mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-11-18 05:28:40 +00:00
383 lines
11 KiB
C
383 lines
11 KiB
C
/*
|
|
conversions
|
|
*/
|
|
|
|
DONNA_INLINE static void
|
|
ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
|
|
curve25519_mul(r->x, p->x, p->t);
|
|
curve25519_mul(r->y, p->y, p->z);
|
|
curve25519_mul(r->z, p->z, p->t);
|
|
}
|
|
|
|
DONNA_INLINE static void
|
|
ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) {
|
|
curve25519_mul(r->x, p->x, p->t);
|
|
curve25519_mul(r->y, p->y, p->z);
|
|
curve25519_mul(r->z, p->z, p->t);
|
|
curve25519_mul(r->t, p->x, p->y);
|
|
}
|
|
|
|
static void
|
|
ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) {
|
|
curve25519_sub(p->ysubx, r->y, r->x);
|
|
curve25519_add(p->xaddy, r->y, r->x);
|
|
curve25519_copy(p->z, r->z);
|
|
curve25519_mul(p->t2d, r->t, ge25519_ec2d);
|
|
}
|
|
|
|
/*
|
|
adding & doubling
|
|
*/
|
|
|
|
static void
|
|
ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) {
|
|
bignum25519 a,b,c;
|
|
|
|
curve25519_square(a, p->x);
|
|
curve25519_square(b, p->y);
|
|
curve25519_square(c, p->z);
|
|
curve25519_add_reduce(c, c, c);
|
|
curve25519_add(r->x, p->x, p->y);
|
|
curve25519_square(r->x, r->x);
|
|
curve25519_add(r->y, b, a);
|
|
curve25519_sub(r->z, b, a);
|
|
curve25519_sub_after_basic(r->x, r->x, r->y);
|
|
curve25519_sub_after_basic(r->t, c, r->z);
|
|
}
|
|
|
|
#ifndef ED25519_NO_PRECOMP
|
|
static void
|
|
ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, unsigned char signbit) {
|
|
const bignum25519 *qb = (const bignum25519 *)q;
|
|
bignum25519 *rb = (bignum25519 *)r;
|
|
bignum25519 a,b,c;
|
|
|
|
curve25519_sub(a, p->y, p->x);
|
|
curve25519_add(b, p->y, p->x);
|
|
curve25519_mul(a, a, qb[signbit]); /* x for +, y for - */
|
|
curve25519_mul(r->x, b, qb[signbit^1]); /* y for +, x for - */
|
|
curve25519_add(r->y, r->x, a);
|
|
curve25519_sub(r->x, r->x, a);
|
|
curve25519_mul(c, p->t, q->t2d);
|
|
curve25519_add_reduce(r->t, p->z, p->z);
|
|
curve25519_copy(r->z, r->t);
|
|
curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
|
|
curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
|
|
}
|
|
#endif
|
|
|
|
static void
|
|
ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, unsigned char signbit) {
|
|
const bignum25519 *qb = (const bignum25519 *)q;
|
|
bignum25519 *rb = (bignum25519 *)r;
|
|
bignum25519 a,b,c;
|
|
|
|
curve25519_sub(a, p->y, p->x);
|
|
curve25519_add(b, p->y, p->x);
|
|
curve25519_mul(a, a, qb[signbit]); /* ysubx for +, xaddy for - */
|
|
curve25519_mul(r->x, b, qb[signbit^1]); /* xaddy for +, ysubx for - */
|
|
curve25519_add(r->y, r->x, a);
|
|
curve25519_sub(r->x, r->x, a);
|
|
curve25519_mul(c, p->t, q->t2d);
|
|
curve25519_mul(r->t, p->z, q->z);
|
|
curve25519_add_reduce(r->t, r->t, r->t);
|
|
curve25519_copy(r->z, r->t);
|
|
curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
|
|
curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
|
|
}
|
|
|
|
static void
|
|
ge25519_double_partial(ge25519 *r, const ge25519 *p) {
|
|
ge25519_p1p1 t;
|
|
ge25519_double_p1p1(&t, p);
|
|
ge25519_p1p1_to_partial(r, &t);
|
|
}
|
|
|
|
static void
|
|
ge25519_double(ge25519 *r, const ge25519 *p) {
|
|
ge25519_p1p1 t;
|
|
ge25519_double_p1p1(&t, p);
|
|
ge25519_p1p1_to_full(r, &t);
|
|
}
|
|
|
|
static void
|
|
ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) {
|
|
bignum25519 a,b,c,e,f,g,h;
|
|
|
|
curve25519_sub(a, r->y, r->x);
|
|
curve25519_add(b, r->y, r->x);
|
|
curve25519_mul(a, a, q->ysubx);
|
|
curve25519_mul(e, b, q->xaddy);
|
|
curve25519_add(h, e, a);
|
|
curve25519_sub(e, e, a);
|
|
curve25519_mul(c, r->t, q->t2d);
|
|
curve25519_add(f, r->z, r->z);
|
|
curve25519_add_after_basic(g, f, c);
|
|
curve25519_sub_after_basic(f, f, c);
|
|
curve25519_mul(r->x, e, f);
|
|
curve25519_mul(r->y, h, g);
|
|
curve25519_mul(r->z, g, f);
|
|
curve25519_mul(r->t, e, h);
|
|
}
|
|
|
|
static void
|
|
ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) {
|
|
bignum25519 a,b,c,x,y,z,t;
|
|
|
|
curve25519_sub(a, p->y, p->x);
|
|
curve25519_add(b, p->y, p->x);
|
|
curve25519_mul(a, a, q->ysubx);
|
|
curve25519_mul(x, b, q->xaddy);
|
|
curve25519_add(y, x, a);
|
|
curve25519_sub(x, x, a);
|
|
curve25519_mul(c, p->t, q->t2d);
|
|
curve25519_mul(t, p->z, q->z);
|
|
curve25519_add(t, t, t);
|
|
curve25519_add_after_basic(z, t, c);
|
|
curve25519_sub_after_basic(t, t, c);
|
|
curve25519_mul(r->xaddy, x, t);
|
|
curve25519_mul(r->ysubx, y, z);
|
|
curve25519_mul(r->z, z, t);
|
|
curve25519_mul(r->t2d, x, y);
|
|
curve25519_copy(y, r->ysubx);
|
|
curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
|
|
curve25519_add(r->xaddy, r->xaddy, y);
|
|
curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
|
|
}
|
|
|
|
|
|
/*
|
|
pack & unpack
|
|
*/
|
|
|
|
static void
|
|
ge25519_pack(unsigned char r[32], const ge25519 *p) {
|
|
bignum25519 tx, ty, zi;
|
|
unsigned char parity[32];
|
|
curve25519_recip(zi, p->z);
|
|
curve25519_mul(tx, p->x, zi);
|
|
curve25519_mul(ty, p->y, zi);
|
|
curve25519_contract(r, ty);
|
|
curve25519_contract(parity, tx);
|
|
r[31] ^= ((parity[0] & 1) << 7);
|
|
}
|
|
|
|
static int ge25519_unpack_negative_vartime(ge25519 *r, const unsigned char p[32]) {
|
|
static const unsigned char zero[32] = {0};
|
|
static const bignum25519 one = {1};
|
|
unsigned char parity = p[31] >> 7;
|
|
unsigned char check[32];
|
|
bignum25519 t, root, num, den, d3;
|
|
|
|
curve25519_expand(r->y, p);
|
|
curve25519_copy(r->z, one);
|
|
curve25519_square(num, r->y); /* x = y^2 */
|
|
curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */
|
|
curve25519_sub_reduce(num, num, r->z); /* x = y^1 - 1 */
|
|
curve25519_add(den, den, r->z); /* 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) */
|
|
curve25519_square(t, den);
|
|
curve25519_mul(d3, t, den);
|
|
curve25519_square(r->x, d3);
|
|
curve25519_mul(r->x, r->x, den);
|
|
curve25519_mul(r->x, r->x, num);
|
|
curve25519_pow_two252m3(r->x, r->x);
|
|
|
|
/* 2. computation of r->x = num * den^3 * (num*den^7)^((p-5)/8) */
|
|
curve25519_mul(r->x, r->x, d3);
|
|
curve25519_mul(r->x, r->x, num);
|
|
|
|
/* 3. Check if either of the roots works: */
|
|
curve25519_square(t, r->x);
|
|
curve25519_mul(t, t, den);
|
|
curve25519_sub_reduce(root, t, num);
|
|
curve25519_contract(check, root);
|
|
if (!ed25519_verify(check, zero, 32)) {
|
|
curve25519_add_reduce(t, t, num);
|
|
curve25519_contract(check, t);
|
|
if (!ed25519_verify(check, zero, 32))
|
|
return 0;
|
|
curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
|
|
}
|
|
|
|
curve25519_contract(check, r->x);
|
|
if ((check[0] & 1) == parity) {
|
|
curve25519_copy(t, r->x);
|
|
curve25519_neg(r->x, t);
|
|
}
|
|
curve25519_mul(r->t, r->x, r->y);
|
|
return 1;
|
|
}
|
|
|
|
/*
|
|
scalarmults
|
|
*/
|
|
|
|
DONNA_INLINE static void ge25519_set_neutral(ge25519 *r)
|
|
{
|
|
memset(r, 0, sizeof(ge25519));
|
|
r->y[0] = 1;
|
|
r->z[0] = 1;
|
|
}
|
|
|
|
#define S1_SWINDOWSIZE 5
|
|
#define S1_TABLE_SIZE (1<<(S1_SWINDOWSIZE-2))
|
|
#ifdef ED25519_NO_PRECOMP
|
|
#define S2_SWINDOWSIZE 5
|
|
#else
|
|
#define S2_SWINDOWSIZE 7
|
|
#endif
|
|
#define S2_TABLE_SIZE (1<<(S2_SWINDOWSIZE-2))
|
|
|
|
/* computes [s1]p1 + [s2]base */
|
|
static void ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) {
|
|
signed char slide1[256], slide2[256];
|
|
ge25519_pniels pre1[S1_TABLE_SIZE];
|
|
#ifdef ED25519_NO_PRECOMP
|
|
ge25519_pniels pre2[S2_TABLE_SIZE];
|
|
#endif
|
|
ge25519 dp;
|
|
ge25519_p1p1 t;
|
|
int32_t i;
|
|
|
|
contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
|
|
contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
|
|
|
|
ge25519_double(&dp, p1);
|
|
ge25519_full_to_pniels(pre1, p1);
|
|
for (i = 0; i < S1_TABLE_SIZE - 1; i++)
|
|
ge25519_pnielsadd(&pre1[i+1], &dp, &pre1[i]);
|
|
|
|
#ifdef ED25519_NO_PRECOMP
|
|
ge25519_double(&dp, &ge25519_basepoint);
|
|
ge25519_full_to_pniels(pre2, &ge25519_basepoint);
|
|
for (i = 0; i < S2_TABLE_SIZE - 1; i++)
|
|
ge25519_pnielsadd(&pre2[i+1], &dp, &pre2[i]);
|
|
#endif
|
|
|
|
ge25519_set_neutral(r);
|
|
|
|
i = 255;
|
|
while ((i >= 0) && !(slide1[i] | slide2[i]))
|
|
i--;
|
|
|
|
for (; i >= 0; i--) {
|
|
ge25519_double_p1p1(&t, r);
|
|
|
|
if (slide1[i]) {
|
|
ge25519_p1p1_to_full(r, &t);
|
|
ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (unsigned char)slide1[i] >> 7);
|
|
}
|
|
|
|
if (slide2[i]) {
|
|
ge25519_p1p1_to_full(r, &t);
|
|
#ifdef ED25519_NO_PRECOMP
|
|
ge25519_pnielsadd_p1p1(&t, r, &pre2[abs(slide2[i]) / 2], (unsigned char)slide2[i] >> 7);
|
|
#else
|
|
ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (unsigned char)slide2[i] >> 7);
|
|
#endif
|
|
}
|
|
|
|
ge25519_p1p1_to_partial(r, &t);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* The following conditional move stuff uses conditional moves.
|
|
* I will check on which compilers this works, and provide suitable
|
|
* workarounds for those where it doesn't.
|
|
*
|
|
* This works on gcc 4.x and above with -O3. Don't use -O2, this will
|
|
* cause the code to not generate conditional moves. Don't use any -march=
|
|
* with less than i686 on x86
|
|
*/
|
|
DONNA_INLINE static void ge25519_cmove_stride4(long * r, long * p, long * pos, long * n, int stride) {
|
|
long x0=r[0], x1=r[1], x2=r[2], x3=r[3], y0, y1, y2, y3;
|
|
for(; p<n; p+=stride) {
|
|
int flag=(p==pos);
|
|
y0 = p[0];
|
|
y1 = p[1];
|
|
y2 = p[2];
|
|
y3 = p[3];
|
|
x0 = flag ? y0 : x0;
|
|
x1 = flag ? y1 : x1;
|
|
x2 = flag ? y2 : x2;
|
|
x3 = flag ? y3 : x3;
|
|
}
|
|
r[0] = x0;
|
|
r[1] = x1;
|
|
r[2] = x2;
|
|
r[3] = x3;
|
|
}
|
|
#define HAS_CMOVE_STRIDE4
|
|
|
|
static void ge25519_move_conditional_niels_array(ge25519_niels * r, const uint8_t p[8][96], int pos, int n) {
|
|
size_t i;
|
|
for(i=0; i<96/sizeof(long); i+=4) {
|
|
ge25519_cmove_stride4(((long*)r)+i,
|
|
((long*)p)+i,
|
|
((long*)(p+pos))+i,
|
|
((long*)(p+n))+i,
|
|
96/sizeof(long));
|
|
}
|
|
}
|
|
|
|
static void
|
|
ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) {
|
|
bignum25519 neg;
|
|
uint32_t sign = (uint32_t)((unsigned char)b >> 7);
|
|
uint32_t mask = ~(sign - 1);
|
|
uint32_t u = (b + mask) ^ mask;
|
|
|
|
/* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */
|
|
uint8_t packed[96] = {0};
|
|
packed[0] = 1;
|
|
packed[32] = 1;
|
|
|
|
ge25519_move_conditional_niels_array((ge25519_niels *)packed, &table[pos*8], u-1, 8);
|
|
|
|
/* expand in to t */
|
|
curve25519_expand(t->ysubx, packed + 0);
|
|
curve25519_expand(t->xaddy, packed + 32);
|
|
curve25519_expand(t->t2d , packed + 64);
|
|
|
|
/* adjust for sign */
|
|
curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
|
|
curve25519_neg(neg, t->t2d);
|
|
curve25519_swap_conditional(t->t2d, neg, sign);
|
|
}
|
|
|
|
/* computes [s]basepoint */
|
|
static void
|
|
ge25519_scalarmult_base_niels(ge25519 *r, const uint8_t basepoint_table[256][96], const bignum256modm s) {
|
|
signed char b[64];
|
|
uint32_t i;
|
|
ge25519_niels t;
|
|
|
|
contract256_window4_modm(b, s);
|
|
|
|
ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
|
|
curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
|
|
curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
|
|
memset(r->z, 0, sizeof(bignum25519));
|
|
curve25519_copy(r->t, t.t2d);
|
|
r->z[0] = 2;
|
|
for (i = 3; i < 64; i += 2) {
|
|
ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
|
|
ge25519_nielsadd2(r, &t);
|
|
}
|
|
ge25519_double_partial(r, r);
|
|
ge25519_double_partial(r, r);
|
|
ge25519_double_partial(r, r);
|
|
ge25519_double(r, r);
|
|
ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
|
|
curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
|
|
ge25519_nielsadd2(r, &t);
|
|
for(i = 2; i < 64; i += 2) {
|
|
ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
|
|
ge25519_nielsadd2(r, &t);
|
|
}
|
|
}
|