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-rw-r--r--security/nss/lib/freebl/ecl/curve25519_64.c508
1 files changed, 504 insertions, 4 deletions
diff --git a/security/nss/lib/freebl/ecl/curve25519_64.c b/security/nss/lib/freebl/ecl/curve25519_64.c
index a2e4296bbf..65f6bd41b5 100644
--- a/security/nss/lib/freebl/ecl/curve25519_64.c
+++ b/security/nss/lib/freebl/ecl/curve25519_64.c
@@ -2,13 +2,513 @@
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
+/*
+ * Derived from public domain C code by Adan Langley and Daniel J. Bernstein
+ */
+
+#include "uint128.h"
+
#include "ecl-priv.h"
-#include "../verified/Hacl_Curve25519.h"
+#include "mpi.h"
+
+#include <stdint.h>
+#include <stdio.h>
+#include <string.h>
+
+typedef uint8_t u8;
+typedef uint64_t felem;
+
+/* Sum two numbers: output += in */
+static void
+fsum(felem *output, const felem *in)
+{
+ unsigned i;
+ for (i = 0; i < 5; ++i) {
+ output[i] += in[i];
+ }
+}
+
+/* Find the difference of two numbers: output = in - output
+ * (note the order of the arguments!)
+ */
+static void
+fdifference_backwards(felem *ioutput, const felem *iin)
+{
+ static const int64_t twotothe51 = ((int64_t)1l << 51);
+ const int64_t *in = (const int64_t *)iin;
+ int64_t *out = (int64_t *)ioutput;
+
+ out[0] = in[0] - out[0];
+ out[1] = in[1] - out[1];
+ out[2] = in[2] - out[2];
+ out[3] = in[3] - out[3];
+ out[4] = in[4] - out[4];
+
+ // An arithmetic shift right of 63 places turns a positive number to 0 and a
+ // negative number to all 1's. This gives us a bitmask that lets us avoid
+ // side-channel prone branches.
+ int64_t t;
+
+#define NEGCHAIN(a, b) \
+ t = out[a] >> 63; \
+ out[a] += twotothe51 & t; \
+ out[b] -= 1 & t;
+
+#define NEGCHAIN19(a, b) \
+ t = out[a] >> 63; \
+ out[a] += twotothe51 & t; \
+ out[b] -= 19 & t;
+
+ NEGCHAIN(0, 1);
+ NEGCHAIN(1, 2);
+ NEGCHAIN(2, 3);
+ NEGCHAIN(3, 4);
+ NEGCHAIN19(4, 0);
+ NEGCHAIN(0, 1);
+ NEGCHAIN(1, 2);
+ NEGCHAIN(2, 3);
+ NEGCHAIN(3, 4);
+}
+
+/* Multiply a number by a scalar: output = in * scalar */
+static void
+fscalar_product(felem *output, const felem *in,
+ const felem scalar)
+{
+ uint128_t tmp, tmp2;
+
+ tmp = mul6464(in[0], scalar);
+ output[0] = mask51(tmp);
+
+ tmp2 = mul6464(in[1], scalar);
+ tmp = add128(tmp2, rshift128(tmp, 51));
+ output[1] = mask51(tmp);
+
+ tmp2 = mul6464(in[2], scalar);
+ tmp = add128(tmp2, rshift128(tmp, 51));
+ output[2] = mask51(tmp);
+
+ tmp2 = mul6464(in[3], scalar);
+ tmp = add128(tmp2, rshift128(tmp, 51));
+ output[3] = mask51(tmp);
+
+ tmp2 = mul6464(in[4], scalar);
+ tmp = add128(tmp2, rshift128(tmp, 51));
+ output[4] = mask51(tmp);
+
+ output[0] += mask_lower(rshift128(tmp, 51)) * 19;
+}
+
+/* Multiply two numbers: output = in2 * in
+ *
+ * output must be distinct to both inputs. The inputs are reduced coefficient
+ * form, the output is not.
+ */
+static void
+fmul(felem *output, const felem *in2, const felem *in)
+{
+ uint128_t t0, t1, t2, t3, t4, t5, t6, t7, t8;
+
+ t0 = mul6464(in[0], in2[0]);
+ t1 = add128(mul6464(in[1], in2[0]), mul6464(in[0], in2[1]));
+ t2 = add128(add128(mul6464(in[0], in2[2]),
+ mul6464(in[2], in2[0])),
+ mul6464(in[1], in2[1]));
+ t3 = add128(add128(add128(mul6464(in[0], in2[3]),
+ mul6464(in[3], in2[0])),
+ mul6464(in[1], in2[2])),
+ mul6464(in[2], in2[1]));
+ t4 = add128(add128(add128(add128(mul6464(in[0], in2[4]),
+ mul6464(in[4], in2[0])),
+ mul6464(in[3], in2[1])),
+ mul6464(in[1], in2[3])),
+ mul6464(in[2], in2[2]));
+ t5 = add128(add128(add128(mul6464(in[4], in2[1]),
+ mul6464(in[1], in2[4])),
+ mul6464(in[2], in2[3])),
+ mul6464(in[3], in2[2]));
+ t6 = add128(add128(mul6464(in[4], in2[2]),
+ mul6464(in[2], in2[4])),
+ mul6464(in[3], in2[3]));
+ t7 = add128(mul6464(in[3], in2[4]), mul6464(in[4], in2[3]));
+ t8 = mul6464(in[4], in2[4]);
+
+ t0 = add128(t0, mul12819(t5));
+ t1 = add128(t1, mul12819(t6));
+ t2 = add128(t2, mul12819(t7));
+ t3 = add128(t3, mul12819(t8));
+
+ t1 = add128(t1, rshift128(t0, 51));
+ t0 = mask51full(t0);
+ t2 = add128(t2, rshift128(t1, 51));
+ t1 = mask51full(t1);
+ t3 = add128(t3, rshift128(t2, 51));
+ t4 = add128(t4, rshift128(t3, 51));
+ t0 = add128(t0, mul12819(rshift128(t4, 51)));
+ t1 = add128(t1, rshift128(t0, 51));
+ t2 = mask51full(t2);
+ t2 = add128(t2, rshift128(t1, 51));
+
+ output[0] = mask51(t0);
+ output[1] = mask51(t1);
+ output[2] = mask_lower(t2);
+ output[3] = mask51(t3);
+ output[4] = mask51(t4);
+}
+
+static void
+fsquare(felem *output, const felem *in)
+{
+ uint128_t t0, t1, t2, t3, t4, t5, t6, t7, t8;
+
+ t0 = mul6464(in[0], in[0]);
+ t1 = lshift128(mul6464(in[0], in[1]), 1);
+ t2 = add128(lshift128(mul6464(in[0], in[2]), 1),
+ mul6464(in[1], in[1]));
+ t3 = add128(lshift128(mul6464(in[0], in[3]), 1),
+ lshift128(mul6464(in[1], in[2]), 1));
+ t4 = add128(add128(lshift128(mul6464(in[0], in[4]), 1),
+ lshift128(mul6464(in[3], in[1]), 1)),
+ mul6464(in[2], in[2]));
+ t5 = add128(lshift128(mul6464(in[4], in[1]), 1),
+ lshift128(mul6464(in[2], in[3]), 1));
+ t6 = add128(lshift128(mul6464(in[4], in[2]), 1),
+ mul6464(in[3], in[3]));
+ t7 = lshift128(mul6464(in[3], in[4]), 1);
+ t8 = mul6464(in[4], in[4]);
+
+ t0 = add128(t0, mul12819(t5));
+ t1 = add128(t1, mul12819(t6));
+ t2 = add128(t2, mul12819(t7));
+ t3 = add128(t3, mul12819(t8));
+
+ t1 = add128(t1, rshift128(t0, 51));
+ t0 = mask51full(t0);
+ t2 = add128(t2, rshift128(t1, 51));
+ t1 = mask51full(t1);
+ t3 = add128(t3, rshift128(t2, 51));
+ t4 = add128(t4, rshift128(t3, 51));
+ t0 = add128(t0, mul12819(rshift128(t4, 51)));
+ t1 = add128(t1, rshift128(t0, 51));
+
+ output[0] = mask51(t0);
+ output[1] = mask_lower(t1);
+ output[2] = mask51(t2);
+ output[3] = mask51(t3);
+ output[4] = mask51(t4);
+}
+
+/* Take a 32-byte number and expand it into polynomial form */
+static void NO_SANITIZE_ALIGNMENT
+fexpand(felem *output, const u8 *in)
+{
+ output[0] = *((const uint64_t *)(in)) & MASK51;
+ output[1] = (*((const uint64_t *)(in + 6)) >> 3) & MASK51;
+ output[2] = (*((const uint64_t *)(in + 12)) >> 6) & MASK51;
+ output[3] = (*((const uint64_t *)(in + 19)) >> 1) & MASK51;
+ output[4] = (*((const uint64_t *)(in + 24)) >> 12) & MASK51;
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * 32-byte array
+ */
+static void
+fcontract(u8 *output, const felem *input)
+{
+ uint128_t t0 = init128x(input[0]);
+ uint128_t t1 = init128x(input[1]);
+ uint128_t t2 = init128x(input[2]);
+ uint128_t t3 = init128x(input[3]);
+ uint128_t t4 = init128x(input[4]);
+ uint128_t tmp = init128x(19);
+
+ t1 = add128(t1, rshift128(t0, 51));
+ t0 = mask51full(t0);
+ t2 = add128(t2, rshift128(t1, 51));
+ t1 = mask51full(t1);
+ t3 = add128(t3, rshift128(t2, 51));
+ t2 = mask51full(t2);
+ t4 = add128(t4, rshift128(t3, 51));
+ t3 = mask51full(t3);
+ t0 = add128(t0, mul12819(rshift128(t4, 51)));
+ t4 = mask51full(t4);
+
+ t1 = add128(t1, rshift128(t0, 51));
+ t0 = mask51full(t0);
+ t2 = add128(t2, rshift128(t1, 51));
+ t1 = mask51full(t1);
+ t3 = add128(t3, rshift128(t2, 51));
+ t2 = mask51full(t2);
+ t4 = add128(t4, rshift128(t3, 51));
+ t3 = mask51full(t3);
+ t0 = add128(t0, mul12819(rshift128(t4, 51)));
+ t4 = mask51full(t4);
+
+ /* now t is between 0 and 2^255-1, properly carried. */
+ /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
+
+ t0 = add128(t0, tmp);
+
+ t1 = add128(t1, rshift128(t0, 51));
+ t0 = mask51full(t0);
+ t2 = add128(t2, rshift128(t1, 51));
+ t1 = mask51full(t1);
+ t3 = add128(t3, rshift128(t2, 51));
+ t2 = mask51full(t2);
+ t4 = add128(t4, rshift128(t3, 51));
+ t3 = mask51full(t3);
+ t0 = add128(t0, mul12819(rshift128(t4, 51)));
+ t4 = mask51full(t4);
+
+ /* now between 19 and 2^255-1 in both cases, and offset by 19. */
+
+ t0 = add128(t0, init128x(0x8000000000000 - 19));
+ tmp = init128x(0x8000000000000 - 1);
+ t1 = add128(t1, tmp);
+ t2 = add128(t2, tmp);
+ t3 = add128(t3, tmp);
+ t4 = add128(t4, tmp);
+
+ /* now between 2^255 and 2^256-20, and offset by 2^255. */
+
+ t1 = add128(t1, rshift128(t0, 51));
+ t0 = mask51full(t0);
+ t2 = add128(t2, rshift128(t1, 51));
+ t1 = mask51full(t1);
+ t3 = add128(t3, rshift128(t2, 51));
+ t2 = mask51full(t2);
+ t4 = add128(t4, rshift128(t3, 51));
+ t3 = mask51full(t3);
+ t4 = mask51full(t4);
+
+ *((uint64_t *)(output)) = mask_lower(t0) | mask_lower(t1) << 51;
+ *((uint64_t *)(output + 8)) = (mask_lower(t1) >> 13) | (mask_lower(t2) << 38);
+ *((uint64_t *)(output + 16)) = (mask_lower(t2) >> 26) | (mask_lower(t3) << 25);
+ *((uint64_t *)(output + 24)) = (mask_lower(t3) >> 39) | (mask_lower(t4) << 12);
+}
+
+/* Input: Q, Q', Q-Q'
+ * Output: 2Q, Q+Q'
+ *
+ * x2 z3: long form
+ * x3 z3: long form
+ * x z: short form, destroyed
+ * xprime zprime: short form, destroyed
+ * qmqp: short form, preserved
+ */
+static void
+fmonty(felem *x2, felem *z2, /* output 2Q */
+ felem *x3, felem *z3, /* output Q + Q' */
+ felem *x, felem *z, /* input Q */
+ felem *xprime, felem *zprime, /* input Q' */
+ const felem *qmqp /* input Q - Q' */)
+{
+ felem origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5],
+ zzzprime[5];
+
+ memcpy(origx, x, 5 * sizeof(felem));
+ fsum(x, z);
+ fdifference_backwards(z, origx); // does x - z
+
+ memcpy(origxprime, xprime, sizeof(felem) * 5);
+ fsum(xprime, zprime);
+ fdifference_backwards(zprime, origxprime);
+ fmul(xxprime, xprime, z);
+ fmul(zzprime, x, zprime);
+ memcpy(origxprime, xxprime, sizeof(felem) * 5);
+ fsum(xxprime, zzprime);
+ fdifference_backwards(zzprime, origxprime);
+ fsquare(x3, xxprime);
+ fsquare(zzzprime, zzprime);
+ fmul(z3, zzzprime, qmqp);
+
+ fsquare(xx, x);
+ fsquare(zz, z);
+ fmul(x2, xx, zz);
+ fdifference_backwards(zz, xx); // does zz = xx - zz
+ fscalar_product(zzz, zz, 121665);
+ fsum(zzz, xx);
+ fmul(z2, zz, zzz);
+}
+
+// -----------------------------------------------------------------------------
+// Maybe swap the contents of two felem arrays (@a and @b), each @len elements
+// long. Perform the swap iff @swap is non-zero.
+//
+// This function performs the swap without leaking any side-channel
+// information.
+// -----------------------------------------------------------------------------
+static void
+swap_conditional(felem *a, felem *b, unsigned len, felem iswap)
+{
+ unsigned i;
+ const felem swap = 1 + ~iswap;
+
+ for (i = 0; i < len; ++i) {
+ const felem x = swap & (a[i] ^ b[i]);
+ a[i] ^= x;
+ b[i] ^= x;
+ }
+}
+
+/* Calculates nQ where Q is the x-coordinate of a point on the curve
+ *
+ * resultx/resultz: the x coordinate of the resulting curve point (short form)
+ * n: a 32-byte number
+ * q: a point of the curve (short form)
+ */
+static void
+cmult(felem *resultx, felem *resultz, const u8 *n, const felem *q)
+{
+ felem a[5] = { 0 }, b[5] = { 1 }, c[5] = { 1 }, d[5] = { 0 };
+ felem *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
+ felem e[5] = { 0 }, f[5] = { 1 }, g[5] = { 0 }, h[5] = { 1 };
+ felem *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
+
+ unsigned i, j;
+
+ memcpy(nqpqx, q, sizeof(felem) * 5);
+
+ for (i = 0; i < 32; ++i) {
+ u8 byte = n[31 - i];
+ for (j = 0; j < 8; ++j) {
+ const felem bit = byte >> 7;
+
+ swap_conditional(nqx, nqpqx, 5, bit);
+ swap_conditional(nqz, nqpqz, 5, bit);
+ fmonty(nqx2, nqz2, nqpqx2, nqpqz2, nqx, nqz, nqpqx, nqpqz, q);
+ swap_conditional(nqx2, nqpqx2, 5, bit);
+ swap_conditional(nqz2, nqpqz2, 5, bit);
+
+ t = nqx;
+ nqx = nqx2;
+ nqx2 = t;
+ t = nqz;
+ nqz = nqz2;
+ nqz2 = t;
+ t = nqpqx;
+ nqpqx = nqpqx2;
+ nqpqx2 = t;
+ t = nqpqz;
+ nqpqz = nqpqz2;
+ nqpqz2 = t;
+
+ byte <<= 1;
+ }
+ }
+
+ memcpy(resultx, nqx, sizeof(felem) * 5);
+ memcpy(resultz, nqz, sizeof(felem) * 5);
+}
+
+// -----------------------------------------------------------------------------
+// Shamelessly copied from djb's code
+// -----------------------------------------------------------------------------
+static void
+crecip(felem *out, const felem *z)
+{
+ felem z2[5];
+ felem z9[5];
+ felem z11[5];
+ felem z2_5_0[5];
+ felem z2_10_0[5];
+ felem z2_20_0[5];
+ felem z2_50_0[5];
+ felem z2_100_0[5];
+ felem t0[5];
+ felem t1[5];
+ int i;
+
+ /* 2 */ fsquare(z2, z);
+ /* 4 */ fsquare(t1, z2);
+ /* 8 */ fsquare(t0, t1);
+ /* 9 */ fmul(z9, t0, z);
+ /* 11 */ fmul(z11, z9, z2);
+ /* 22 */ fsquare(t0, z11);
+ /* 2^5 - 2^0 = 31 */ fmul(z2_5_0, t0, z9);
+
+ /* 2^6 - 2^1 */ fsquare(t0, z2_5_0);
+ /* 2^7 - 2^2 */ fsquare(t1, t0);
+ /* 2^8 - 2^3 */ fsquare(t0, t1);
+ /* 2^9 - 2^4 */ fsquare(t1, t0);
+ /* 2^10 - 2^5 */ fsquare(t0, t1);
+ /* 2^10 - 2^0 */ fmul(z2_10_0, t0, z2_5_0);
+
+ /* 2^11 - 2^1 */ fsquare(t0, z2_10_0);
+ /* 2^12 - 2^2 */ fsquare(t1, t0);
+ /* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) {
+ fsquare(t0, t1);
+ fsquare(t1, t0);
+ }
+ /* 2^20 - 2^0 */ fmul(z2_20_0, t1, z2_10_0);
+
+ /* 2^21 - 2^1 */ fsquare(t0, z2_20_0);
+ /* 2^22 - 2^2 */ fsquare(t1, t0);
+ /* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) {
+ fsquare(t0, t1);
+ fsquare(t1, t0);
+ }
+ /* 2^40 - 2^0 */ fmul(t0, t1, z2_20_0);
+
+ /* 2^41 - 2^1 */ fsquare(t1, t0);
+ /* 2^42 - 2^2 */ fsquare(t0, t1);
+ /* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) {
+ fsquare(t1, t0);
+ fsquare(t0, t1);
+ }
+ /* 2^50 - 2^0 */ fmul(z2_50_0, t0, z2_10_0);
+
+ /* 2^51 - 2^1 */ fsquare(t0, z2_50_0);
+ /* 2^52 - 2^2 */ fsquare(t1, t0);
+ /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) {
+ fsquare(t0, t1);
+ fsquare(t1, t0);
+ }
+ /* 2^100 - 2^0 */ fmul(z2_100_0, t1, z2_50_0);
+
+ /* 2^101 - 2^1 */ fsquare(t1, z2_100_0);
+ /* 2^102 - 2^2 */ fsquare(t0, t1);
+ /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) {
+ fsquare(t1, t0);
+ fsquare(t0, t1);
+ }
+ /* 2^200 - 2^0 */ fmul(t1, t0, z2_100_0);
+
+ /* 2^201 - 2^1 */ fsquare(t0, t1);
+ /* 2^202 - 2^2 */ fsquare(t1, t0);
+ /* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) {
+ fsquare(t0, t1);
+ fsquare(t1, t0);
+ }
+ /* 2^250 - 2^0 */ fmul(t0, t1, z2_50_0);
+
+ /* 2^251 - 2^1 */ fsquare(t1, t0);
+ /* 2^252 - 2^2 */ fsquare(t0, t1);
+ /* 2^253 - 2^3 */ fsquare(t1, t0);
+ /* 2^254 - 2^4 */ fsquare(t0, t1);
+ /* 2^255 - 2^5 */ fsquare(t1, t0);
+ /* 2^255 - 21 */ fmul(out, t1, z11);
+}
SECStatus
-ec_Curve25519_mul(uint8_t *mypublic, const uint8_t *secret, const uint8_t *basepoint)
+ec_Curve25519_mul(uint8_t *mypublic, const uint8_t *secret,
+ const uint8_t *basepoint)
{
- // Note: this cast is safe because HaCl* state has a post-condition that only "mypublic" changed.
- Hacl_Curve25519_crypto_scalarmult(mypublic, (uint8_t *)secret, (uint8_t *)basepoint);
+ felem bp[5], x[5], z[5], zmone[5];
+ uint8_t e[32];
+ int i;
+
+ for (i = 0; i < 32; ++i) {
+ e[i] = secret[i];
+ }
+ e[0] &= 248;
+ e[31] &= 127;
+ e[31] |= 64;
+ fexpand(bp, basepoint);
+ cmult(x, z, e, bp);
+ crecip(zmone, z);
+ fmul(z, x, zmone);
+ fcontract(mypublic, z);
+
return 0;
}
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