+/*
+ * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+#if BR_INT128 || BR_UMUL128
+
+#if BR_INT128
+
+/*
+ * Compute x*y+v1+v2. Operands are 64-bit, and result is 128-bit, with
+ * high word in "hi" and low word in "lo".
+ */
+#define FMA1(hi, lo, x, y, v1, v2) do { \
+ unsigned __int128 fmaz; \
+ fmaz = (unsigned __int128)(x) * (unsigned __int128)(y) \
+ + (unsigned __int128)(v1) + (unsigned __int128)(v2); \
+ (hi) = (uint64_t)(fmaz >> 64); \
+ (lo) = (uint64_t)fmaz; \
+ } while (0)
+
+/*
+ * Compute x1*y1+x2*y2+v1+v2. Operands are 64-bit, and result is 128-bit,
+ * with high word in "hi" and low word in "lo".
+ *
+ * Callers should ensure that the two inner products, and the v1 and v2
+ * operands, are multiple of 4 (this is not used by this specific definition
+ * but may help other implementations).
+ */
+#define FMA2(hi, lo, x1, y1, x2, y2, v1, v2) do { \
+ unsigned __int128 fmaz; \
+ fmaz = (unsigned __int128)(x1) * (unsigned __int128)(y1) \
+ + (unsigned __int128)(x2) * (unsigned __int128)(y2) \
+ + (unsigned __int128)(v1) + (unsigned __int128)(v2); \
+ (hi) = (uint64_t)(fmaz >> 64); \
+ (lo) = (uint64_t)fmaz; \
+ } while (0)
+
+#elif BR_UMUL128
+
+#include <intrin.h>
+
+#define FMA1(hi, lo, x, y, v1, v2) do { \
+ uint64_t fmahi, fmalo; \
+ unsigned char fmacc; \
+ fmalo = _umul128((x), (y), &fmahi); \
+ fmacc = _addcarry_u64(0, fmalo, (v1), &fmalo); \
+ _addcarry_u64(fmacc, fmahi, 0, &fmahi); \
+ fmacc = _addcarry_u64(0, fmalo, (v2), &(lo)); \
+ _addcarry_u64(fmacc, fmahi, 0, &(hi)); \
+ } while (0)
+
+/*
+ * Normally we should use _addcarry_u64() for FMA2 too, but it makes
+ * Visual Studio crash. Instead we use this version, which leverages
+ * the fact that the vx operands, and the products, are multiple of 4.
+ * This is unfortunately slower.
+ */
+#define FMA2(hi, lo, x1, y1, x2, y2, v1, v2) do { \
+ uint64_t fma1hi, fma1lo; \
+ uint64_t fma2hi, fma2lo; \
+ uint64_t fmatt; \
+ fma1lo = _umul128((x1), (y1), &fma1hi); \
+ fma2lo = _umul128((x2), (y2), &fma2hi); \
+ fmatt = (fma1lo >> 2) + (fma2lo >> 2) \
+ + ((v1) >> 2) + ((v2) >> 2); \
+ (lo) = fmatt << 2; \
+ (hi) = fma1hi + fma2hi + (fmatt >> 62); \
+ } while (0)
+
+/*
+ * The FMA2 macro definition we would prefer to use, but it triggers
+ * an internal compiler error in Visual Studio 2015.
+ *
+#define FMA2(hi, lo, x1, y1, x2, y2, v1, v2) do { \
+ uint64_t fma1hi, fma1lo; \
+ uint64_t fma2hi, fma2lo; \
+ unsigned char fmacc; \
+ fma1lo = _umul128((x1), (y1), &fma1hi); \
+ fma2lo = _umul128((x2), (y2), &fma2hi); \
+ fmacc = _addcarry_u64(0, fma1lo, (v1), &fma1lo); \
+ _addcarry_u64(fmacc, fma1hi, 0, &fma1hi); \
+ fmacc = _addcarry_u64(0, fma2lo, (v2), &fma2lo); \
+ _addcarry_u64(fmacc, fma2hi, 0, &fma2hi); \
+ fmacc = _addcarry_u64(0, fma1lo, fma2lo, &(lo)); \
+ _addcarry_u64(fmacc, fma1hi, fma2hi, &(hi)); \
+ } while (0)
+ */
+
+#endif
+
+#define MASK62 ((uint64_t)0x3FFFFFFFFFFFFFFF)
+#define MUL62_lo(x, y) (((uint64_t)(x) * (uint64_t)(y)) & MASK62)
+
+/*
+ * Subtract b from a, and return the final carry. If 'ctl32' is 0, then
+ * a[] is kept unmodified, but the final carry is still computed and
+ * returned.
+ */
+static uint32_t
+i62_sub(uint64_t *a, const uint64_t *b, size_t num, uint32_t ctl32)
+{
+ uint64_t cc, mask;
+ size_t u;
+
+ cc = 0;
+ ctl32 = -ctl32;
+ mask = (uint64_t)ctl32 | ((uint64_t)ctl32 << 32);
+ for (u = 0; u < num; u ++) {
+ uint64_t aw, bw, dw;
+
+ aw = a[u];
+ bw = b[u];
+ dw = aw - bw - cc;
+ cc = dw >> 63;
+ dw &= MASK62;
+ a[u] = aw ^ (mask & (dw ^ aw));
+ }
+ return (uint32_t)cc;
+}
+
+/*
+ * Montgomery multiplication, over arrays of 62-bit values. The
+ * destination array (d) must be distinct from the other operands
+ * (x, y and m). All arrays are in little-endian format (least
+ * significant word comes first) over 'num' words.
+ */
+static void
+montymul(uint64_t *d, const uint64_t *x, const uint64_t *y,
+ const uint64_t *m, size_t num, uint64_t m0i)
+{
+ uint64_t dh;
+ size_t u, num4;
+
+ num4 = 1 + ((num - 1) & ~(size_t)3);
+ memset(d, 0, num * sizeof *d);
+ dh = 0;
+ for (u = 0; u < num; u ++) {
+ size_t v;
+ uint64_t f, xu;
+ uint64_t r, zh;
+ uint64_t hi, lo;
+
+ xu = x[u] << 2;
+ f = MUL62_lo(d[0] + MUL62_lo(x[u], y[0]), m0i) << 2;
+
+ FMA2(hi, lo, xu, y[0], f, m[0], d[0] << 2, 0);
+ r = hi;
+
+ for (v = 1; v < num4; v += 4) {
+ FMA2(hi, lo, xu, y[v + 0],
+ f, m[v + 0], d[v + 0] << 2, r << 2);
+ r = hi + (r >> 62);
+ d[v - 1] = lo >> 2;
+ FMA2(hi, lo, xu, y[v + 1],
+ f, m[v + 1], d[v + 1] << 2, r << 2);
+ r = hi + (r >> 62);
+ d[v + 0] = lo >> 2;
+ FMA2(hi, lo, xu, y[v + 2],
+ f, m[v + 2], d[v + 2] << 2, r << 2);
+ r = hi + (r >> 62);
+ d[v + 1] = lo >> 2;
+ FMA2(hi, lo, xu, y[v + 3],
+ f, m[v + 3], d[v + 3] << 2, r << 2);
+ r = hi + (r >> 62);
+ d[v + 2] = lo >> 2;
+ }
+ for (; v < num; v ++) {
+ FMA2(hi, lo, xu, y[v], f, m[v], d[v] << 2, r << 2);
+ r = hi + (r >> 62);
+ d[v - 1] = lo >> 2;
+ }
+
+ zh = dh + r;
+ d[num - 1] = zh & MASK62;
+ dh = zh >> 62;
+ }
+ i62_sub(d, m, num, (uint32_t)dh | NOT(i62_sub(d, m, num, 0)));
+}
+
+/*
+ * Conversion back from Montgomery representation.
+ */
+static void
+frommonty(uint64_t *x, const uint64_t *m, size_t num, uint64_t m0i)
+{
+ size_t u, v;
+
+ for (u = 0; u < num; u ++) {
+ uint64_t f, cc;
+
+ f = MUL62_lo(x[0], m0i) << 2;
+ cc = 0;
+ for (v = 0; v < num; v ++) {
+ uint64_t hi, lo;
+
+ FMA1(hi, lo, f, m[v], x[v] << 2, cc);
+ cc = hi << 2;
+ if (v != 0) {
+ x[v - 1] = lo >> 2;
+ }
+ }
+ x[num - 1] = cc >> 2;
+ }
+ i62_sub(x, m, num, NOT(i62_sub(x, m, num, 0)));
+}
+
+/* see inner.h */
+uint32_t
+br_i62_modpow_opt(uint32_t *x31, const unsigned char *e, size_t elen,
+ const uint32_t *m31, uint32_t m0i31, uint64_t *tmp, size_t twlen)
+{
+ size_t u, mw31num, mw62num;
+ uint64_t *x, *m, *t1, *t2;
+ uint64_t m0i;
+ uint32_t acc;
+ int win_len, acc_len;
+
+ /*
+ * Get modulus size, in words.
+ */
+ mw31num = (m31[0] + 31) >> 5;
+ mw62num = (mw31num + 1) >> 1;
+
+ /*
+ * In order to apply this function, we must have enough room tp
+ * copy the operand and modulus into the temporary array, along
+ * with at least two temporaries. If there is not enough room,
+ * switch to br_i31_modpow(). We also use br_i31_modpow() if the
+ * modulus length is not at least four words (94 bits or more).
+ */
+ if (mw31num < 4 || (mw62num << 2) > twlen) {
+ /*
+ * We assume here that we can split an aligned uint64_t
+ * into two properly aligned uint32_t. Since both types
+ * are supposed to have an exact width with no padding,
+ * then this property must hold.
+ */
+ size_t txlen;
+
+ txlen = mw31num + 1;
+ if (twlen < txlen) {
+ return 0;
+ }
+ br_i31_modpow(x31, e, elen, m31, m0i31,
+ (uint32_t *)tmp, (uint32_t *)tmp + txlen);
+ return 1;
+ }
+
+ /*
+ * Convert x to Montgomery representation: this means that
+ * we replace x with x*2^z mod m, where z is the smallest multiple
+ * of the word size such that 2^z >= m. We want to reuse the 31-bit
+ * functions here (for constant-time operation), but we need z
+ * for a 62-bit word size.
+ */
+ for (u = 0; u < mw62num; u ++) {
+ br_i31_muladd_small(x31, 0, m31);
+ br_i31_muladd_small(x31, 0, m31);
+ }
+
+ /*
+ * Assemble operands into arrays of 62-bit words. Note that
+ * all the arrays of 62-bit words that we will handle here
+ * are without any leading size word.
+ *
+ * We also adjust tmp and twlen to account for the words used
+ * for these extra arrays.
+ */
+ m = tmp;
+ x = tmp + mw62num;
+ tmp += (mw62num << 1);
+ twlen -= (mw62num << 1);
+ for (u = 0; u < mw31num; u += 2) {
+ size_t v;
+
+ v = u >> 1;
+ if ((u + 1) == mw31num) {
+ m[v] = (uint64_t)m31[u + 1];
+ x[v] = (uint64_t)x31[u + 1];
+ } else {
+ m[v] = (uint64_t)m31[u + 1]
+ + ((uint64_t)m31[u + 2] << 31);
+ x[v] = (uint64_t)x31[u + 1]
+ + ((uint64_t)x31[u + 2] << 31);
+ }
+ }
+
+ /*
+ * Compute window size. We support windows up to 5 bits; for a
+ * window of size k bits, we need 2^k+1 temporaries (for k = 1,
+ * we use special code that uses only 2 temporaries).
+ */
+ for (win_len = 5; win_len > 1; win_len --) {
+ if ((((uint32_t)1 << win_len) + 1) * mw62num <= twlen) {
+ break;
+ }
+ }
+
+ t1 = tmp;
+ t2 = tmp + mw62num;
+
+ /*
+ * Compute m0i, which is equal to -(1/m0) mod 2^62. We were
+ * provided with m0i31, which already fulfills this property
+ * modulo 2^31; the single expression below is then sufficient.
+ */
+ m0i = (uint64_t)m0i31;
+ m0i = MUL62_lo(m0i, (uint64_t)2 + MUL62_lo(m0i, m[0]));
+
+ /*
+ * Compute window contents. If the window has size one bit only,
+ * then t2 is set to x; otherwise, t2[0] is left untouched, and
+ * t2[k] is set to x^k (for k >= 1).
+ */
+ if (win_len == 1) {
+ memcpy(t2, x, mw62num * sizeof *x);
+ } else {
+ uint64_t *base;
+
+ memcpy(t2 + mw62num, x, mw62num * sizeof *x);
+ base = t2 + mw62num;
+ for (u = 2; u < ((unsigned)1 << win_len); u ++) {
+ montymul(base + mw62num, base, x, m, mw62num, m0i);
+ base += mw62num;
+ }
+ }
+
+ /*
+ * Set x to 1, in Montgomery representation. We again use the
+ * 31-bit code.
+ */
+ br_i31_zero(x31, m31[0]);
+ x31[(m31[0] + 31) >> 5] = 1;
+ br_i31_muladd_small(x31, 0, m31);
+ if (mw31num & 1) {
+ br_i31_muladd_small(x31, 0, m31);
+ }
+ for (u = 0; u < mw31num; u += 2) {
+ size_t v;
+
+ v = u >> 1;
+ if ((u + 1) == mw31num) {
+ x[v] = (uint64_t)x31[u + 1];
+ } else {
+ x[v] = (uint64_t)x31[u + 1]
+ + ((uint64_t)x31[u + 2] << 31);
+ }
+ }
+
+ /*
+ * We process bits from most to least significant. At each
+ * loop iteration, we have acc_len bits in acc.
+ */
+ acc = 0;
+ acc_len = 0;
+ while (acc_len > 0 || elen > 0) {
+ int i, k;
+ uint32_t bits;
+ uint64_t mask1, mask2;
+
+ /*
+ * Get the next bits.
+ */
+ k = win_len;
+ if (acc_len < win_len) {
+ if (elen > 0) {
+ acc = (acc << 8) | *e ++;
+ elen --;
+ acc_len += 8;
+ } else {
+ k = acc_len;
+ }
+ }
+ bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1);
+ acc_len -= k;
+
+ /*
+ * We could get exactly k bits. Compute k squarings.
+ */
+ for (i = 0; i < k; i ++) {
+ montymul(t1, x, x, m, mw62num, m0i);
+ memcpy(x, t1, mw62num * sizeof *x);
+ }
+
+ /*
+ * Window lookup: we want to set t2 to the window
+ * lookup value, assuming the bits are non-zero. If
+ * the window length is 1 bit only, then t2 is
+ * already set; otherwise, we do a constant-time lookup.
+ */
+ if (win_len > 1) {
+ uint64_t *base;
+
+ memset(t2, 0, mw62num * sizeof *t2);
+ base = t2 + mw62num;
+ for (u = 1; u < ((uint32_t)1 << k); u ++) {
+ uint64_t mask;
+ size_t v;
+
+ mask = -(uint64_t)EQ(u, bits);
+ for (v = 0; v < mw62num; v ++) {
+ t2[v] |= mask & base[v];
+ }
+ base += mw62num;
+ }
+ }
+
+ /*
+ * Multiply with the looked-up value. We keep the product
+ * only if the exponent bits are not all-zero.
+ */
+ montymul(t1, x, t2, m, mw62num, m0i);
+ mask1 = -(uint64_t)EQ(bits, 0);
+ mask2 = ~mask1;
+ for (u = 0; u < mw62num; u ++) {
+ x[u] = (mask1 & x[u]) | (mask2 & t1[u]);
+ }
+ }
+
+ /*
+ * Convert back from Montgomery representation.
+ */
+ frommonty(x, m, mw62num, m0i);
+
+ /*
+ * Convert result into 31-bit words.
+ */
+ for (u = 0; u < mw31num; u += 2) {
+ uint64_t zw;
+
+ zw = x[u >> 1];
+ x31[u + 1] = (uint32_t)zw & 0x7FFFFFFF;
+ if ((u + 1) < mw31num) {
+ x31[u + 2] = (uint32_t)(zw >> 31);
+ }
+ }
+ return 1;
+}
+
+#else
+
+/* see inner.h */
+uint32_t
+br_i62_modpow_opt(uint32_t *x31, const unsigned char *e, size_t elen,
+ const uint32_t *m31, uint32_t m0i31, uint64_t *tmp, size_t twlen)
+{
+ size_t mwlen;
+
+ mwlen = (m31[0] + 63) >> 5;
+ if (twlen < mwlen) {
+ return 0;
+ }
+ return br_i31_modpow_opt(x31, e, elen, m31, m0i31,
+ (uint32_t *)tmp, twlen << 1);
+}
+
+#endif
projects / BearSSL / commitdiff