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Merge commits '1b13415d 374e2b54 96294c00 8d2960c8 ce765a5b b2f6712d eedd7810 b327abfc 5d8fa825 3d05c86d bcffeb14 de657c20 060e32cb 0ba2b945 48b1d939 6b9507ad 5373693e 2e6cf9ba 6ee14550 26a98992 4d7fe609 ea26b71c 65c79fe2 727bec5b 0b4640ae 199d27ce cbf3053f 49be5be9 b10ddd2b 4fd00f4b ba9cb6f3 ee7aaf21 ' into temp-merge-1395

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- Replace fe_equal_var with fe_equal
- Use CHECK_ILLEGAL instead of CHECK/ecount
- Turn on secp256k1-zkp specific modules in CI
This commit is contained in:
Jonas Nick
2023-09-19 14:44:41 +00:00
parent b911b3cbd5 ee7aaf213e
commit 775f5e242b
43 changed files with 2063 additions and 1996 deletions
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165
src/group_impl.h
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@@ -77,6 +77,8 @@ static void secp256k1_ge_verify(const secp256k1_ge *a) {
#ifdef VERIFY
secp256k1_fe_verify(&a->x);
secp256k1_fe_verify(&a->y);
secp256k1_fe_verify_magnitude(&a->x, SECP256K1_GE_X_MAGNITUDE_MAX);
secp256k1_fe_verify_magnitude(&a->y, SECP256K1_GE_Y_MAGNITUDE_MAX);
VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
#endif
(void)a;
@@ -87,6 +89,9 @@ static void secp256k1_gej_verify(const secp256k1_gej *a) {
secp256k1_fe_verify(&a->x);
secp256k1_fe_verify(&a->y);
secp256k1_fe_verify(&a->z);
secp256k1_fe_verify_magnitude(&a->x, SECP256K1_GEJ_X_MAGNITUDE_MAX);
secp256k1_fe_verify_magnitude(&a->y, SECP256K1_GEJ_Y_MAGNITUDE_MAX);
secp256k1_fe_verify_magnitude(&a->z, SECP256K1_GEJ_Z_MAGNITUDE_MAX);
VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
#endif
(void)a;
@@ -99,11 +104,13 @@ static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, c
secp256k1_gej_verify(a);
secp256k1_fe_verify(zi);
VERIFY_CHECK(!a->infinity);
secp256k1_fe_sqr(&zi2, zi);
secp256k1_fe_mul(&zi3, &zi2, zi);
secp256k1_fe_mul(&r->x, &a->x, &zi2);
secp256k1_fe_mul(&r->y, &a->y, &zi3);
r->infinity = a->infinity;
secp256k1_ge_verify(r);
}
@@ -114,39 +121,47 @@ static void secp256k1_ge_set_ge_zinv(secp256k1_ge *r, const secp256k1_ge *a, con
secp256k1_ge_verify(a);
secp256k1_fe_verify(zi);
VERIFY_CHECK(!a->infinity);
secp256k1_fe_sqr(&zi2, zi);
secp256k1_fe_mul(&zi3, &zi2, zi);
secp256k1_fe_mul(&r->x, &a->x, &zi2);
secp256k1_fe_mul(&r->y, &a->y, &zi3);
r->infinity = a->infinity;
secp256k1_ge_verify(r);
}
static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
secp256k1_fe_verify(x);
secp256k1_fe_verify(y);
r->infinity = 0;
r->x = *x;
r->y = *y;
secp256k1_ge_verify(r);
}
static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
secp256k1_ge_verify(a);
return a->infinity;
}
static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
secp256k1_ge_verify(a);
*r = *a;
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
secp256k1_ge_verify(r);
}
static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
secp256k1_fe z2, z3;
secp256k1_gej_verify(a);
r->infinity = a->infinity;
secp256k1_fe_inv(&a->z, &a->z);
secp256k1_fe_sqr(&z2, &a->z);
@@ -156,12 +171,15 @@ static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
secp256k1_fe_set_int(&a->z, 1);
r->x = a->x;
r->y = a->y;
secp256k1_gej_verify(a);
secp256k1_ge_verify(r);
}
static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
secp256k1_fe z2, z3;
secp256k1_gej_verify(a);
if (secp256k1_gej_is_infinity(a)) {
secp256k1_ge_set_infinity(r);
return;
@@ -174,6 +192,8 @@ static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
secp256k1_fe_mul(&a->y, &a->y, &z3);
secp256k1_fe_set_int(&a->z, 1);
secp256k1_ge_set_xy(r, &a->x, &a->y);
secp256k1_gej_verify(a);
secp256k1_ge_verify(r);
}
@@ -181,9 +201,13 @@ static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a
secp256k1_fe u;
size_t i;
size_t last_i = SIZE_MAX;
#ifdef VERIFY
for (i = 0; i < len; i++) {
secp256k1_gej_verify(&a[i]);
}
#endif
for (i = 0; i < len; i++) {
if (a[i].infinity) {
secp256k1_ge_set_infinity(&r[i]);
} else {
@@ -217,36 +241,46 @@ static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a
if (!a[i].infinity) {
secp256k1_ge_set_gej_zinv(&r[i], &a[i], &r[i].x);
}
}
#ifdef VERIFY
for (i = 0; i < len; i++) {
secp256k1_ge_verify(&r[i]);
}
#endif
}
static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr) {
size_t i = len - 1;
size_t i;
secp256k1_fe zs;
if (len > 0) {
/* Verify inputs a[len-1] and zr[len-1]. */
#ifdef VERIFY
for (i = 0; i < len; i++) {
secp256k1_ge_verify(&a[i]);
secp256k1_fe_verify(&zr[i]);
}
#endif
if (len > 0) {
i = len - 1;
/* Ensure all y values are in weak normal form for fast negation of points */
secp256k1_fe_normalize_weak(&a[i].y);
zs = zr[i];
/* Work our way backwards, using the z-ratios to scale the x/y values. */
while (i > 0) {
/* Verify all inputs a[i] and zr[i]. */
secp256k1_fe_verify(&zr[i]);
secp256k1_ge_verify(&a[i]);
if (i != len - 1) {
secp256k1_fe_mul(&zs, &zs, &zr[i]);
}
i--;
secp256k1_ge_set_ge_zinv(&a[i], &a[i], &zs);
/* Verify the output a[i]. */
secp256k1_ge_verify(&a[i]);
}
}
#ifdef VERIFY
for (i = 0; i < len; i++) {
secp256k1_ge_verify(&a[i]);
}
#endif
}
static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
@@ -254,6 +288,7 @@ static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_fe_clear(&r->z);
secp256k1_gej_verify(r);
}
@@ -261,6 +296,7 @@ static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
r->infinity = 1;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_ge_verify(r);
}
@@ -269,17 +305,22 @@ static void secp256k1_gej_clear(secp256k1_gej *r) {
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_fe_clear(&r->z);
secp256k1_gej_verify(r);
}
static void secp256k1_ge_clear(secp256k1_ge *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_ge_verify(r);
}
static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) {
secp256k1_fe x2, x3;
secp256k1_fe_verify(x);
r->x = *x;
secp256k1_fe_sqr(&x2, x);
secp256k1_fe_mul(&x3, x, &x2);
@@ -295,16 +336,19 @@ static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int o
if (secp256k1_fe_is_odd(&r->y) != odd) {
secp256k1_fe_negate(&r->y, &r->y, 1);
}
secp256k1_ge_verify(r);
return ret;
}
static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
secp256k1_ge_verify(a);
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_set_int(&r->z, 1);
secp256k1_gej_verify(r);
}
@@ -312,6 +356,7 @@ static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b)
secp256k1_gej tmp;
secp256k1_gej_verify(b);
secp256k1_gej_verify(a);
secp256k1_gej_neg(&tmp, a);
secp256k1_gej_add_var(&tmp, &tmp, b, NULL);
return secp256k1_gej_is_infinity(&tmp);
@@ -319,37 +364,39 @@ static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b)
static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
secp256k1_fe r;
#ifdef VERIFY
secp256k1_fe_verify(x);
VERIFY_CHECK(a->x.magnitude <= 31);
secp256k1_gej_verify(a);
#ifdef VERIFY
VERIFY_CHECK(!a->infinity);
#endif
secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
return secp256k1_fe_equal_var(&r, &a->x);
return secp256k1_fe_equal(&r, &a->x);
}
static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
secp256k1_gej_verify(a);
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
r->z = a->z;
secp256k1_fe_normalize_weak(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
secp256k1_gej_verify(r);
}
static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
secp256k1_gej_verify(a);
return a->infinity;
}
static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
secp256k1_fe y2, x3;
secp256k1_ge_verify(a);
if (a->infinity) {
return 0;
}
@@ -357,14 +404,14 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_add_int(&x3, SECP256K1_B);
return secp256k1_fe_equal_var(&y2, &x3);
return secp256k1_fe_equal(&y2, &x3);
}
static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a) {
/* Operations: 3 mul, 4 sqr, 8 add/half/mul_int/negate */
secp256k1_fe l, s, t;
secp256k1_gej_verify(a);
r->infinity = a->infinity;
/* Formula used:
@@ -391,10 +438,13 @@ static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp25
secp256k1_fe_mul(&r->y, &t, &l); /* Y3 = L*(X3 + T) (1) */
secp256k1_fe_add(&r->y, &s); /* Y3 = L*(X3 + T) + S^2 (2) */
secp256k1_fe_negate(&r->y, &r->y, 2); /* Y3 = -(L*(X3 + T) + S^2) (3) */
secp256k1_gej_verify(r);
}
static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
secp256k1_gej_verify(a);
/** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
* Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
* y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
@@ -405,7 +455,6 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
* the infinity flag even though the point doubles to infinity, and the result
* point will be gibberish (z = 0 but infinity = 0).
*/
secp256k1_gej_verify(a);
if (a->infinity) {
secp256k1_gej_set_infinity(r);
if (rzr != NULL) {
@@ -420,15 +469,16 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
}
secp256k1_gej_double(r, a);
secp256k1_gej_verify(r);
}
static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
/* 12 mul, 4 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */
secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, h2, h3, t;
secp256k1_gej_verify(a);
secp256k1_gej_verify(b);
if (a->infinity) {
VERIFY_CHECK(rzr == NULL);
*r = *b;
@@ -483,14 +533,16 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
secp256k1_fe_mul(&r->y, &t, &i);
secp256k1_fe_mul(&h3, &h3, &s1);
secp256k1_fe_add(&r->y, &h3);
secp256k1_gej_verify(r);
}
static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
/* 8 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
/* Operations: 8 mul, 3 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */
secp256k1_fe z12, u1, u2, s1, s2, h, i, h2, h3, t;
secp256k1_gej_verify(a);
secp256k1_ge_verify(b);
if (a->infinity) {
VERIFY_CHECK(rzr == NULL);
secp256k1_gej_set_ge(r, b);
@@ -505,11 +557,11 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
}
secp256k1_fe_sqr(&z12, &a->z);
u1 = a->x; secp256k1_fe_normalize_weak(&u1);
u1 = a->x;
secp256k1_fe_mul(&u2, &b->x, &z12);
s1 = a->y; secp256k1_fe_normalize_weak(&s1);
s1 = a->y;
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&h, &u1, SECP256K1_GEJ_X_MAGNITUDE_MAX); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
@@ -543,16 +595,18 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
secp256k1_fe_mul(&r->y, &t, &i);
secp256k1_fe_mul(&h3, &h3, &s1);
secp256k1_fe_add(&r->y, &h3);
secp256k1_gej_verify(r);
if (rzr != NULL) secp256k1_fe_verify(rzr);
}
static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
/* 9 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
/* Operations: 9 mul, 3 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */
secp256k1_fe az, z12, u1, u2, s1, s2, h, i, h2, h3, t;
secp256k1_gej_verify(a);
secp256k1_ge_verify(b);
secp256k1_fe_verify(bzinv);
if (a->infinity) {
secp256k1_fe bzinv2, bzinv3;
r->infinity = b->infinity;
@@ -561,6 +615,7 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
secp256k1_fe_mul(&r->x, &b->x, &bzinv2);
secp256k1_fe_mul(&r->y, &b->y, &bzinv3);
secp256k1_fe_set_int(&r->z, 1);
secp256k1_gej_verify(r);
return;
}
if (b->infinity) {
@@ -579,11 +634,11 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
secp256k1_fe_mul(&az, &a->z, bzinv);
secp256k1_fe_sqr(&z12, &az);
u1 = a->x; secp256k1_fe_normalize_weak(&u1);
u1 = a->x;
secp256k1_fe_mul(&u2, &b->x, &z12);
s1 = a->y; secp256k1_fe_normalize_weak(&s1);
s1 = a->y;
secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&h, &u1, SECP256K1_GEJ_X_MAGNITUDE_MAX); secp256k1_fe_add(&h, &u2);
secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
if (secp256k1_fe_normalizes_to_zero_var(&h)) {
if (secp256k1_fe_normalizes_to_zero_var(&i)) {
@@ -611,19 +666,19 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
secp256k1_fe_mul(&r->y, &t, &i);
secp256k1_fe_mul(&h3, &h3, &s1);
secp256k1_fe_add(&r->y, &h3);
secp256k1_gej_verify(r);
}
static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
/* Operations: 7 mul, 5 sqr, 24 add/cmov/half/mul_int/negate/normalize_weak/normalizes_to_zero */
/* Operations: 7 mul, 5 sqr, 21 add/cmov/half/mul_int/negate/normalizes_to_zero */
secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
secp256k1_fe m_alt, rr_alt;
int degenerate;
secp256k1_gej_verify(a);
secp256k1_ge_verify(b);
VERIFY_CHECK(!b->infinity);
VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
/* In:
* Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
@@ -676,17 +731,17 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
*/
secp256k1_fe_sqr(&zz, &a->z); /* z = Z1^2 */
u1 = a->x; secp256k1_fe_normalize_weak(&u1); /* u1 = U1 = X1*Z2^2 (1) */
u1 = a->x; /* u1 = U1 = X1*Z2^2 (GEJ_X_M) */
secp256k1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */
s1 = a->y; secp256k1_fe_normalize_weak(&s1); /* s1 = S1 = Y1*Z2^3 (1) */
s1 = a->y; /* s1 = S1 = Y1*Z2^3 (GEJ_Y_M) */
secp256k1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z1^2 (1) */
secp256k1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */
t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */
m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */
t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (GEJ_X_M+1) */
m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (GEJ_Y_M+1) */
secp256k1_fe_sqr(&rr, &t); /* rr = T^2 (1) */
secp256k1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 */
secp256k1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (2) */
secp256k1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (3) */
secp256k1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 (2) */
secp256k1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (1) */
secp256k1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (2) */
/* If lambda = R/M = R/0 we have a problem (except in the "trivial"
* case that Z = z1z2 = 0, and this is special-cased later on). */
degenerate = secp256k1_fe_normalizes_to_zero(&m);
@@ -696,24 +751,25 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
* non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
* so we set R/M equal to this. */
rr_alt = s1;
secp256k1_fe_mul_int(&rr_alt, 2); /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
secp256k1_fe_add(&m_alt, &u1); /* Malt = X1*Z2^2 - X2*Z1^2 */
secp256k1_fe_mul_int(&rr_alt, 2); /* rr_alt = Y1*Z2^3 - Y2*Z1^3 (GEJ_Y_M*2) */
secp256k1_fe_add(&m_alt, &u1); /* Malt = X1*Z2^2 - X2*Z1^2 (GEJ_X_M+2) */
secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);
secp256k1_fe_cmov(&m_alt, &m, !degenerate);
secp256k1_fe_cmov(&rr_alt, &rr, !degenerate); /* rr_alt (GEJ_Y_M*2) */
secp256k1_fe_cmov(&m_alt, &m, !degenerate); /* m_alt (GEJ_X_M+2) */
/* Now Ralt / Malt = lambda and is guaranteed not to be Ralt / 0.
* From here on out Ralt and Malt represent the numerator
* and denominator of lambda; R and M represent the explicit
* expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
secp256k1_fe_sqr(&n, &m_alt); /* n = Malt^2 (1) */
secp256k1_fe_negate(&q, &t, 2); /* q = -T (3) */
secp256k1_fe_negate(&q, &t,
SECP256K1_GEJ_X_MAGNITUDE_MAX + 1); /* q = -T (GEJ_X_M+2) */
secp256k1_fe_mul(&q, &q, &n); /* q = Q = -T*Malt^2 (1) */
/* These two lines use the observation that either M == Malt or M == 0,
* so M^3 * Malt is either Malt^4 (which is computed by squaring), or
* zero (which is "computed" by cmov). So the cost is one squaring
* versus two multiplications. */
secp256k1_fe_sqr(&n, &n);
secp256k1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (2) */
secp256k1_fe_sqr(&n, &n); /* n = Malt^4 (1) */
secp256k1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (GEJ_Y_M+1) */
secp256k1_fe_sqr(&t, &rr_alt); /* t = Ralt^2 (1) */
secp256k1_fe_mul(&r->z, &a->z, &m_alt); /* r->z = Z3 = Malt*Z (1) */
secp256k1_fe_add(&t, &q); /* t = Ralt^2 + Q (2) */
@@ -721,9 +777,10 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
secp256k1_fe_mul_int(&t, 2); /* t = 2*X3 (4) */
secp256k1_fe_add(&t, &q); /* t = 2*X3 + Q (5) */
secp256k1_fe_mul(&t, &t, &rr_alt); /* t = Ralt*(2*X3 + Q) (1) */
secp256k1_fe_add(&t, &n); /* t = Ralt*(2*X3 + Q) + M^3*Malt (3) */
secp256k1_fe_negate(&r->y, &t, 3); /* r->y = -(Ralt*(2*X3 + Q) + M^3*Malt) (4) */
secp256k1_fe_half(&r->y); /* r->y = Y3 = -(Ralt*(2*X3 + Q) + M^3*Malt)/2 (3) */
secp256k1_fe_add(&t, &n); /* t = Ralt*(2*X3 + Q) + M^3*Malt (GEJ_Y_M+2) */
secp256k1_fe_negate(&r->y, &t,
SECP256K1_GEJ_Y_MAGNITUDE_MAX + 2); /* r->y = -(Ralt*(2*X3 + Q) + M^3*Malt) (GEJ_Y_M+3) */
secp256k1_fe_half(&r->y); /* r->y = Y3 = -(Ralt*(2*X3 + Q) + M^3*Malt)/2 ((GEJ_Y_M+3)/2 + 1) */
/* In case a->infinity == 1, replace r with (b->x, b->y, 1). */
secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
@@ -747,6 +804,7 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
* We have degenerate = false, r->z = (y1 + y2) * Z.
* Then r->infinity = ((y1 + y2)Z == 0) = (y1 == -y2) = false. */
r->infinity = secp256k1_fe_normalizes_to_zero(&r->z);
secp256k1_gej_verify(r);
}
@@ -758,11 +816,13 @@ static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
#ifdef VERIFY
VERIFY_CHECK(!secp256k1_fe_normalizes_to_zero_var(s));
#endif
secp256k1_fe_sqr(&zz, s);
secp256k1_fe_mul(&r->x, &r->x, &zz); /* r->x *= s^2 */
secp256k1_fe_mul(&r->y, &r->y, &zz);
secp256k1_fe_mul(&r->y, &r->y, s); /* r->y *= s^3 */
secp256k1_fe_mul(&r->z, &r->z, s); /* r->z *= s */
secp256k1_gej_verify(r);
}
@@ -770,6 +830,7 @@ static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge
secp256k1_fe x, y;
secp256k1_ge_verify(a);
VERIFY_CHECK(!a->infinity);
x = a->x;
secp256k1_fe_normalize(&x);
y = a->y;
@@ -782,17 +843,19 @@ static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storag
secp256k1_fe_from_storage(&r->x, &a->x);
secp256k1_fe_from_storage(&r->y, &a->y);
r->infinity = 0;
secp256k1_ge_verify(r);
}
static SECP256K1_INLINE void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag) {
secp256k1_gej_verify(r);
secp256k1_gej_verify(a);
secp256k1_fe_cmov(&r->x, &a->x, flag);
secp256k1_fe_cmov(&r->y, &a->y, flag);
secp256k1_fe_cmov(&r->z, &a->z, flag);
r->infinity ^= (r->infinity ^ a->infinity) & flag;
secp256k1_gej_verify(r);
}
@@ -802,9 +865,11 @@ static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r,
}
static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
*r = *a;
secp256k1_ge_verify(a);
*r = *a;
secp256k1_fe_mul(&r->x, &r->x, &secp256k1_const_beta);
secp256k1_ge_verify(r);
}
@@ -826,8 +891,8 @@ static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
#ifdef EXHAUSTIVE_TEST_ORDER
secp256k1_gej out;
int i;
secp256k1_ge_verify(ge);
/* A very simple EC multiplication ladder that avoids a dependency on ecmult. */
secp256k1_gej_set_infinity(&out);
for (i = 0; i < 32; ++i) {
@@ -838,6 +903,8 @@ static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
}
return secp256k1_gej_is_infinity(&out);
#else
secp256k1_ge_verify(ge);
(void)ge;
/* The real secp256k1 group has cofactor 1, so the subgroup is the entire curve. */
return 1;