From a24112de66c2118dcaec89d4e651d1d3eeb181f7 Mon Sep 17 00:00:00 2001 From: Ken MacKay Date: Tue, 12 Nov 2024 08:44:34 -0800 Subject: [PATCH] Implement mitigation for hcca attack --- uECC.c | 78 ++++++++++++++++++++++++++++++---------------------------- 1 file changed, 41 insertions(+), 37 deletions(-) diff --git a/uECC.c b/uECC.c index a3d502c..1be5ffd 100644 --- a/uECC.c +++ b/uECC.c @@ -789,42 +789,45 @@ static void XYcZ_initial_double(uECC_word_t * X1, /* Input P = (x1, y1, Z), Q = (x2, y2, Z) Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3) or P => P', Q => P + Q + sub = x1' - x3 (used for subsequent call to XYcZ_addC()). */ static void XYcZ_add(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * X2, uECC_word_t * Y2, + uECC_word_t * sub, uECC_Curve curve) { /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ uECC_word_t t5[uECC_MAX_WORDS]; wordcount_t num_words = curve->num_words; - uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ - uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ - uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ - uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ - uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ - uECC_vli_modSquare_fast(t5, Y2, curve); /* t5 = (y2 - y1)^2 = D */ + uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ + uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ + uECC_vli_modMult_fast(X1, X1, t5, curve); /* x1' = x1*A = B */ + uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ + uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ + uECC_vli_modSquare_fast(t5, Y2, curve); /* t5 = (y2 - y1)^2 = D */ - uECC_vli_modSub(t5, t5, X1, curve->p, num_words); /* t5 = D - B */ - uECC_vli_modSub(t5, t5, X2, curve->p, num_words); /* t5 = D - B - C = x3 */ - uECC_vli_modSub(X2, X2, X1, curve->p, num_words); /* t3 = C - B */ - uECC_vli_modMult_fast(Y1, Y1, X2, curve); /* t2 = y1*(C - B) */ - uECC_vli_modSub(X2, X1, t5, curve->p, num_words); /* t3 = B - x3 */ - uECC_vli_modMult_fast(Y2, Y2, X2, curve); /* t4 = (y2 - y1)*(B - x3) */ - uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y3 */ + uECC_vli_modSub(t5, t5, X1, curve->p, num_words); /* t5 = D - B */ + uECC_vli_modSub(t5, t5, X2, curve->p, num_words); /* t5 = D - B - C = x3 */ + uECC_vli_modSub(X2, X2, X1, curve->p, num_words); /* t3 = C - B */ + uECC_vli_modMult_fast(Y1, Y1, X2, curve); /* y1' = y1*(C - B) */ + uECC_vli_modSub(sub, X1, t5, curve->p, num_words); /* s = B - x3 */ + uECC_vli_modMult_fast(Y2, Y2, sub, curve); /* t4 = (y2 - y1)*(B - x3) */ + uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y3 */ - uECC_vli_set(X2, t5, num_words); + uECC_vli_set(X2, t5, num_words); /* move x3 to output */ } -/* Input P = (x1, y1, Z), Q = (x2, y2, Z) - Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) +/* Input P = (x1, y1, Z), Q = (x2, y2, Z), sub = x1 - x2 + Output P - Q = (x3', y3', Z3), P + Q = (x3, y3, Z3) or P => P - Q, Q => P + Q */ static void XYcZ_addC(uECC_word_t * X1, uECC_word_t * Y1, uECC_word_t * X2, uECC_word_t * Y2, + uECC_word_t * sub, uECC_Curve curve) { /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ uECC_word_t t5[uECC_MAX_WORDS]; @@ -832,30 +835,29 @@ static void XYcZ_addC(uECC_word_t * X1, uECC_word_t t7[uECC_MAX_WORDS]; wordcount_t num_words = curve->num_words; - uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ - uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ - uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ - uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ + uECC_vli_modSquare_fast(t5, sub, curve); /* t5 = (x2 - x1)^2 = A */ + uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ + uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ uECC_vli_modAdd(t5, Y2, Y1, curve->p, num_words); /* t5 = y2 + y1 */ uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ uECC_vli_modSub(t6, X2, X1, curve->p, num_words); /* t6 = C - B */ - uECC_vli_modMult_fast(Y1, Y1, t6, curve); /* t2 = y1 * (C - B) = E */ + uECC_vli_modMult_fast(Y1, Y1, t6, curve); /* t2 = y1 * (C - B) = E */ uECC_vli_modAdd(t6, X1, X2, curve->p, num_words); /* t6 = B + C */ - uECC_vli_modSquare_fast(X2, Y2, curve); /* t3 = (y2 - y1)^2 = D */ + uECC_vli_modSquare_fast(X2, Y2, curve); /* t3 = (y2 - y1)^2 = D */ uECC_vli_modSub(X2, X2, t6, curve->p, num_words); /* t3 = D - (B + C) = x3 */ uECC_vli_modSub(t7, X1, X2, curve->p, num_words); /* t7 = B - x3 */ - uECC_vli_modMult_fast(Y2, Y2, t7, curve); /* t4 = (y2 - y1)*(B - x3) */ + uECC_vli_modMult_fast(Y2, Y2, t7, curve); /* t4 = (y2 - y1)*(B - x3) */ uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = (y2 - y1)*(B - x3) - E = y3 */ - uECC_vli_modSquare_fast(t7, t5, curve); /* t7 = (y2 + y1)^2 = F */ + uECC_vli_modSquare_fast(t7, t5, curve); /* t7 = (y2 + y1)^2 = F */ uECC_vli_modSub(t7, t7, t6, curve->p, num_words); /* t7 = F - (B + C) = x3' */ uECC_vli_modSub(t6, t7, X1, curve->p, num_words); /* t6 = x3' - B */ - uECC_vli_modMult_fast(t6, t6, t5, curve); /* t6 = (y2+y1)*(x3' - B) */ + uECC_vli_modMult_fast(t6, t6, t5, curve); /* t6 = (y2+y1)*(x3' - B) */ uECC_vli_modSub(Y1, t6, Y1, curve->p, num_words); /* t2 = (y2+y1)*(x3' - B) - E = y3' */ - uECC_vli_set(X1, t7, num_words); + uECC_vli_set(X1, t7, num_words); /* move x3' to output */ } /* result may overlap point. */ @@ -869,6 +871,7 @@ static void EccPoint_mult(uECC_word_t * result, uECC_word_t Rx[2][uECC_MAX_WORDS]; uECC_word_t Ry[2][uECC_MAX_WORDS]; uECC_word_t z[uECC_MAX_WORDS]; + uECC_word_t sub[uECC_MAX_WORDS]; bitcount_t i; uECC_word_t nb; wordcount_t num_words = curve->num_words; @@ -877,27 +880,27 @@ static void EccPoint_mult(uECC_word_t * result, uECC_vli_set(Ry[1], point + num_words, num_words); XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initial_Z, curve); + uECC_vli_modSub(sub, Rx[0], Rx[1], curve->p, num_words); for (i = num_bits - 2; i > 0; --i) { nb = !uECC_vli_testBit(scalar, i); - XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve); - XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve); + XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], sub, curve); + XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], sub, curve); } nb = !uECC_vli_testBit(scalar, 0); - XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve); + XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], sub, curve); /* Find final 1/Z value. */ uECC_vli_modSub(z, Rx[1], Rx[0], curve->p, num_words); /* X1 - X0 */ - uECC_vli_modMult_fast(z, z, Ry[1 - nb], curve); /* Yb * (X1 - X0) */ - uECC_vli_modMult_fast(z, z, point, curve); /* xP * Yb * (X1 - X0) */ + uECC_vli_modMult_fast(z, z, Ry[1 - nb], curve); /* Yb * (X1 - X0) */ + uECC_vli_modMult_fast(z, z, point, curve); /* xP * Yb * (X1 - X0) */ uECC_vli_modInv(z, z, curve->p, num_words); /* 1 / (xP * Yb * (X1 - X0)) */ - /* yP / (xP * Yb * (X1 - X0)) */ - uECC_vli_modMult_fast(z, z, point + num_words, curve); - uECC_vli_modMult_fast(z, z, Rx[1 - nb], curve); /* Xb * yP / (xP * Yb * (X1 - X0)) */ + uECC_vli_modMult_fast(z, z, point + num_words, curve); /* yP / (xP * Yb * (X1 - X0)) */ + uECC_vli_modMult_fast(z, z, Rx[1 - nb], curve); /* Xb * yP / (xP * Yb * (X1 - X0)) */ /* End 1/Z calculation */ - XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve); + XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], sub, curve); apply_z(Rx[0], Ry[0], z, curve); uECC_vli_set(result, Rx[0], num_words); @@ -1551,7 +1554,8 @@ int uECC_verify(const uint8_t *public_key, uECC_vli_set(tx, curve->G, num_words); uECC_vli_set(ty, curve->G + num_words, num_words); uECC_vli_modSub(z, sum, tx, curve->p, num_words); /* z = x2 - x1 */ - XYcZ_add(tx, ty, sum, sum + num_words, curve); + /* Note: safe to use tx for 'sub' param, since tx is not used after XYcZ_add. */ + XYcZ_add(tx, ty, sum, sum + num_words, tx, curve); uECC_vli_modInv(z, z, curve->p, num_words); /* z = 1/z */ apply_z(sum, sum + num_words, z, curve); @@ -1581,7 +1585,7 @@ int uECC_verify(const uint8_t *public_key, uECC_vli_set(ty, point + num_words, num_words); apply_z(tx, ty, z, curve); uECC_vli_modSub(tz, rx, tx, curve->p, num_words); /* Z = x2 - x1 */ - XYcZ_add(tx, ty, rx, ry, curve); + XYcZ_add(tx, ty, rx, ry, tx, curve); uECC_vli_modMult_fast(z, z, tz, curve); } }