From: Saulo Alessandre <saulo.alessandre@xxxxxxxxxx>
* crypto/ecc.c
- ecc_get_curve - modified to recognize NIST_P384 and NISTP521;
- vli_rshift - created for use on vli_mmod_fast_521 for ecdsa;
- vli_mod_add - exported for use on ecdsa.c;
- vli_mmod_fast_384 - implements fast elliptic curve nist p384 [4];
- vli_mmod_fast_521 - implements fast elliptic curve nist p521 [4];
- vli_mmod_fast - changed params to receive struct ecc_curve*;
changed condition to use correct way to detect nist algo; added new curves
(384 and 521);
- vli_mmod_fast - changed params to receive ecc_curve;
- vli_mod_slow - moved from .h to .c and exported for use on ecdsa.c;
- vli_mod_mult_fast - changed params to receive struct ecc_curve*; exported
for use on ecdsa.c;
- vli_mod_square_fast - changed params to receive struct ecc_curve*;
exported for use on ecdsa.c;
- ecc_point_is_zero - exported for use on ecdsa.c;
- ecc_point_double_jacobian - changed params to receive struct ecc_curve*;
- apply_z - changed params to receive struct ecc_curve*;
- xycz_initial_double - changed params to receive struct ecc_curve*;
- xycz_add - changed params to receive struct ecc_curve*;
- xycz_add_c - changed params to receive struct ecc_curve*;
- ecc_point_mult - changed to pass struct ecc_curve* forward;
- ecc_point_mult_shamir - changed to pass struct ecc_curve* forward;
- ecc_is_pubkey_valid_partial - changed to pass struct ecc_curve*;
* crypto/ecc.h
- NIST_P384 and NIST_P521 constants defined;
- ecc_point_is_zero - added to export;
- vli_mod_slow - added to export;
- vli_mod_add - added to export
- vli_mod_fast - added to export;
- vli_mod_mult_fast - added to export.
---
crypto/ecc.c | 338 +++++++++++++++++++++++++++++++++++++++------------
crypto/ecc.h | 59 ++++++++-
2 files changed, 318 insertions(+), 79 deletions(-)
diff --git a/crypto/ecc.c b/crypto/ecc.c
index c80aa25994a0..f9e8b155f493 100644
--- a/crypto/ecc.c
+++ b/crypto/ecc.c
@@ -50,6 +50,10 @@ static inline const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
return fips_enabled ? NULL : &nist_p192;
case ECC_CURVE_NIST_P256:
return &nist_p256;
+ case ECC_CURVE_NIST_P384:
+ return &nist_p384;
+ case ECC_CURVE_NIST_P521:
+ return &nist_p521;
default:
return NULL;
}
@@ -235,6 +239,25 @@ static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
return carry;
}
+/* Computes result = in >> c, returning carry. */
+static u64 vli_rshift(u64 *result, const u64 *in, unsigned int shift,
+ unsigned int ndigits)
+{
+ u64 carry = 0;
+ int i;
+
+ for (i = 0; i < ndigits; i++) {
+ if (i + 1 < ndigits)
+ carry = in[i + 1] << (64 - shift);
+ else
+ carry = 0;
+
+ result[i] = (in[i] >> shift) | carry;
+ }
+
+ return carry;
+}
+
/* Computes vli = vli >> 1. */
static void vli_rshift1(u64 *vli, unsigned int ndigits)
{
@@ -474,7 +497,7 @@ static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
/* Computes result = (left + right) % mod.
* Assumes that left < mod and right < mod, result != mod.
*/
-static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
+void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
const u64 *mod, unsigned int ndigits)
{
u64 carry;
@@ -487,6 +510,7 @@ static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
if (carry || vli_cmp(result, mod, ndigits) >= 0)
vli_sub(result, result, mod, ndigits);
}
+EXPORT_SYMBOL(vli_mod_add);
/* Computes result = (left - right) % mod.
* Assumes that left < mod and right < mod, result != mod.
@@ -775,18 +799,156 @@ static void vli_mmod_fast_256(u64 *result, const u64 *product,
}
}
+#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
+#define AND64H(x64) (x64 & 0xffFFffFF00000000ull)
+#define AND64L(x64) (x64 & 0x00000000ffFFffFFull)
+
+/* Computes result = product % curve_prime
+ * from "Mathematical routines for the NIST prime elliptic curves"
+ */
+static void vli_mmod_fast_384(u64 *result, const u64 *product,
+ const u64 *curve_prime, u64 *tmp)
+{
+ int carry;
+ const unsigned int ndigits = 6;
+
+ /* t */
+ vli_set(result, product, ndigits);
+
+ /* s1 */
+ tmp[0] = 0; // 0 || 0
+ tmp[1] = 0; // 0 || 0
+ tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
+ tmp[3] = product[11]>>32; // 0 ||a23
+ tmp[4] = 0; // 0 || 0
+ tmp[5] = 0; // 0 || 0
+ carry = vli_lshift(tmp, tmp, 1, ndigits);
+ carry += vli_add(result, result, tmp, ndigits);
+
+ /* s2 */
+ tmp[0] = product[6]; //a13||a12
+ tmp[1] = product[7]; //a15||a14
+ tmp[2] = product[8]; //a17||a16
+ tmp[3] = product[9]; //a19||a18
+ tmp[4] = product[10]; //a21||a20
+ tmp[5] = product[11]; //a23||a22
+ carry += vli_add(result, result, tmp, ndigits);
+
+ /* s3 */
+ tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
+ tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
+ tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13
+ tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
+ tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
+ tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
+ carry += vli_add(result, result, tmp, ndigits);
+
+ /* s4 */
+ tmp[0] = AND64H(product[11]); //a23|| 0
+ tmp[1] = (product[10]<<32); //a20|| 0
+ tmp[2] = product[6]; //a13||a12
+ tmp[3] = product[7]; //a15||a14
+ tmp[4] = product[8]; //a17||a16
+ tmp[5] = product[9]; //a19||a18
+ carry += vli_add(result, result, tmp, ndigits);
+
+ /* s5 */
+ tmp[0] = 0; // 0|| 0
+ tmp[1] = 0; // 0|| 0
+ tmp[2] = product[10]; //a21||a20
+ tmp[3] = product[11]; //a23||a22
+ tmp[4] = 0; // 0|| 0
+ tmp[5] = 0; // 0|| 0
+ carry += vli_add(result, result, tmp, ndigits);
+
+ /* s6 */
+ tmp[0] = AND64L(product[10]); // 0 ||a20
+ tmp[1] = AND64H(product[10]); //a21|| 0
+ tmp[2] = product[11]; //a23||a22
+ tmp[3] = 0; // 0 || 0
+ tmp[4] = 0; // 0 || 0
+ tmp[5] = 0; // 0 || 0
+ carry += vli_add(result, result, tmp, ndigits);
+
+ /* d1 */
+ tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23
+ tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13
+ tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15
+ tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17
+ tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19
+ tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
+ carry -= vli_sub(result, result, tmp, ndigits);
+
+ /* d2 */
+ tmp[0] = (product[10]<<32); //a20|| 0
+ tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21
+ tmp[2] = (product[11]>>32); // 0 ||a23
+ tmp[3] = 0; // 0 || 0
+ tmp[4] = 0; // 0 || 0
+ tmp[5] = 0; // 0 || 0
+ carry -= vli_sub(result, result, tmp, ndigits);
+
+ /* d3 */
+ tmp[0] = 0; // 0 || 0
+ tmp[1] = AND64H(product[11]); //a23|| 0
+ tmp[2] = product[11]>>32; // 0 ||a23
+ tmp[3] = 0; // 0 || 0
+ tmp[4] = 0; // 0 || 0
+ tmp[5] = 0; // 0 || 0
+ carry -= vli_sub(result, result, tmp, ndigits);
+
+ if (carry < 0) {
+ do {
+ carry += vli_add(result, result, curve_prime, ndigits);
+ } while (carry < 0);
+ } else {
+ while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
+ carry -= vli_sub(result, result, curve_prime, ndigits);
+ }
+
+}
+
+#undef SL32OR32
+#undef AND64H
+#undef AND64L
+
+/* Computes result = product % curve_prime
+ * from "Mathematical routines for the NIST prime elliptic curves"
+ */
+static void vli_mmod_fast_521(u64 *result, const u64 *product,
+ const u64 *curve_prime, u64 *tmp)
+{
+ int carry;
+ const unsigned int ndigits = 9;
+
+ /* t 512 bits + 9 bits a0 .. a520 */
+ vli_set(result, product, 9);
+ result[8] &= 0x000001ff;
+
+ /* t 512 bits + 9 bits a521 .. a1041 */
+ vli_set(tmp, product + 8, ndigits);
+ vli_rshift(tmp, tmp, 9, ndigits);
+
+ carry = vli_add(result, result, tmp, ndigits);
+
+ while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
+ carry -= vli_sub(result, result, curve_prime, ndigits);
+}
+
/* Computes result = product % curve_prime for different curve_primes.
*
* Note that curve_primes are distinguished just by heuristic check and
* not by complete conformance check.
*/
static bool vli_mmod_fast(u64 *result, u64 *product,
- const u64 *curve_prime, unsigned int ndigits)
+ const struct ecc_curve *curve)
{
u64 tmp[2 * ECC_MAX_DIGITS];
+ const u64 *curve_prime = curve->p;
+ const unsigned int ndigits = curve->g.ndigits;
- /* Currently, both NIST primes have -1 in lowest qword. */
- if (curve_prime[0] != -1ull) {
+ /* Currently, all NIST have name nist_*. */
+ if (strncmp(curve->name, "nist_", 5) != 0) {
/* Try to handle Pseudo-Marsenne primes. */
if (curve_prime[ndigits - 1] == -1ull) {
vli_mmod_special(result, product, curve_prime,
@@ -809,6 +971,12 @@ static bool vli_mmod_fast(u64 *result, u64 *product,
case 4:
vli_mmod_fast_256(result, product, curve_prime, tmp);
break;
+ case 6:
+ vli_mmod_fast_384(result, product, curve_prime, tmp);
+ break;
+ case 9:
+ vli_mmod_fast_521(result, product, curve_prime, tmp);
+ break;
default:
pr_err_ratelimited("ecc: unsupported digits size!\n");
return false;
@@ -830,25 +998,38 @@ void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
}
EXPORT_SYMBOL(vli_mod_mult_slow);
+/* Computes result = input % curve_prime. */
+void vli_mod_slow(u64 *result, const u64 *input,
+ const u64 *mod, unsigned int ndigits)
+{
+ u64 product[ECC_MAX_DIGITS * 2] = { 0 };
+
+ vli_set(&product[0], input, ndigits);
+ vli_mmod_slow(result, product, mod, ndigits);
+}
+EXPORT_SYMBOL(vli_mod_slow);
+
/* Computes result = (left * right) % curve_prime. */
-static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
- const u64 *curve_prime, unsigned int ndigits)
+void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
+ const struct ecc_curve *curve)
{
u64 product[2 * ECC_MAX_DIGITS];
- vli_mult(product, left, right, ndigits);
- vli_mmod_fast(result, product, curve_prime, ndigits);
+ vli_mult(product, left, right, curve->g.ndigits);
+ vli_mmod_fast(result, product, curve);
}
+EXPORT_SYMBOL(vli_mod_mult_fast);
/* Computes result = left^2 % curve_prime. */
-static void vli_mod_square_fast(u64 *result, const u64 *left,
- const u64 *curve_prime, unsigned int ndigits)
+void vli_mod_square_fast(u64 *result, const u64 *left,
+ const struct ecc_curve *curve)
{
u64 product[2 * ECC_MAX_DIGITS];
- vli_square(product, left, ndigits);
- vli_mmod_fast(result, product, curve_prime, ndigits);
+ vli_square(product, left, curve->g.ndigits);
+ vli_mmod_fast(result, product, curve);
}
+EXPORT_SYMBOL(vli_mod_square_fast);
#define EVEN(vli) (!(vli[0] & 1))
/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
@@ -933,11 +1114,12 @@ EXPORT_SYMBOL(vli_mod_inv);
/* ------ Point operations ------ */
/* Returns true if p_point is the point at infinity, false otherwise. */
-static bool ecc_point_is_zero(const struct ecc_point *point)
+bool ecc_point_is_zero(const struct ecc_point *point)
{
return (vli_is_zero(point->x, point->ndigits) &&
vli_is_zero(point->y, point->ndigits));
}
+EXPORT_SYMBOL(ecc_point_is_zero);
/* Point multiplication algorithm using Montgomery's ladder with co-Z
* coordinates. From https://eprint.iacr.org/2011/338.pdf
@@ -945,25 +1127,27 @@ static bool ecc_point_is_zero(const struct ecc_point *point)
/* Double in place */
static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
- u64 *curve_prime, unsigned int ndigits)
+ const struct ecc_curve *curve)
{
/* t1 = x, t2 = y, t3 = z */
u64 t4[ECC_MAX_DIGITS];
u64 t5[ECC_MAX_DIGITS];
+ const u64 *curve_prime = curve->p;
+ const unsigned int ndigits = curve->g.ndigits;
if (vli_is_zero(z1, ndigits))
return;
/* t4 = y1^2 */
- vli_mod_square_fast(t4, y1, curve_prime, ndigits);
+ vli_mod_square_fast(t4, y1, curve);
/* t5 = x1*y1^2 = A */
- vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits);
+ vli_mod_mult_fast(t5, x1, t4, curve);
/* t4 = y1^4 */
- vli_mod_square_fast(t4, t4, curve_prime, ndigits);
+ vli_mod_square_fast(t4, t4, curve);
/* t2 = y1*z1 = z3 */
- vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits);
+ vli_mod_mult_fast(y1, y1, z1, curve);
/* t3 = z1^2 */
- vli_mod_square_fast(z1, z1, curve_prime, ndigits);
+ vli_mod_square_fast(z1, z1, curve);
/* t1 = x1 + z1^2 */
vli_mod_add(x1, x1, z1, curve_prime, ndigits);
@@ -972,7 +1156,7 @@ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
/* t3 = x1 - z1^2 */
vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
/* t1 = x1^2 - z1^4 */
- vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits);
+ vli_mod_mult_fast(x1, x1, z1, curve);
/* t3 = 2*(x1^2 - z1^4) */
vli_mod_add(z1, x1, x1, curve_prime, ndigits);
@@ -989,7 +1173,7 @@ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
/* t1 = 3/2*(x1^2 - z1^4) = B */
/* t3 = B^2 */
- vli_mod_square_fast(z1, x1, curve_prime, ndigits);
+ vli_mod_square_fast(z1, x1, curve);
/* t3 = B^2 - A */
vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
/* t3 = B^2 - 2A = x3 */
@@ -997,7 +1181,7 @@ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
/* t5 = A - x3 */
vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
/* t1 = B * (A - x3) */
- vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
+ vli_mod_mult_fast(x1, x1, t5, curve);
/* t4 = B * (A - x3) - y1^4 = y3 */
vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
@@ -1007,23 +1191,22 @@ static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
}
/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
-static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime,
- unsigned int ndigits)
+static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
{
u64 t1[ECC_MAX_DIGITS];
- vli_mod_square_fast(t1, z, curve_prime, ndigits); /* z^2 */
- vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */
- vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits); /* z^3 */
- vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* y1 * z^3 */
+ vli_mod_square_fast(t1, z, curve); /* z^2 */
+ vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */
+ vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */
+ vli_mod_mult_fast(y1, y1, t1, curve); /* y1 * z^3 */
}
/* P = (x1, y1) => 2P, (x2, y2) => P' */
static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
- u64 *p_initial_z, u64 *curve_prime,
- unsigned int ndigits)
+ u64 *p_initial_z, const struct ecc_curve *curve)
{
u64 z[ECC_MAX_DIGITS];
+ const unsigned int ndigits = curve->g.ndigits;
vli_set(x2, x1, ndigits);
vli_set(y2, y1, ndigits);
@@ -1034,35 +1217,37 @@ static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
if (p_initial_z)
vli_set(z, p_initial_z, ndigits);
- apply_z(x1, y1, z, curve_prime, ndigits);
+ apply_z(x1, y1, z, curve);
- ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits);
+ ecc_point_double_jacobian(x1, y1, z, curve);
- apply_z(x2, y2, z, curve_prime, ndigits);
+ apply_z(x2, y2, z, curve);
}
/* 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
*/
-static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
- unsigned int ndigits)
+static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
+ const struct ecc_curve *curve)
{
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
u64 t5[ECC_MAX_DIGITS];
+ const u64 *curve_prime = curve->p;
+ const unsigned int ndigits = curve->g.ndigits;
/* t5 = x2 - x1 */
vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
/* t5 = (x2 - x1)^2 = A */
- vli_mod_square_fast(t5, t5, curve_prime, ndigits);
+ vli_mod_square_fast(t5, t5, curve);
/* t1 = x1*A = B */
- vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
+ vli_mod_mult_fast(x1, x1, t5, curve);
/* t3 = x2*A = C */
- vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
+ vli_mod_mult_fast(x2, x2, t5, curve);
/* t4 = y2 - y1 */
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
/* t5 = (y2 - y1)^2 = D */
- vli_mod_square_fast(t5, y2, curve_prime, ndigits);
+ vli_mod_square_fast(t5, y2, curve);
/* t5 = D - B */
vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
@@ -1071,11 +1256,11 @@ static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
/* t3 = C - B */
vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
/* t2 = y1*(C - B) */
- vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits);
+ vli_mod_mult_fast(y1, y1, x2, curve);
/* t3 = B - x3 */
vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
/* t4 = (y2 - y1)*(B - x3) */
- vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits);
+ vli_mod_mult_fast(y2, y2, x2, curve);
/* t4 = y3 */
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
@@ -1086,22 +1271,24 @@ static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
* Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
* or P => P - Q, Q => P + Q
*/
-static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
- unsigned int ndigits)
+static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
+ const struct ecc_curve *curve)
{
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
u64 t5[ECC_MAX_DIGITS];
u64 t6[ECC_MAX_DIGITS];
u64 t7[ECC_MAX_DIGITS];
+ const u64 *curve_prime = curve->p;
+ const unsigned int ndigits = curve->g.ndigits;
/* t5 = x2 - x1 */
vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
/* t5 = (x2 - x1)^2 = A */
- vli_mod_square_fast(t5, t5, curve_prime, ndigits);
+ vli_mod_square_fast(t5, t5, curve);
/* t1 = x1*A = B */
- vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
+ vli_mod_mult_fast(x1, x1, t5, curve);
/* t3 = x2*A = C */
- vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
+ vli_mod_mult_fast(x2, x2, t5, curve);
/* t4 = y2 + y1 */
vli_mod_add(t5, y2, y1, curve_prime, ndigits);
/* t4 = y2 - y1 */
@@ -1110,29 +1297,29 @@ static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
/* t6 = C - B */
vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
/* t2 = y1 * (C - B) */
- vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits);
+ vli_mod_mult_fast(y1, y1, t6, curve);
/* t6 = B + C */
vli_mod_add(t6, x1, x2, curve_prime, ndigits);
/* t3 = (y2 - y1)^2 */
- vli_mod_square_fast(x2, y2, curve_prime, ndigits);
+ vli_mod_square_fast(x2, y2, curve);
/* t3 = x3 */
vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
/* t7 = B - x3 */
vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
/* t4 = (y2 - y1)*(B - x3) */
- vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits);
+ vli_mod_mult_fast(y2, y2, t7, curve);
/* t4 = y3 */
vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
/* t7 = (y2 + y1)^2 = F */
- vli_mod_square_fast(t7, t5, curve_prime, ndigits);
+ vli_mod_square_fast(t7, t5, curve);
/* t7 = x3' */
vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
/* t6 = x3' - B */
vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
/* t6 = (y2 + y1)*(x3' - B) */
- vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits);
+ vli_mod_mult_fast(t6, t6, t5, curve);
/* t2 = y3' */
vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
@@ -1162,41 +1349,37 @@ static void ecc_point_mult(struct ecc_point *result,
vli_set(rx[1], point->x, ndigits);
vli_set(ry[1], point->y, ndigits);
- xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime,
- ndigits);
+ xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve);
for (i = num_bits - 2; i > 0; i--) {
nb = !vli_test_bit(scalar, i);
- xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
- ndigits);
- xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime,
- ndigits);
+ xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
+ xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
}
nb = !vli_test_bit(scalar, 0);
- xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
- ndigits);
+ xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
/* Find final 1/Z value. */
/* X1 - X0 */
vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
/* Yb * (X1 - X0) */
- vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits);
+ vli_mod_mult_fast(z, z, ry[1 - nb], curve);
/* xP * Yb * (X1 - X0) */
- vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits);
+ vli_mod_mult_fast(z, z, point->x, curve);
/* 1 / (xP * Yb * (X1 - X0)) */
vli_mod_inv(z, z, curve_prime, point->ndigits);
/* yP / (xP * Yb * (X1 - X0)) */
- vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits);
+ vli_mod_mult_fast(z, z, point->y, curve);
/* Xb * yP / (xP * Yb * (X1 - X0)) */
- vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits);
+ vli_mod_mult_fast(z, z, rx[1 - nb], curve);
/* End 1/Z calculation */
- xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits);
+ xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
- apply_z(rx[0], ry[0], z, curve_prime, ndigits);
+ apply_z(rx[0], ry[0], z, curve);
vli_set(result->x, rx[0], ndigits);
vli_set(result->y, ry[0], ndigits);
@@ -1217,9 +1400,9 @@ static void ecc_point_add(const struct ecc_point *result,
vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
vli_set(px, p->x, ndigits);
vli_set(py, p->y, ndigits);
- xycz_add(px, py, result->x, result->y, curve->p, ndigits);
+ xycz_add(px, py, result->x, result->y, curve);
vli_mod_inv(z, z, curve->p, ndigits);
- apply_z(result->x, result->y, z, curve->p, ndigits);
+ apply_z(result->x, result->y, z, curve);
}
/* Computes R = u1P + u2Q mod p using Shamir's trick.
@@ -1248,8 +1431,7 @@ void ecc_point_mult_shamir(const struct ecc_point *result,
points[2] = q;
points[3] = ∑
- num_bits = max(vli_num_bits(u1, ndigits),
- vli_num_bits(u2, ndigits));
+ num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
i = num_bits - 1;
idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
point = points[idx];
@@ -1260,7 +1442,7 @@ void ecc_point_mult_shamir(const struct ecc_point *result,
z[0] = 1;
for (--i; i >= 0; i--) {
- ecc_point_double_jacobian(rx, ry, z, curve->p, ndigits);
+ ecc_point_double_jacobian(rx, ry, z, curve);
idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
point = points[idx];
if (point) {
@@ -1270,14 +1452,14 @@ void ecc_point_mult_shamir(const struct ecc_point *result,
vli_set(tx, point->x, ndigits);
vli_set(ty, point->y, ndigits);
- apply_z(tx, ty, z, curve->p, ndigits);
+ apply_z(tx, ty, z, curve);
vli_mod_sub(tz, rx, tx, curve->p, ndigits);
- xycz_add(tx, ty, rx, ry, curve->p, ndigits);
- vli_mod_mult_fast(z, z, tz, curve->p, ndigits);
+ xycz_add(tx, ty, rx, ry, curve);
+ vli_mod_mult_fast(z, z, tz, curve);
}
}
vli_mod_inv(z, z, curve->p, ndigits);
- apply_z(rx, ry, z, curve->p, ndigits);
+ apply_z(rx, ry, z, curve);
}
EXPORT_SYMBOL(ecc_point_mult_shamir);
@@ -1441,10 +1623,10 @@ int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
return -EINVAL;
/* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
- vli_mod_square_fast(yy, pk->y, curve->p, pk->ndigits); /* y^2 */
- vli_mod_square_fast(xxx, pk->x, curve->p, pk->ndigits); /* x^2 */
- vli_mod_mult_fast(xxx, xxx, pk->x, curve->p, pk->ndigits); /* x^3 */
- vli_mod_mult_fast(w, curve->a, pk->x, curve->p, pk->ndigits); /* a·x */
+ vli_mod_square_fast(yy, pk->y, curve); /* y^2 */
+ vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
+ vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
+ vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */
vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
diff --git a/crypto/ecc.h b/crypto/ecc.h
index d4e546b9ad79..f02ea6cfd10d 100644
--- a/crypto/ecc.h
+++ b/crypto/ecc.h
@@ -29,7 +29,9 @@
/* One digit is u64 qword. */
#define ECC_CURVE_NIST_P192_DIGITS 3
#define ECC_CURVE_NIST_P256_DIGITS 4
-#define ECC_MAX_DIGITS (512 / 64)
+#define ECC_CURVE_NIST_P384_DIGITS 6
+#define ECC_CURVE_NIST_P521_DIGITS 9
+#define ECC_MAX_DIGITS (ECC_CURVE_NIST_P521_DIGITS)
#define ECC_DIGITS_TO_BYTES_SHIFT 3
@@ -147,6 +149,9 @@ int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
struct ecc_point *pk);
+/* Returns true if p_point is the point at infinity, false otherwise. */
+bool ecc_point_is_zero(const struct ecc_point *point);
+
/**
* ecc_is_pubkey_valid_full() - Full public key validation
*
@@ -225,6 +230,22 @@ void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits);
void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
unsigned int ndigits);
+/**
+ * vli_mod_slow() - Computes result = product % mod, where product is 2N words
+ * long.
+ * Reference: Ken MacKay's micro-ecc.
+ * Currently only designed to work for curve_p or curve_n.
+ *
+ * @result: where to write result value
+ * @product: vli number to operate mod on
+ * @mod: modulus
+ * @ndigits: length of all vlis
+ *
+ * Note: Assumes that mod is big enough curve order.
+ */
+void vli_mod_slow(u64 *result, const u64 *input, const u64 *mod,
+ unsigned int ndigits);
+
/**
* vli_mod_mult_slow() - Modular multiplication
*
@@ -239,6 +260,42 @@ void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
const u64 *mod, unsigned int ndigits);
+/* Computes result = (left + right) % mod.
+ * Assumes that left < mod and right < mod, result != mod.
+ */
+void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
+ const u64 *mod, unsigned int ndigits);
+
+/**
+ * vli_mod_fast() - Computes result = product % curve_prime for different
+ * curve_primes.
+ *
+ * Note that curve_primes are distinguished just by heuristic check and
+ * not by complete conformance check.
+ *
+ * @result: where to write result value
+ * @input: vli number to multiply with @right
+ * @mod: mod
+ * @ndigits: length of all vlis
+ *
+ * Note: Assumes that mod is big enough curve order.
+ */
+void vli_mod_fast(u64 *result, const u64 *input, const struct ecc_curve *curve);
+
+/**
+ * vli_mod_mult_fast() - Modular multiplication
+ *
+ * @result: where to write result value
+ * @left: vli number to multiply with @right
+ * @right: vli number to multiply with @left
+ * @mod: modulus
+ * @ndigits: length of all vlis
+ *
+ * Note: Assumes that mod is big enough curve order.
+ */
+void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
+ const struct ecc_curve *curve);
+
/**
* ecc_point_mult_shamir() - Add two points multiplied by scalars
*
--
2.25.1
