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-rw-r--r--src/crypto/fipsmodule/ec/p224-64.c542
1 files changed, 271 insertions, 271 deletions
diff --git a/src/crypto/fipsmodule/ec/p224-64.c b/src/crypto/fipsmodule/ec/p224-64.c
index 67dfcc85..ec5a93d2 100644
--- a/src/crypto/fipsmodule/ec/p224-64.c
+++ b/src/crypto/fipsmodule/ec/p224-64.c
@@ -12,10 +12,10 @@
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
-/* A 64-bit implementation of the NIST P-224 elliptic curve point multiplication
- *
- * Inspired by Daniel J. Bernstein's public domain nistp224 implementation
- * and Adam Langley's public domain 64-bit C implementation of curve25519. */
+// A 64-bit implementation of the NIST P-224 elliptic curve point multiplication
+//
+// Inspired by Daniel J. Bernstein's public domain nistp224 implementation
+// and Adam Langley's public domain 64-bit C implementation of curve25519.
#include <openssl/base.h>
@@ -34,18 +34,18 @@
#include "../../internal.h"
-/* Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
- * using 64-bit coefficients called 'limbs', and sometimes (for multiplication
- * results) as b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 +
- * 2^336*b_6 using 128-bit coefficients called 'widelimbs'. A 4-p224_limb
- * representation is an 'p224_felem'; a 7-p224_widelimb representation is a
- * 'p224_widefelem'. Even within felems, bits of adjacent limbs overlap, and we
- * don't always reduce the representations: we ensure that inputs to each
- * p224_felem multiplication satisfy a_i < 2^60, so outputs satisfy b_i <
- * 4*2^60*2^60, and fit into a 128-bit word without overflow. The coefficients
- * are then again partially reduced to obtain an p224_felem satisfying a_i <
- * 2^57. We only reduce to the unique minimal representation at the end of the
- * computation. */
+// Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
+// using 64-bit coefficients called 'limbs', and sometimes (for multiplication
+// results) as b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 +
+// 2^336*b_6 using 128-bit coefficients called 'widelimbs'. A 4-p224_limb
+// representation is an 'p224_felem'; a 7-p224_widelimb representation is a
+// 'p224_widefelem'. Even within felems, bits of adjacent limbs overlap, and we
+// don't always reduce the representations: we ensure that inputs to each
+// p224_felem multiplication satisfy a_i < 2^60, so outputs satisfy b_i <
+// 4*2^60*2^60, and fit into a 128-bit word without overflow. The coefficients
+// are then again partially reduced to obtain an p224_felem satisfying a_i <
+// 2^57. We only reduce to the unique minimal representation at the end of the
+// computation.
typedef uint64_t p224_limb;
typedef uint128_t p224_widelimb;
@@ -53,40 +53,40 @@ typedef uint128_t p224_widelimb;
typedef p224_limb p224_felem[4];
typedef p224_widelimb p224_widefelem[7];
-/* Field element represented as a byte arrary. 28*8 = 224 bits is also the
- * group order size for the elliptic curve, and we also use this type for
- * scalars for point multiplication. */
+// Field element represented as a byte arrary. 28*8 = 224 bits is also the
+// group order size for the elliptic curve, and we also use this type for
+// scalars for point multiplication.
typedef uint8_t p224_felem_bytearray[28];
-/* Precomputed multiples of the standard generator
- * Points are given in coordinates (X, Y, Z) where Z normally is 1
- * (0 for the point at infinity).
- * For each field element, slice a_0 is word 0, etc.
- *
- * The table has 2 * 16 elements, starting with the following:
- * index | bits | point
- * ------+---------+------------------------------
- * 0 | 0 0 0 0 | 0G
- * 1 | 0 0 0 1 | 1G
- * 2 | 0 0 1 0 | 2^56G
- * 3 | 0 0 1 1 | (2^56 + 1)G
- * 4 | 0 1 0 0 | 2^112G
- * 5 | 0 1 0 1 | (2^112 + 1)G
- * 6 | 0 1 1 0 | (2^112 + 2^56)G
- * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G
- * 8 | 1 0 0 0 | 2^168G
- * 9 | 1 0 0 1 | (2^168 + 1)G
- * 10 | 1 0 1 0 | (2^168 + 2^56)G
- * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G
- * 12 | 1 1 0 0 | (2^168 + 2^112)G
- * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G
- * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G
- * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G
- * followed by a copy of this with each element multiplied by 2^28.
- *
- * The reason for this is so that we can clock bits into four different
- * locations when doing simple scalar multiplies against the base point,
- * and then another four locations using the second 16 elements. */
+// Precomputed multiples of the standard generator
+// Points are given in coordinates (X, Y, Z) where Z normally is 1
+// (0 for the point at infinity).
+// For each field element, slice a_0 is word 0, etc.
+//
+// The table has 2 * 16 elements, starting with the following:
+// index | bits | point
+// ------+---------+------------------------------
+// 0 | 0 0 0 0 | 0G
+// 1 | 0 0 0 1 | 1G
+// 2 | 0 0 1 0 | 2^56G
+// 3 | 0 0 1 1 | (2^56 + 1)G
+// 4 | 0 1 0 0 | 2^112G
+// 5 | 0 1 0 1 | (2^112 + 1)G
+// 6 | 0 1 1 0 | (2^112 + 2^56)G
+// 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G
+// 8 | 1 0 0 0 | 2^168G
+// 9 | 1 0 0 1 | (2^168 + 1)G
+// 10 | 1 0 1 0 | (2^168 + 2^56)G
+// 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G
+// 12 | 1 1 0 0 | (2^168 + 2^112)G
+// 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G
+// 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G
+// 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G
+// followed by a copy of this with each element multiplied by 2^28.
+//
+// The reason for this is so that we can clock bits into four different
+// locations when doing simple scalar multiplies against the base point,
+// and then another four locations using the second 16 elements.
static const p224_felem g_p224_pre_comp[2][16][3] = {
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf},
@@ -187,7 +187,7 @@ static uint64_t p224_load_u64(const uint8_t in[8]) {
return ret;
}
-/* Helper functions to convert field elements to/from internal representation */
+// Helper functions to convert field elements to/from internal representation
static void p224_bin28_to_felem(p224_felem out, const uint8_t in[28]) {
out[0] = p224_load_u64(in) & 0x00ffffffffffffff;
out[1] = p224_load_u64(in + 7) & 0x00ffffffffffffff;
@@ -204,16 +204,16 @@ static void p224_felem_to_bin28(uint8_t out[28], const p224_felem in) {
}
}
-/* To preserve endianness when using BN_bn2bin and BN_bin2bn */
+// To preserve endianness when using BN_bn2bin and BN_bin2bn
static void p224_flip_endian(uint8_t *out, const uint8_t *in, size_t len) {
for (size_t i = 0; i < len; ++i) {
out[i] = in[len - 1 - i];
}
}
-/* From OpenSSL BIGNUM to internal representation */
+// From OpenSSL BIGNUM to internal representation
static int p224_BN_to_felem(p224_felem out, const BIGNUM *bn) {
- /* BN_bn2bin eats leading zeroes */
+ // BN_bn2bin eats leading zeroes
p224_felem_bytearray b_out;
OPENSSL_memset(b_out, 0, sizeof(b_out));
size_t num_bytes = BN_num_bytes(bn);
@@ -230,7 +230,7 @@ static int p224_BN_to_felem(p224_felem out, const BIGNUM *bn) {
return 1;
}
-/* From internal representation to OpenSSL BIGNUM */
+// From internal representation to OpenSSL BIGNUM
static BIGNUM *p224_felem_to_BN(BIGNUM *out, const p224_felem in) {
p224_felem_bytearray b_in, b_out;
p224_felem_to_bin28(b_in, in);
@@ -238,10 +238,10 @@ static BIGNUM *p224_felem_to_BN(BIGNUM *out, const p224_felem in) {
return BN_bin2bn(b_out, sizeof(b_out), out);
}
-/* Field operations, using the internal representation of field elements.
- * NB! These operations are specific to our point multiplication and cannot be
- * expected to be correct in general - e.g., multiplication with a large scalar
- * will cause an overflow. */
+// Field operations, using the internal representation of field elements.
+// NB! These operations are specific to our point multiplication and cannot be
+// expected to be correct in general - e.g., multiplication with a large scalar
+// will cause an overflow.
static void p224_felem_assign(p224_felem out, const p224_felem in) {
out[0] = in[0];
@@ -250,7 +250,7 @@ static void p224_felem_assign(p224_felem out, const p224_felem in) {
out[3] = in[3];
}
-/* Sum two field elements: out += in */
+// Sum two field elements: out += in
static void p224_felem_sum(p224_felem out, const p224_felem in) {
out[0] += in[0];
out[1] += in[1];
@@ -258,8 +258,8 @@ static void p224_felem_sum(p224_felem out, const p224_felem in) {
out[3] += in[3];
}
-/* Get negative value: out = -in */
-/* Assumes in[i] < 2^57 */
+// Get negative value: out = -in
+// Assumes in[i] < 2^57
static void p224_felem_neg(p224_felem out, const p224_felem in) {
static const p224_limb two58p2 =
(((p224_limb)1) << 58) + (((p224_limb)1) << 2);
@@ -268,15 +268,15 @@ static void p224_felem_neg(p224_felem out, const p224_felem in) {
static const p224_limb two58m42m2 =
(((p224_limb)1) << 58) - (((p224_limb)1) << 42) - (((p224_limb)1) << 2);
- /* Set to 0 mod 2^224-2^96+1 to ensure out > in */
+ // Set to 0 mod 2^224-2^96+1 to ensure out > in
out[0] = two58p2 - in[0];
out[1] = two58m42m2 - in[1];
out[2] = two58m2 - in[2];
out[3] = two58m2 - in[3];
}
-/* Subtract field elements: out -= in */
-/* Assumes in[i] < 2^57 */
+// Subtract field elements: out -= in
+// Assumes in[i] < 2^57
static void p224_felem_diff(p224_felem out, const p224_felem in) {
static const p224_limb two58p2 =
(((p224_limb)1) << 58) + (((p224_limb)1) << 2);
@@ -285,7 +285,7 @@ static void p224_felem_diff(p224_felem out, const p224_felem in) {
static const p224_limb two58m42m2 =
(((p224_limb)1) << 58) - (((p224_limb)1) << 42) - (((p224_limb)1) << 2);
- /* Add 0 mod 2^224-2^96+1 to ensure out > in */
+ // Add 0 mod 2^224-2^96+1 to ensure out > in
out[0] += two58p2;
out[1] += two58m42m2;
out[2] += two58m2;
@@ -297,8 +297,8 @@ static void p224_felem_diff(p224_felem out, const p224_felem in) {
out[3] -= in[3];
}
-/* Subtract in unreduced 128-bit mode: out -= in */
-/* Assumes in[i] < 2^119 */
+// Subtract in unreduced 128-bit mode: out -= in
+// Assumes in[i] < 2^119
static void p224_widefelem_diff(p224_widefelem out, const p224_widefelem in) {
static const p224_widelimb two120 = ((p224_widelimb)1) << 120;
static const p224_widelimb two120m64 =
@@ -307,7 +307,7 @@ static void p224_widefelem_diff(p224_widefelem out, const p224_widefelem in) {
(((p224_widelimb)1) << 104) -
(((p224_widelimb)1) << 64);
- /* Add 0 mod 2^224-2^96+1 to ensure out > in */
+ // Add 0 mod 2^224-2^96+1 to ensure out > in
out[0] += two120;
out[1] += two120m64;
out[2] += two120m64;
@@ -325,8 +325,8 @@ static void p224_widefelem_diff(p224_widefelem out, const p224_widefelem in) {
out[6] -= in[6];
}
-/* Subtract in mixed mode: out128 -= in64 */
-/* in[i] < 2^63 */
+// Subtract in mixed mode: out128 -= in64
+// in[i] < 2^63
static void p224_felem_diff_128_64(p224_widefelem out, const p224_felem in) {
static const p224_widelimb two64p8 =
(((p224_widelimb)1) << 64) + (((p224_widelimb)1) << 8);
@@ -336,7 +336,7 @@ static void p224_felem_diff_128_64(p224_widefelem out, const p224_felem in) {
(((p224_widelimb)1) << 48) -
(((p224_widelimb)1) << 8);
- /* Add 0 mod 2^224-2^96+1 to ensure out > in */
+ // Add 0 mod 2^224-2^96+1 to ensure out > in
out[0] += two64p8;
out[1] += two64m48m8;
out[2] += two64m8;
@@ -348,8 +348,8 @@ static void p224_felem_diff_128_64(p224_widefelem out, const p224_felem in) {
out[3] -= in[3];
}
-/* Multiply a field element by a scalar: out = out * scalar
- * The scalars we actually use are small, so results fit without overflow */
+// Multiply a field element by a scalar: out = out * scalar
+// The scalars we actually use are small, so results fit without overflow
static void p224_felem_scalar(p224_felem out, const p224_limb scalar) {
out[0] *= scalar;
out[1] *= scalar;
@@ -357,8 +357,8 @@ static void p224_felem_scalar(p224_felem out, const p224_limb scalar) {
out[3] *= scalar;
}
-/* Multiply an unreduced field element by a scalar: out = out * scalar
- * The scalars we actually use are small, so results fit without overflow */
+// Multiply an unreduced field element by a scalar: out = out * scalar
+// The scalars we actually use are small, so results fit without overflow
static void p224_widefelem_scalar(p224_widefelem out,
const p224_widelimb scalar) {
out[0] *= scalar;
@@ -370,7 +370,7 @@ static void p224_widefelem_scalar(p224_widefelem out,
out[6] *= scalar;
}
-/* Square a field element: out = in^2 */
+// Square a field element: out = in^2
static void p224_felem_square(p224_widefelem out, const p224_felem in) {
p224_limb tmp0, tmp1, tmp2;
tmp0 = 2 * in[0];
@@ -385,7 +385,7 @@ static void p224_felem_square(p224_widefelem out, const p224_felem in) {
out[6] = ((p224_widelimb)in[3]) * in[3];
}
-/* Multiply two field elements: out = in1 * in2 */
+// Multiply two field elements: out = in1 * in2
static void p224_felem_mul(p224_widefelem out, const p224_felem in1,
const p224_felem in2) {
out[0] = ((p224_widelimb)in1[0]) * in2[0];
@@ -400,9 +400,9 @@ static void p224_felem_mul(p224_widefelem out, const p224_felem in1,
out[6] = ((p224_widelimb)in1[3]) * in2[3];
}
-/* Reduce seven 128-bit coefficients to four 64-bit coefficients.
- * Requires in[i] < 2^126,
- * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */
+// Reduce seven 128-bit coefficients to four 64-bit coefficients.
+// Requires in[i] < 2^126,
+// ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16
static void p224_felem_reduce(p224_felem out, const p224_widefelem in) {
static const p224_widelimb two127p15 =
(((p224_widelimb)1) << 127) + (((p224_widelimb)1) << 15);
@@ -413,14 +413,14 @@ static void p224_felem_reduce(p224_felem out, const p224_widefelem in) {
(((p224_widelimb)1) << 55);
p224_widelimb output[5];
- /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
+ // Add 0 mod 2^224-2^96+1 to ensure all differences are positive
output[0] = in[0] + two127p15;
output[1] = in[1] + two127m71m55;
output[2] = in[2] + two127m71;
output[3] = in[3];
output[4] = in[4];
- /* Eliminate in[4], in[5], in[6] */
+ // Eliminate in[4], in[5], in[6]
output[4] += in[6] >> 16;
output[3] += (in[6] & 0xffff) << 40;
output[2] -= in[6];
@@ -433,90 +433,90 @@ static void p224_felem_reduce(p224_felem out, const p224_widefelem in) {
output[1] += (output[4] & 0xffff) << 40;
output[0] -= output[4];
- /* Carry 2 -> 3 -> 4 */
+ // Carry 2 -> 3 -> 4
output[3] += output[2] >> 56;
output[2] &= 0x00ffffffffffffff;
output[4] = output[3] >> 56;
output[3] &= 0x00ffffffffffffff;
- /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */
+ // Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72
- /* Eliminate output[4] */
+ // Eliminate output[4]
output[2] += output[4] >> 16;
- /* output[2] < 2^56 + 2^56 = 2^57 */
+ // output[2] < 2^56 + 2^56 = 2^57
output[1] += (output[4] & 0xffff) << 40;
output[0] -= output[4];
- /* Carry 0 -> 1 -> 2 -> 3 */
+ // Carry 0 -> 1 -> 2 -> 3
output[1] += output[0] >> 56;
out[0] = output[0] & 0x00ffffffffffffff;
output[2] += output[1] >> 56;
- /* output[2] < 2^57 + 2^72 */
+ // output[2] < 2^57 + 2^72
out[1] = output[1] & 0x00ffffffffffffff;
output[3] += output[2] >> 56;
- /* output[3] <= 2^56 + 2^16 */
+ // output[3] <= 2^56 + 2^16
out[2] = output[2] & 0x00ffffffffffffff;
- /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
- * out[3] <= 2^56 + 2^16 (due to final carry),
- * so out < 2*p */
+ // out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
+ // out[3] <= 2^56 + 2^16 (due to final carry),
+ // so out < 2*p
out[3] = output[3];
}
-/* Reduce to unique minimal representation.
- * Requires 0 <= in < 2*p (always call p224_felem_reduce first) */
+// Reduce to unique minimal representation.
+// Requires 0 <= in < 2*p (always call p224_felem_reduce first)
static void p224_felem_contract(p224_felem out, const p224_felem in) {
static const int64_t two56 = ((p224_limb)1) << 56;
- /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */
- /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */
+ // 0 <= in < 2*p, p = 2^224 - 2^96 + 1
+ // if in > p , reduce in = in - 2^224 + 2^96 - 1
int64_t tmp[4], a;
tmp[0] = in[0];
tmp[1] = in[1];
tmp[2] = in[2];
tmp[3] = in[3];
- /* Case 1: a = 1 iff in >= 2^224 */
+ // Case 1: a = 1 iff in >= 2^224
a = (in[3] >> 56);
tmp[0] -= a;
tmp[1] += a << 40;
tmp[3] &= 0x00ffffffffffffff;
- /* Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 and
- * the lower part is non-zero */
+ // Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 and
+ // the lower part is non-zero
a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) |
(((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63);
a &= 0x00ffffffffffffff;
- /* turn a into an all-one mask (if a = 0) or an all-zero mask */
+ // turn a into an all-one mask (if a = 0) or an all-zero mask
a = (a - 1) >> 63;
- /* subtract 2^224 - 2^96 + 1 if a is all-one */
+ // subtract 2^224 - 2^96 + 1 if a is all-one
tmp[3] &= a ^ 0xffffffffffffffff;
tmp[2] &= a ^ 0xffffffffffffffff;
tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
tmp[0] -= 1 & a;
- /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must
- * be non-zero, so we only need one step */
+ // eliminate negative coefficients: if tmp[0] is negative, tmp[1] must
+ // be non-zero, so we only need one step
a = tmp[0] >> 63;
tmp[0] += two56 & a;
tmp[1] -= 1 & a;
- /* carry 1 -> 2 -> 3 */
+ // carry 1 -> 2 -> 3
tmp[2] += tmp[1] >> 56;
tmp[1] &= 0x00ffffffffffffff;
tmp[3] += tmp[2] >> 56;
tmp[2] &= 0x00ffffffffffffff;
- /* Now 0 <= out < p */
+ // Now 0 <= out < p
out[0] = tmp[0];
out[1] = tmp[1];
out[2] = tmp[2];
out[3] = tmp[3];
}
-/* Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field
- * elements are reduced to in < 2^225, so we only need to check three cases: 0,
- * 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 */
+// Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field
+// elements are reduced to in < 2^225, so we only need to check three cases: 0,
+// 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2
static p224_limb p224_felem_is_zero(const p224_felem in) {
p224_limb zero = in[0] | in[1] | in[2] | in[3];
zero = (((int64_t)(zero)-1) >> 63) & 1;
@@ -532,92 +532,92 @@ static p224_limb p224_felem_is_zero(const p224_felem in) {
return (zero | two224m96p1 | two225m97p2);
}
-/* Invert a field element */
-/* Computation chain copied from djb's code */
+// Invert a field element
+// Computation chain copied from djb's code
static void p224_felem_inv(p224_felem out, const p224_felem in) {
p224_felem ftmp, ftmp2, ftmp3, ftmp4;
p224_widefelem tmp;
p224_felem_square(tmp, in);
- p224_felem_reduce(ftmp, tmp); /* 2 */
+ p224_felem_reduce(ftmp, tmp); // 2
p224_felem_mul(tmp, in, ftmp);
- p224_felem_reduce(ftmp, tmp); /* 2^2 - 1 */
+ p224_felem_reduce(ftmp, tmp); // 2^2 - 1
p224_felem_square(tmp, ftmp);
- p224_felem_reduce(ftmp, tmp); /* 2^3 - 2 */
+ p224_felem_reduce(ftmp, tmp); // 2^3 - 2
p224_felem_mul(tmp, in, ftmp);
- p224_felem_reduce(ftmp, tmp); /* 2^3 - 1 */
+ p224_felem_reduce(ftmp, tmp); // 2^3 - 1
p224_felem_square(tmp, ftmp);
- p224_felem_reduce(ftmp2, tmp); /* 2^4 - 2 */
+ p224_felem_reduce(ftmp2, tmp); // 2^4 - 2
p224_felem_square(tmp, ftmp2);
- p224_felem_reduce(ftmp2, tmp); /* 2^5 - 4 */
+ p224_felem_reduce(ftmp2, tmp); // 2^5 - 4
p224_felem_square(tmp, ftmp2);
- p224_felem_reduce(ftmp2, tmp); /* 2^6 - 8 */
+ p224_felem_reduce(ftmp2, tmp); // 2^6 - 8
p224_felem_mul(tmp, ftmp2, ftmp);
- p224_felem_reduce(ftmp, tmp); /* 2^6 - 1 */
+ p224_felem_reduce(ftmp, tmp); // 2^6 - 1
p224_felem_square(tmp, ftmp);
- p224_felem_reduce(ftmp2, tmp); /* 2^7 - 2 */
- for (size_t i = 0; i < 5; ++i) { /* 2^12 - 2^6 */
+ p224_felem_reduce(ftmp2, tmp); // 2^7 - 2
+ for (size_t i = 0; i < 5; ++i) { // 2^12 - 2^6
p224_felem_square(tmp, ftmp2);
p224_felem_reduce(ftmp2, tmp);
}
p224_felem_mul(tmp, ftmp2, ftmp);
- p224_felem_reduce(ftmp2, tmp); /* 2^12 - 1 */
+ p224_felem_reduce(ftmp2, tmp); // 2^12 - 1
p224_felem_square(tmp, ftmp2);
- p224_felem_reduce(ftmp3, tmp); /* 2^13 - 2 */
- for (size_t i = 0; i < 11; ++i) {/* 2^24 - 2^12 */
+ p224_felem_reduce(ftmp3, tmp); // 2^13 - 2
+ for (size_t i = 0; i < 11; ++i) { // 2^24 - 2^12
p224_felem_square(tmp, ftmp3);
p224_felem_reduce(ftmp3, tmp);
}
p224_felem_mul(tmp, ftmp3, ftmp2);
- p224_felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
+ p224_felem_reduce(ftmp2, tmp); // 2^24 - 1
p224_felem_square(tmp, ftmp2);
- p224_felem_reduce(ftmp3, tmp); /* 2^25 - 2 */
- for (size_t i = 0; i < 23; ++i) {/* 2^48 - 2^24 */
+ p224_felem_reduce(ftmp3, tmp); // 2^25 - 2
+ for (size_t i = 0; i < 23; ++i) { // 2^48 - 2^24
p224_felem_square(tmp, ftmp3);
p224_felem_reduce(ftmp3, tmp);
}
p224_felem_mul(tmp, ftmp3, ftmp2);
- p224_felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
+ p224_felem_reduce(ftmp3, tmp); // 2^48 - 1
p224_felem_square(tmp, ftmp3);
- p224_felem_reduce(ftmp4, tmp); /* 2^49 - 2 */
- for (size_t i = 0; i < 47; ++i) {/* 2^96 - 2^48 */
+ p224_felem_reduce(ftmp4, tmp); // 2^49 - 2
+ for (size_t i = 0; i < 47; ++i) { // 2^96 - 2^48
p224_felem_square(tmp, ftmp4);
p224_felem_reduce(ftmp4, tmp);
}
p224_felem_mul(tmp, ftmp3, ftmp4);
- p224_felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
+ p224_felem_reduce(ftmp3, tmp); // 2^96 - 1
p224_felem_square(tmp, ftmp3);
- p224_felem_reduce(ftmp4, tmp); /* 2^97 - 2 */
- for (size_t i = 0; i < 23; ++i) {/* 2^120 - 2^24 */
+ p224_felem_reduce(ftmp4, tmp); // 2^97 - 2
+ for (size_t i = 0; i < 23; ++i) { // 2^120 - 2^24
p224_felem_square(tmp, ftmp4);
p224_felem_reduce(ftmp4, tmp);
}
p224_felem_mul(tmp, ftmp2, ftmp4);
- p224_felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
- for (size_t i = 0; i < 6; ++i) { /* 2^126 - 2^6 */
+ p224_felem_reduce(ftmp2, tmp); // 2^120 - 1
+ for (size_t i = 0; i < 6; ++i) { // 2^126 - 2^6
p224_felem_square(tmp, ftmp2);
p224_felem_reduce(ftmp2, tmp);
}
p224_felem_mul(tmp, ftmp2, ftmp);
- p224_felem_reduce(ftmp, tmp); /* 2^126 - 1 */
+ p224_felem_reduce(ftmp, tmp); // 2^126 - 1
p224_felem_square(tmp, ftmp);
- p224_felem_reduce(ftmp, tmp); /* 2^127 - 2 */
+ p224_felem_reduce(ftmp, tmp); // 2^127 - 2
p224_felem_mul(tmp, ftmp, in);
- p224_felem_reduce(ftmp, tmp); /* 2^127 - 1 */
- for (size_t i = 0; i < 97; ++i) {/* 2^224 - 2^97 */
+ p224_felem_reduce(ftmp, tmp); // 2^127 - 1
+ for (size_t i = 0; i < 97; ++i) { // 2^224 - 2^97
p224_felem_square(tmp, ftmp);
p224_felem_reduce(ftmp, tmp);
}
p224_felem_mul(tmp, ftmp, ftmp3);
- p224_felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */
+ p224_felem_reduce(out, tmp); // 2^224 - 2^96 - 1
}
-/* Copy in constant time:
- * if icopy == 1, copy in to out,
- * if icopy == 0, copy out to itself. */
+// Copy in constant time:
+// if icopy == 1, copy in to out,
+// if icopy == 0, copy out to itself.
static void p224_copy_conditional(p224_felem out, const p224_felem in,
p224_limb icopy) {
- /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
+ // icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one
const p224_limb copy = -icopy;
for (size_t i = 0; i < 4; ++i) {
const p224_limb tmp = copy & (in[i] ^ out[i]);
@@ -625,19 +625,19 @@ static void p224_copy_conditional(p224_felem out, const p224_felem in,
}
}
-/* ELLIPTIC CURVE POINT OPERATIONS
- *
- * Points are represented in Jacobian projective coordinates:
- * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
- * or to the point at infinity if Z == 0. */
-
-/* Double an elliptic curve point:
- * (X', Y', Z') = 2 * (X, Y, Z), where
- * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
- * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
- * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
- * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
- * while x_out == y_in is not (maybe this works, but it's not tested). */
+// ELLIPTIC CURVE POINT OPERATIONS
+//
+// Points are represented in Jacobian projective coordinates:
+// (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
+// or to the point at infinity if Z == 0.
+
+// Double an elliptic curve point:
+// (X', Y', Z') = 2 * (X, Y, Z), where
+// X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
+// Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
+// Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
+// Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
+// while x_out == y_in is not (maybe this works, but it's not tested).
static void p224_point_double(p224_felem x_out, p224_felem y_out,
p224_felem z_out, const p224_felem x_in,
const p224_felem y_in, const p224_felem z_in) {
@@ -647,82 +647,82 @@ static void p224_point_double(p224_felem x_out, p224_felem y_out,
p224_felem_assign(ftmp, x_in);
p224_felem_assign(ftmp2, x_in);
- /* delta = z^2 */
+ // delta = z^2
p224_felem_square(tmp, z_in);
p224_felem_reduce(delta, tmp);
- /* gamma = y^2 */
+ // gamma = y^2
p224_felem_square(tmp, y_in);
p224_felem_reduce(gamma, tmp);
- /* beta = x*gamma */
+ // beta = x*gamma
p224_felem_mul(tmp, x_in, gamma);
p224_felem_reduce(beta, tmp);
- /* alpha = 3*(x-delta)*(x+delta) */
+ // alpha = 3*(x-delta)*(x+delta)
p224_felem_diff(ftmp, delta);
- /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
+ // ftmp[i] < 2^57 + 2^58 + 2 < 2^59
p224_felem_sum(ftmp2, delta);
- /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
+ // ftmp2[i] < 2^57 + 2^57 = 2^58
p224_felem_scalar(ftmp2, 3);
- /* ftmp2[i] < 3 * 2^58 < 2^60 */
+ // ftmp2[i] < 3 * 2^58 < 2^60
p224_felem_mul(tmp, ftmp, ftmp2);
- /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
+ // tmp[i] < 2^60 * 2^59 * 4 = 2^121
p224_felem_reduce(alpha, tmp);
- /* x' = alpha^2 - 8*beta */
+ // x' = alpha^2 - 8*beta
p224_felem_square(tmp, alpha);
- /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
+ // tmp[i] < 4 * 2^57 * 2^57 = 2^116
p224_felem_assign(ftmp, beta);
p224_felem_scalar(ftmp, 8);
- /* ftmp[i] < 8 * 2^57 = 2^60 */
+ // ftmp[i] < 8 * 2^57 = 2^60
p224_felem_diff_128_64(tmp, ftmp);
- /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
+ // tmp[i] < 2^116 + 2^64 + 8 < 2^117
p224_felem_reduce(x_out, tmp);
- /* z' = (y + z)^2 - gamma - delta */
+ // z' = (y + z)^2 - gamma - delta
p224_felem_sum(delta, gamma);
- /* delta[i] < 2^57 + 2^57 = 2^58 */
+ // delta[i] < 2^57 + 2^57 = 2^58
p224_felem_assign(ftmp, y_in);
p224_felem_sum(ftmp, z_in);
- /* ftmp[i] < 2^57 + 2^57 = 2^58 */
+ // ftmp[i] < 2^57 + 2^57 = 2^58
p224_felem_square(tmp, ftmp);
- /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
+ // tmp[i] < 4 * 2^58 * 2^58 = 2^118
p224_felem_diff_128_64(tmp, delta);
- /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
+ // tmp[i] < 2^118 + 2^64 + 8 < 2^119
p224_felem_reduce(z_out, tmp);
- /* y' = alpha*(4*beta - x') - 8*gamma^2 */
+ // y' = alpha*(4*beta - x') - 8*gamma^2
p224_felem_scalar(beta, 4);
- /* beta[i] < 4 * 2^57 = 2^59 */
+ // beta[i] < 4 * 2^57 = 2^59
p224_felem_diff(beta, x_out);
- /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
+ // beta[i] < 2^59 + 2^58 + 2 < 2^60
p224_felem_mul(tmp, alpha, beta);
- /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
+ // tmp[i] < 4 * 2^57 * 2^60 = 2^119
p224_felem_square(tmp2, gamma);
- /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
+ // tmp2[i] < 4 * 2^57 * 2^57 = 2^116
p224_widefelem_scalar(tmp2, 8);
- /* tmp2[i] < 8 * 2^116 = 2^119 */
+ // tmp2[i] < 8 * 2^116 = 2^119
p224_widefelem_diff(tmp, tmp2);
- /* tmp[i] < 2^119 + 2^120 < 2^121 */
+ // tmp[i] < 2^119 + 2^120 < 2^121
p224_felem_reduce(y_out, tmp);
}
-/* Add two elliptic curve points:
- * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
- * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
- * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
- * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 *
- * X_1)^2 - X_3) -
- * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
- * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2)
- *
- * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. */
-
-/* This function is not entirely constant-time: it includes a branch for
- * checking whether the two input points are equal, (while not equal to the
- * point at infinity). This case never happens during single point
- * multiplication, so there is no timing leak for ECDH or ECDSA signing. */
+// Add two elliptic curve points:
+// (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
+// X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
+// 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
+// Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 *
+// X_1)^2 - X_3) -
+// Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
+// Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2)
+//
+// This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0.
+
+// This function is not entirely constant-time: it includes a branch for
+// checking whether the two input points are equal, (while not equal to the
+// point at infinity). This case never happens during single point
+// multiplication, so there is no timing leak for ECDH or ECDSA signing.
static void p224_point_add(p224_felem x3, p224_felem y3, p224_felem z3,
const p224_felem x1, const p224_felem y1,
const p224_felem z1, const int mixed,
@@ -733,136 +733,136 @@ static void p224_point_add(p224_felem x3, p224_felem y3, p224_felem z3,
p224_limb z1_is_zero, z2_is_zero, x_equal, y_equal;
if (!mixed) {
- /* ftmp2 = z2^2 */
+ // ftmp2 = z2^2
p224_felem_square(tmp, z2);
p224_felem_reduce(ftmp2, tmp);
- /* ftmp4 = z2^3 */
+ // ftmp4 = z2^3
p224_felem_mul(tmp, ftmp2, z2);
p224_felem_reduce(ftmp4, tmp);
- /* ftmp4 = z2^3*y1 */
+ // ftmp4 = z2^3*y1
p224_felem_mul(tmp2, ftmp4, y1);
p224_felem_reduce(ftmp4, tmp2);
- /* ftmp2 = z2^2*x1 */
+ // ftmp2 = z2^2*x1
p224_felem_mul(tmp2, ftmp2, x1);
p224_felem_reduce(ftmp2, tmp2);
} else {
- /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
+ // We'll assume z2 = 1 (special case z2 = 0 is handled later)
- /* ftmp4 = z2^3*y1 */
+ // ftmp4 = z2^3*y1
p224_felem_assign(ftmp4, y1);
- /* ftmp2 = z2^2*x1 */
+ // ftmp2 = z2^2*x1
p224_felem_assign(ftmp2, x1);
}
- /* ftmp = z1^2 */
+ // ftmp = z1^2
p224_felem_square(tmp, z1);
p224_felem_reduce(ftmp, tmp);
- /* ftmp3 = z1^3 */
+ // ftmp3 = z1^3
p224_felem_mul(tmp, ftmp, z1);
p224_felem_reduce(ftmp3, tmp);
- /* tmp = z1^3*y2 */
+ // tmp = z1^3*y2
p224_felem_mul(tmp, ftmp3, y2);
- /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
+ // tmp[i] < 4 * 2^57 * 2^57 = 2^116
- /* ftmp3 = z1^3*y2 - z2^3*y1 */
+ // ftmp3 = z1^3*y2 - z2^3*y1
p224_felem_diff_128_64(tmp, ftmp4);
- /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
+ // tmp[i] < 2^116 + 2^64 + 8 < 2^117
p224_felem_reduce(ftmp3, tmp);
- /* tmp = z1^2*x2 */
+ // tmp = z1^2*x2
p224_felem_mul(tmp, ftmp, x2);
- /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
+ // tmp[i] < 4 * 2^57 * 2^57 = 2^116
- /* ftmp = z1^2*x2 - z2^2*x1 */
+ // ftmp = z1^2*x2 - z2^2*x1
p224_felem_diff_128_64(tmp, ftmp2);
- /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
+ // tmp[i] < 2^116 + 2^64 + 8 < 2^117
p224_felem_reduce(ftmp, tmp);
- /* the formulae are incorrect if the points are equal
- * so we check for this and do doubling if this happens */
+ // the formulae are incorrect if the points are equal
+ // so we check for this and do doubling if this happens
x_equal = p224_felem_is_zero(ftmp);
y_equal = p224_felem_is_zero(ftmp3);
z1_is_zero = p224_felem_is_zero(z1);
z2_is_zero = p224_felem_is_zero(z2);
- /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
+ // In affine coordinates, (X_1, Y_1) == (X_2, Y_2)
if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
p224_point_double(x3, y3, z3, x1, y1, z1);
return;
}
- /* ftmp5 = z1*z2 */
+ // ftmp5 = z1*z2
if (!mixed) {
p224_felem_mul(tmp, z1, z2);
p224_felem_reduce(ftmp5, tmp);
} else {
- /* special case z2 = 0 is handled later */
+ // special case z2 = 0 is handled later
p224_felem_assign(ftmp5, z1);
}
- /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */
+ // z_out = (z1^2*x2 - z2^2*x1)*(z1*z2)
p224_felem_mul(tmp, ftmp, ftmp5);
p224_felem_reduce(z_out, tmp);
- /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
+ // ftmp = (z1^2*x2 - z2^2*x1)^2
p224_felem_assign(ftmp5, ftmp);
p224_felem_square(tmp, ftmp);
p224_felem_reduce(ftmp, tmp);
- /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
+ // ftmp5 = (z1^2*x2 - z2^2*x1)^3
p224_felem_mul(tmp, ftmp, ftmp5);
p224_felem_reduce(ftmp5, tmp);
- /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
+ // ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2
p224_felem_mul(tmp, ftmp2, ftmp);
p224_felem_reduce(ftmp2, tmp);
- /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
+ // tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3
p224_felem_mul(tmp, ftmp4, ftmp5);
- /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
+ // tmp[i] < 4 * 2^57 * 2^57 = 2^116
- /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
+ // tmp2 = (z1^3*y2 - z2^3*y1)^2
p224_felem_square(tmp2, ftmp3);
- /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
+ // tmp2[i] < 4 * 2^57 * 2^57 < 2^116
- /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
+ // tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3
p224_felem_diff_128_64(tmp2, ftmp5);
- /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
+ // tmp2[i] < 2^116 + 2^64 + 8 < 2^117
- /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
+ // ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2
p224_felem_assign(ftmp5, ftmp2);
p224_felem_scalar(ftmp5, 2);
- /* ftmp5[i] < 2 * 2^57 = 2^58 */
+ // ftmp5[i] < 2 * 2^57 = 2^58
/* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
p224_felem_diff_128_64(tmp2, ftmp5);
- /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
+ // tmp2[i] < 2^117 + 2^64 + 8 < 2^118
p224_felem_reduce(x_out, tmp2);
- /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */
+ // ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out
p224_felem_diff(ftmp2, x_out);
- /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
+ // ftmp2[i] < 2^57 + 2^58 + 2 < 2^59
- /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */
+ // tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out)
p224_felem_mul(tmp2, ftmp3, ftmp2);
- /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
+ // tmp2[i] < 4 * 2^57 * 2^59 = 2^118
/* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) -
z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
p224_widefelem_diff(tmp2, tmp);
- /* tmp2[i] < 2^118 + 2^120 < 2^121 */
+ // tmp2[i] < 2^118 + 2^120 < 2^121
p224_felem_reduce(y_out, tmp2);
- /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is
- * the point at infinity, so we need to check for this separately */
+ // the result (x_out, y_out, z_out) is incorrect if one of the inputs is
+ // the point at infinity, so we need to check for this separately
- /* if point 1 is at infinity, copy point 2 to output, and vice versa */
+ // if point 1 is at infinity, copy point 2 to output, and vice versa
p224_copy_conditional(x_out, x2, z1_is_zero);
p224_copy_conditional(x_out, x1, z2_is_zero);
p224_copy_conditional(y_out, y2, z1_is_zero);
@@ -874,8 +874,8 @@ static void p224_point_add(p224_felem x3, p224_felem y3, p224_felem z3,
p224_felem_assign(z3, z_out);
}
-/* p224_select_point selects the |idx|th point from a precomputation table and
- * copies it to out. */
+// p224_select_point selects the |idx|th point from a precomputation table and
+// copies it to out.
static void p224_select_point(const uint64_t idx, size_t size,
const p224_felem pre_comp[/*size*/][3],
p224_felem out[3]) {
@@ -896,7 +896,7 @@ static void p224_select_point(const uint64_t idx, size_t size,
}
}
-/* p224_get_bit returns the |i|th bit in |in| */
+// p224_get_bit returns the |i|th bit in |in|
static char p224_get_bit(const p224_felem_bytearray in, size_t i) {
if (i >= 224) {
return 0;
@@ -904,11 +904,11 @@ static char p224_get_bit(const p224_felem_bytearray in, size_t i) {
return (in[i >> 3] >> (i & 7)) & 1;
}
-/* Interleaved point multiplication using precomputed point multiples:
- * The small point multiples 0*P, 1*P, ..., 16*P are in p_pre_comp, the scalars
- * in p_scalar, if non-NULL. If g_scalar is non-NULL, we also add this multiple
- * of the generator, using certain (large) precomputed multiples in
- * g_p224_pre_comp. Output point (X, Y, Z) is stored in x_out, y_out, z_out */
+// Interleaved point multiplication using precomputed point multiples:
+// The small point multiples 0*P, 1*P, ..., 16*P are in p_pre_comp, the scalars
+// in p_scalar, if non-NULL. If g_scalar is non-NULL, we also add this multiple
+// of the generator, using certain (large) precomputed multiples in
+// g_p224_pre_comp. Output point (X, Y, Z) is stored in x_out, y_out, z_out
static void p224_batch_mul(p224_felem x_out, p224_felem y_out, p224_felem z_out,
const uint8_t *p_scalar, const uint8_t *g_scalar,
const p224_felem p_pre_comp[17][3]) {
@@ -916,28 +916,28 @@ static void p224_batch_mul(p224_felem x_out, p224_felem y_out, p224_felem z_out,
uint64_t bits;
uint8_t sign, digit;
- /* set nq to the point at infinity */
+ // set nq to the point at infinity
OPENSSL_memset(nq, 0, 3 * sizeof(p224_felem));
- /* Loop over both scalars msb-to-lsb, interleaving additions of multiples of
- * the generator (two in each of the last 28 rounds) and additions of p (every
- * 5th round). */
- int skip = 1; /* save two point operations in the first round */
+ // Loop over both scalars msb-to-lsb, interleaving additions of multiples of
+ // the generator (two in each of the last 28 rounds) and additions of p (every
+ // 5th round).
+ int skip = 1; // save two point operations in the first round
size_t i = p_scalar != NULL ? 220 : 27;
for (;;) {
- /* double */
+ // double
if (!skip) {
p224_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
}
- /* add multiples of the generator */
+ // add multiples of the generator
if (g_scalar != NULL && i <= 27) {
- /* first, look 28 bits upwards */
+ // first, look 28 bits upwards
bits = p224_get_bit(g_scalar, i + 196) << 3;
bits |= p224_get_bit(g_scalar, i + 140) << 2;
bits |= p224_get_bit(g_scalar, i + 84) << 1;
bits |= p224_get_bit(g_scalar, i + 28);
- /* select the point to add, in constant time */
+ // select the point to add, in constant time
p224_select_point(bits, 16, g_p224_pre_comp[1], tmp);
if (!skip) {
@@ -948,18 +948,18 @@ static void p224_batch_mul(p224_felem x_out, p224_felem y_out, p224_felem z_out,
skip = 0;
}
- /* second, look at the current position */
+ // second, look at the current position
bits = p224_get_bit(g_scalar, i + 168) << 3;
bits |= p224_get_bit(g_scalar, i + 112) << 2;
bits |= p224_get_bit(g_scalar, i + 56) << 1;
bits |= p224_get_bit(g_scalar, i);
- /* select the point to add, in constant time */
+ // select the point to add, in constant time
p224_select_point(bits, 16, g_p224_pre_comp[0], tmp);
p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */,
tmp[0], tmp[1], tmp[2]);
}
- /* do other additions every 5 doublings */
+ // do other additions every 5 doublings
if (p_scalar != NULL && i % 5 == 0) {
bits = p224_get_bit(p_scalar, i + 4) << 5;
bits |= p224_get_bit(p_scalar, i + 3) << 4;
@@ -969,9 +969,9 @@ static void p224_batch_mul(p224_felem x_out, p224_felem y_out, p224_felem z_out,
bits |= p224_get_bit(p_scalar, i - 1);
ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
- /* select the point to add or subtract */
+ // select the point to add or subtract
p224_select_point(digit, 17, p_pre_comp, tmp);
- p224_felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */
+ p224_felem_neg(tmp[3], tmp[1]); // (X, -Y, Z) is the negative point
p224_copy_conditional(tmp[1], tmp[3], sign);
if (!skip) {
@@ -993,8 +993,8 @@ static void p224_batch_mul(p224_felem x_out, p224_felem y_out, p224_felem z_out,
p224_felem_assign(z_out, nq[2]);
}
-/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
- * (X', Y') = (X/Z^2, Y/Z^3) */
+// Takes the Jacobian coordinates (X, Y, Z) of a point and returns
+// (X', Y') = (X/Z^2, Y/Z^3)
static int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
const EC_POINT *point,
BIGNUM *x, BIGNUM *y,
@@ -1065,15 +1065,15 @@ static int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
}
if (p != NULL && p_scalar != NULL) {
- /* We treat NULL scalars as 0, and NULL points as points at infinity, i.e.,
- * they contribute nothing to the linear combination. */
+ // We treat NULL scalars as 0, and NULL points as points at infinity, i.e.,
+ // they contribute nothing to the linear combination.
OPENSSL_memset(&p_secret, 0, sizeof(p_secret));
OPENSSL_memset(&p_pre_comp, 0, sizeof(p_pre_comp));
size_t num_bytes;
- /* reduce g_scalar to 0 <= g_scalar < 2^224 */
+ // reduce g_scalar to 0 <= g_scalar < 2^224
if (BN_num_bits(p_scalar) > 224 || BN_is_negative(p_scalar)) {
- /* this is an unusual input, and we don't guarantee
- * constant-timeness */
+ // this is an unusual input, and we don't guarantee
+ // constant-timeness
if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
@@ -1084,7 +1084,7 @@ static int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
}
p224_flip_endian(p_secret, tmp, num_bytes);
- /* precompute multiples */
+ // precompute multiples
if (!p224_BN_to_felem(x_out, &p->X) ||
!p224_BN_to_felem(y_out, &p->Y) ||
!p224_BN_to_felem(z_out, &p->Z)) {
@@ -1112,9 +1112,9 @@ static int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
if (g_scalar != NULL) {
OPENSSL_memset(g_secret, 0, sizeof(g_secret));
size_t num_bytes;
- /* reduce g_scalar to 0 <= g_scalar < 2^224 */
+ // reduce g_scalar to 0 <= g_scalar < 2^224
if (BN_num_bits(g_scalar) > 224 || BN_is_negative(g_scalar)) {
- /* this is an unusual input, and we don't guarantee constant-timeness */
+ // this is an unusual input, and we don't guarantee constant-timeness
if (!BN_nnmod(tmp_scalar, g_scalar, &group->order, ctx)) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
@@ -1130,7 +1130,7 @@ static int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
x_out, y_out, z_out, (p != NULL && p_scalar != NULL) ? p_secret : NULL,
g_scalar != NULL ? g_secret : NULL, (const p224_felem(*)[3])p_pre_comp);
- /* reduce the output to its unique minimal representation */
+ // reduce the output to its unique minimal representation
p224_felem_contract(x_in, x_out);
p224_felem_contract(y_in, y_out);
p224_felem_contract(z_in, z_out);
@@ -1162,4 +1162,4 @@ DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistp224_method) {
out->field_decode = NULL;
};
-#endif /* 64_BIT && !WINDOWS && !SMALL */
+#endif // 64_BIT && !WINDOWS && !SMALL
generated by cgit v1.2.3 (git 2.25.1) at 2024-07-25 10:02:22 +0000