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Save _normalize_weak calls in group add methods
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Also update the operations count comments in each of the affected
functions accordingly and remove a redundant VERIFY_CHECK in
secp256k1_gej_add_ge (the infinity value range check [0,1] is already
covered by secp256k1_gej_verify above).

Co-authored-by: Sebastian Falbesoner <sebastian.falbesoner@gmail.com>
Co-authored-by: Tim Ruffing <crypto@timruffing.de>
Co-authored-by: Jonas Nick <jonasd.nick@gmail.com>
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@peterdettman @theStack
@real-or-random @jonasnick
4 people committed Jul 28, 2023
1 parent c83afa6 commit b7c685e
Showing 1 changed file with 28 additions and 27 deletions.
55 changes: 28 additions & 27 deletions src/group_impl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -534,7 +534,7 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
}

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);
Expand All @@ -553,11 +553,11 @@ 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)) {
Expand Down Expand Up @@ -597,7 +597,7 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
}

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);
Expand Down Expand Up @@ -630,11 +630,11 @@ 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)) {
Expand Down Expand Up @@ -668,14 +668,13 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,


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.
Expand Down Expand Up @@ -728,17 +727,17 @@ 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);
Expand All @@ -748,34 +747,36 @@ 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) */
r->x = t; /* r->x = X3 = Ralt^2 + Q (2) */
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);
Expand Down

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