--- /dev/null
+/*
+ * 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"
+
+/*
+ * Constant-time division. The divisor must not be larger than 16 bits,
+ * and the quotient must fit on 17 bits.
+ */
+static uint32_t
+divrem16(uint32_t x, uint32_t d, uint32_t *r)
+{
+ int i;
+ uint32_t q;
+
+ q = 0;
+ d <<= 16;
+ for (i = 16; i >= 0; i --) {
+ uint32_t ctl;
+
+ ctl = LE(d, x);
+ q |= ctl << i;
+ x -= (-ctl) & d;
+ d >>= 1;
+ }
+ if (r != NULL) {
+ *r = x;
+ }
+ return q;
+}
+
+/* see inner.h */
+void
+br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m)
+{
+ /*
+ * Constant-time: we accept to leak the exact bit length of the
+ * modulus m.
+ */
+ unsigned m_bitlen, mblr;
+ size_t u, mlen;
+ uint32_t hi, a0, a, b, q;
+ uint32_t cc, tb, over, under;
+
+ /*
+ * Simple case: the modulus fits on one word.
+ */
+ m_bitlen = m[0];
+ if (m_bitlen == 0) {
+ return;
+ }
+ if (m_bitlen <= 15) {
+ uint32_t rem;
+
+ divrem16(((uint32_t)x[1] << 15) | z, m[1], &rem);
+ x[1] = rem;
+ return;
+ }
+ mlen = (m_bitlen + 15) >> 4;
+ mblr = m_bitlen & 15;
+
+ /*
+ * Principle: we estimate the quotient (x*2^15+z)/m by
+ * doing a 30/15 division with the high words.
+ *
+ * Let:
+ * w = 2^15
+ * a = (w*a0 + a1) * w^N + a2
+ * b = b0 * w^N + b2
+ * such that:
+ * 0 <= a0 < w
+ * 0 <= a1 < w
+ * 0 <= a2 < w^N
+ * w/2 <= b0 < w
+ * 0 <= b2 < w^N
+ * a < w*b
+ * I.e. the two top words of a are a0:a1, the top word of b is
+ * b0, we ensured that b0 is "full" (high bit set), and a is
+ * such that the quotient q = a/b fits on one word (0 <= q < w).
+ *
+ * If a = b*q + r (with 0 <= r < q), then we can estimate q by
+ * using a division on the top words:
+ * a0*w + a1 = b0*u + v (with 0 <= v < b0)
+ * Then the following holds:
+ * 0 <= u <= w
+ * u-2 <= q <= u
+ */
+ hi = x[mlen];
+ if (mblr == 0) {
+ a0 = x[mlen];
+ memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
+ x[1] = z;
+ a = (a0 << 15) + x[mlen];
+ b = m[mlen];
+ } else {
+ a0 = (x[mlen] << (15 - mblr)) | (x[mlen - 1] >> mblr);
+ memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
+ x[1] = z;
+ a = (a0 << 15) | (((x[mlen] << (15 - mblr))
+ | (x[mlen - 1] >> mblr)) & 0x7FFF);
+ b = (m[mlen] << (15 - mblr)) | (m[mlen - 1] >> mblr);
+ }
+ q = divrem16(a, b, NULL);
+
+ /*
+ * We computed an estimate for q, but the real one may be q,
+ * q-1 or q-2; moreover, the division may have returned a value
+ * 8000 or even 8001 if the two high words were identical, and
+ * we want to avoid values beyond 7FFF. We thus adjust q so
+ * that the "true" multiplier will be q+1, q or q-1, and q is
+ * in the 0000..7FFF range.
+ */
+ q = MUX(EQ(b, a0), 0x7FFF, q - 1 + ((q - 1) >> 31));
+
+ /*
+ * We subtract q*m from x (x has an extra high word of value 'hi').
+ * Since q may be off by 1 (in either direction), we may have to
+ * add or subtract m afterwards.
+ *
+ * The 'tb' flag will be true (1) at the end of the loop if the
+ * result is greater than or equal to the modulus (not counting
+ * 'hi' or the carry).
+ */
+ cc = 0;
+ tb = 1;
+ for (u = 1; u <= mlen; u ++) {
+ uint32_t mw, zl, xw, nxw;
+
+ mw = m[u];
+ zl = MUL15(mw, q) + cc;
+ cc = zl >> 15;
+ zl &= 0x7FFF;
+ xw = x[u];
+ nxw = xw - zl;
+ cc += nxw >> 31;
+ nxw &= 0x7FFF;
+ x[u] = nxw;
+ tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
+ }
+
+ /*
+ * If we underestimated q, then either cc < hi (one extra bit
+ * beyond the top array word), or cc == hi and tb is true (no
+ * extra bit, but the result is not lower than the modulus).
+ *
+ * If we overestimated q, then cc > hi.
+ */
+ over = GT(cc, hi);
+ under = ~over & (tb | LT(cc, hi));
+ br_i15_add(x, m, over);
+ br_i15_sub(x, m, under);
+}
projects / BearSSL / blobdiff