= 19;
r5 = (r5 / 2) * 19;
r6 *= 19;
r7 = (r7 / 2) * 19;
r8 *= 19; r9 *= 19;
m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9));
m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9));
m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
r3 *= 2; r5 *= 2;
r7 *= 2; r9 *= 2;
m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9));
m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9));
m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
m8 += (mul32x32_64(r9, s9));
r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
r1 += p;
out[0] = r0; out[1] = r1;
out[2] = r2; out[3] = r3;
out[4] = r4; out[5] = r5;
out[6] = r6; out[7] = r7;
out[8] = r8; out[9] = r9;
}
/* out = in*in */
void
curve25519_square(bignum25519 out, const bignum25519 in) {
word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
word32 d6,d7,d8,d9;
word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
word32 p;
r0 = in[0]; r1 = in[1];
r2 = in[2]; r3 = in[3];
r4 = in[4]; r5 = in[5];
r6 = in[6]; r7 = in[7];
r8 = in[8]; r9 = in[9];
m0 = mul32x32_64(r0, r0);
r0 *= 2;
m1 = mul32x32_64(r0, r1);
m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
r1 *= 2;
m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
r2 *= 2;
m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
r3 *= 2;
m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
d6 = r6 * 19;
d7 = r7 * 2 * 19;
d8 = r8 * 19;
d9 = r9 * 2 * 19;
m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
m7 += (mul32x32_64(d9, r8 ));
m8 += (mul32x32_64(d9, r9 ));
r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
r1 += p;
out[0] = r0; out[1] = r1;
out[2] = r2; out[3] = r3;
out[4] = r4; out[5] = r5;
out[6] = r6; out[7] = r7;
out[8] = r8; out[9] = r9;
}
/* out = in ^ (2 * count) */
void
curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
word32 r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
word32 d6,d7,d8,d9,p;
word64 m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
r0 = in[0]; r1 = in[1];
r2 = in[2]; r3 = in[3];
r4 = in[4]; r5 = in[5];
r6 = in[6]; r7 = in[7];
r8 = in[8]; r9 = in[9];
do {
m0 = mul32x32_64(r0, r0);
r0 *= 2;
m1 = mul32x32_64(r0, r1);
m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
r1 *= 2;
m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
r2 *= 2;
m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
r3 *= 2;
m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
d6 = r6 * 19;
d7 = r7 * 2 * 19;
d8 = r8 * 19;
d9 = r9 * 2 * 19;
m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
m7 += (mul32x32_64(d9, r8 ));
m8 += (mul32x32_64(d9, r9 ));
r0 = (word32)m0 & reduce_mask_26; c = (m0 >> 26);
m1 += c; r1 = (word32)m1 & reduce_mask_25; c = (m1 >> 25);
m2 += c; r2 = (word32)m2 & reduce_mask_26; c = (m2 >> 26);
m3 += c; r3 = (word32)m3 & reduce_mask_25; c = (m3 >> 25);
m4 += c; r4 = (word32)m4 & reduce_mask_26; c = (m4 >> 26);
m5 += c; r5 = (word32)m5 & reduce_mask_25; c = (m5 >> 25);
m6 += c; r6 = (word32)m6 & reduce_mask_26; c = (m6 >> 26);
m7 += c; r7 = (word32)m7 & reduce_mask_25; c = (m7 >> 25);
m8 += c; r8 = (word32)m8 & reduce_mask_26; c = (m8 >> 26);
m9 += c; r9 = (word32)m9 & reduce_mask_25; p = (word32)(m9 >> 25);
m0 = r0 + mul32x32_64(p,19); r0 = (word32)m0 & reduce_mask_26; p = (word32)(m0 >> 26);
r1 += p;
} while (--count);
out[0] = r0; out[1] = r1;
out[2] = r2; out[3] = r3;
out[4] = r4; out[5] = r5;
out[6] = r6; out[7] = r7;
out[8] = r8; out[9] = r9;
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
void
curve25519_expand(bignum25519 out, const byte in[32]) {
word32 x0,x1,x2,x3,x4,x5,x6,x7;
GetBlock<word32, LittleEndian> block(in);
block(x0)(x1)(x2)(x3)(x4)(x5)(x6)(x7);
out[0] = ( x0 ) & 0x3ffffff;
out[1] = ((((word64)x1 << 32) | x0) >> 26) & 0x1ffffff;
out[2] = ((((word64)x2 << 32) | x1) >> 19) & 0x3ffffff;
out[3] = ((((word64)x3 << 32) | x2) >> 13) & 0x1ffffff;
out[4] = (( x3) >> 6) & 0x3ffffff;
out[5] = ( x4 ) & 0x1ffffff;
out[6] = ((((word64)x5 << 32) | x4) >> 25) & 0x3ffffff;
out[7] = ((((word64)x6 << 32) | x5) >> 19) & 0x1ffffff;
out[8] = ((((word64)x7 << 32) | x6) >> 12) & 0x3ffffff;
out[9] = (( x7) >> 6) & 0x1ffffff;
}
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array
*/
void
curve25519_contract(byte out[32], const bignum25519 in) {
bignum25519 f;
curve25519_copy(f, in);
#define carry_pass() \
f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
#define carry_pass_full() \
carry_pass() \
f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
#define carry_pass_final() \
carry_pass() \
f[9] &= reduce_mask_25;
carry_pass_full()
carry_pass_full()
/* now t is between 0 and 2^255-1, properly carried. */
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
f[0] += 19;
carry_pass_full()
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
f[0] += (reduce_mask_26 + 1) - 19;
f[1] += (reduce_mask_25 + 1) - 1;
f[2] += (reduce_mask_26 + 1) - 1;
f[3] += (reduce_mask_25 + 1) - 1;
f[4] += (reduce_mask_26 + 1) - 1;
f[5] += (reduce_mask_25 + 1) - 1;
f[6] += (reduce_mask_26 + 1) - 1;
f[7] += (reduce_mask_25 + 1) - 1;
f[8] += (reduce_mask_26 + 1) - 1;
f[9] += (reduce_mask_25 + 1) - 1;
/* now between 2^255 and 2^256-20, and offset by 2^255. */
carry_pass_final()
#undef carry_pass
#undef carry_full
#undef carry_final
f[1] <<= 2; f[2] <<= 3;
f[3] <<= 5; f[4] <<= 6;
f[6] <<= 1; f[7] <<= 3;
f[8] <<= 4; f[9] <<= 6;
#define F(i, s) \
out[s+0] |= (byte)( f[i] & 0xff); \
out[s+1] = (byte)((f[i] >> 8) & 0xff); \
out[s+2] = (byte)((f[i] >> 16) & 0xff); \
out[s+3] = (byte)((f[i] >> 24) & 0xff);
out[0] = out[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
}
/* out = (flag) ? in : out */
inline void
curve25519_move_conditional_bytes(byte out[96], const byte in[96], word32 flag)
{
// TODO: enable this code path once we can test and benchmark it.
// It is about 48 insns shorter, it avoids punning which may be UB,
// and it is guaranteed constant time.
#if defined(__GNUC__) && defined(__i686__) && 0
const word32 iter = 96/sizeof(word32);
word32* outl = reinterpret_cast<word32*>(out);
const word32* inl = reinterpret_cast<const word32*>(in);
word32 idx=0, val;
__asm__ __volatile__ (
".att_syntax ;\n"
"cmpl $0, %[flag] ;\n" // compare, set ZERO flag
"movl %[iter], %%ecx ;\n" // load iteration count
"1: ;\n"
" movl (%[idx],%[out]), %[val] ;\n" // val = out[idx]
" cmovnzl (%[idx],%[in]), %[val] ;\n" // copy in[idx] to val if NZ
" movl %[val], (%[idx],%[out]) ;\n" // out[idx] = val
" leal 4(%[idx]), %[idx] ;\n" // increment index
" loopnz 1b ;\n" // does not affect flags
: [out] "+S" (outl), [in] "+D" (inl),
[idx] "+b" (idx), [val] "=r" (val)
: [flag] "g" (flag), [iter] "I" (iter)
: "ecx", "memory", "cc"
);
#else
const word32 nb = flag - 1, b = ~nb;
const word32 *inl = (const word32 *)in;
word32 *outl = (word32 *)out;
outl[0] = (outl[0] & nb) | (inl[0] & b);
outl[1] = (outl[1] & nb) | (inl[1] & b);
outl[2] = (outl[2] & nb) | (inl[2] & b);
outl[3] = (outl[3] & nb) | (inl[3] & b);
outl[4] = (outl[4] & nb) | (inl[4] & b);
outl[5] = (outl[5] & nb) | (inl[5] & b);
outl[6] = (outl[6] & nb) | (inl[6] & b);
outl[7] = (outl[7] & nb) | (inl[7] & b);
outl[8] = (outl[8] & nb) | (inl[8] & b);
outl[9] = (outl[9] & nb) | (inl[9] & b);
outl[10] = (outl[10] & nb) | (inl[10] & b);
outl[11] = (outl[11] & nb) | (inl[11] & b);
outl[12] = (outl[12] & nb) | (inl[12] & b);
outl[13] = (outl[13] & nb) | (inl[13] & b);
outl[14] = (outl[14] & nb) | (inl[14] & b);
outl[15] = (outl[15] & nb) | (inl[15] & b);
outl[16] = (outl[16] & nb) | (inl[16] & b);
outl[17] = (outl[17] & nb) | (inl[17] & b);
outl[18] = (outl[18] & nb) | (inl[18] & b);
outl[19] = (outl[19] & nb) | (inl[19] & b);
outl[20] = (outl[20] & nb) | (inl[20] & b);
outl[21] = (outl[21] & nb) | (inl[21] & b);
outl[22] = (outl[22] & nb) | (inl[22] & b);
outl[23] = (outl[23] & nb) | (inl[23] & b);
#endif
}
/* if (iswap) swap(a, b) */
inline void
curve25519_swap_conditional(bignum25519 a, bignum25519 b, word32 iswap) {
const word32 swap = (word32)(-(sword32)iswap);
word32 x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5;