X-Git-Url: https://www.bearssl.org/gitweb//home/git/?p=BearSSL;a=blobdiff_plain;f=src%2Fint%2Fi15_muladd.c;fp=src%2Fint%2Fi15_muladd.c;h=c4b72168e8b029e5bb542343f1eeee34160c7225;hp=0000000000000000000000000000000000000000;hb=2f454aad577ae53798935cc32438a2d3f02ba31f;hpb=bd3036844bd20b2b8d7bce7fee5ad010ce401915

diff --git a/src/int/i15_muladd.c b/src/int/i15_muladd.c
new file mode 100644
index 0000000..c4b7216
--- /dev/null
+++ b/src/int/i15_muladd.c
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+/*
+ * 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);
+}