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+/* Copyright 2008, Google Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are
+ * met:
+ *
+ * * Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * * Redistributions in binary form must reproduce the above
+ * copyright notice, this list of conditions and the following disclaimer
+ * in the documentation and/or other materials provided with the
+ * distribution.
+ * * Neither the name of Google Inc. nor the names of its
+ * contributors may be used to endorse or promote products derived from
+ * this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+ * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+ * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * curve25519-donna: Curve25519 elliptic curve, public key function
+ *
+ * http://code.google.com/p/curve25519-donna/
+ *
+ * Adam Langley <agl@imperialviolet.org>
+ *
+ * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
+ *
+ * More information about curve25519 can be found here
+ * http://cr.yp.to/ecdh.html
+ *
+ * djb's sample implementation of curve25519 is written in a special assembly
+ * language called qhasm and uses the floating point registers.
+ *
+ * This is, almost, a clean room reimplementation from the curve25519 paper. It
+ * uses many of the tricks described therein. Only the crecip function is taken
+ * from the sample implementation. */
+
+#include <string.h>
+#include <stdint.h>
+
+#ifdef _MSC_VER
+#define inline __inline
+#endif
+
+typedef uint8_t u8;
+typedef int32_t s32;
+typedef int64_t limb;
+
+/* Field element representation:
+ *
+ * Field elements are written as an array of signed, 64-bit limbs, least
+ * significant first. The value of the field element is:
+ * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
+ *
+ * i.e. the limbs are 26, 25, 26, 25, ... bits wide. */
+
+/* Sum two numbers: output += in */
+static void fsum(limb *output, const limb *in) {
+ unsigned i;
+ for (i = 0; i < 10; i += 2) {
+ output[0+i] = output[0+i] + in[0+i];
+ output[1+i] = output[1+i] + in[1+i];
+ }
+}
+
+/* Find the difference of two numbers: output = in - output
+ * (note the order of the arguments!). */
+static void fdifference(limb *output, const limb *in) {
+ unsigned i;
+ for (i = 0; i < 10; ++i) {
+ output[i] = in[i] - output[i];
+ }
+}
+
+/* Multiply a number by a scalar: output = in * scalar */
+static void fscalar_product(limb *output, const limb *in, const limb scalar) {
+ unsigned i;
+ for (i = 0; i < 10; ++i) {
+ output[i] = in[i] * scalar;
+ }
+}
+
+/* Multiply two numbers: output = in2 * in
+ *
+ * output must be distinct to both inputs. The inputs are reduced coefficient
+ * form, the output is not.
+ *
+ * output[x] <= 14 * the largest product of the input limbs. */
+static void fproduct(limb *output, const limb *in2, const limb *in) {
+ output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]);
+ output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[0]);
+ output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[0]);
+ output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[0]);
+ output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
+ 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[0])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[0]);
+ output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[0]);
+ output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[2])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[0]);
+ output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[0]);
+ output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
+ 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[2])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[0]);
+ output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[2]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[1]) +
+ ((limb) ((s32) in2[0])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[0]);
+ output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[1])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[1])) +
+ ((limb) ((s32) in2[4])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[2]);
+ output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[4]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[3]) +
+ ((limb) ((s32) in2[2])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[2]);
+ output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
+ 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[3])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[3])) +
+ ((limb) ((s32) in2[4])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[4]);
+ output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[7])) * ((s32) in[6]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[5]) +
+ ((limb) ((s32) in2[4])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[4]);
+ output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[5])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[5])) +
+ ((limb) ((s32) in2[6])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[6]);
+ output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
+ ((limb) ((s32) in2[8])) * ((s32) in[7]) +
+ ((limb) ((s32) in2[6])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[6]);
+ output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[7]));
+ output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
+ ((limb) ((s32) in2[9])) * ((s32) in[8]);
+ output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]);
+}
+
+/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
+ *
+ * On entry: |output[i]| < 14*2^54
+ * On exit: |output[0..8]| < 280*2^54 */
+static void freduce_degree(limb *output) {
+ /* Each of these shifts and adds ends up multiplying the value by 19.
+ *
+ * For output[0..8], the absolute entry value is < 14*2^54 and we add, at
+ * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */
+ output[8] += output[18] << 4;
+ output[8] += output[18] << 1;
+ output[8] += output[18];
+ output[7] += output[17] << 4;
+ output[7] += output[17] << 1;
+ output[7] += output[17];
+ output[6] += output[16] << 4;
+ output[6] += output[16] << 1;
+ output[6] += output[16];
+ output[5] += output[15] << 4;
+ output[5] += output[15] << 1;
+ output[5] += output[15];
+ output[4] += output[14] << 4;
+ output[4] += output[14] << 1;
+ output[4] += output[14];
+ output[3] += output[13] << 4;
+ output[3] += output[13] << 1;
+ output[3] += output[13];
+ output[2] += output[12] << 4;
+ output[2] += output[12] << 1;
+ output[2] += output[12];
+ output[1] += output[11] << 4;
+ output[1] += output[11] << 1;
+ output[1] += output[11];
+ output[0] += output[10] << 4;
+ output[0] += output[10] << 1;
+ output[0] += output[10];
+}
+
+#if (-1 & 3) != 3
+#error "This code only works on a two's complement system"
+#endif
+
+/* return v / 2^26, using only shifts and adds.
+ *
+ * On entry: v can take any value. */
+static inline limb
+div_by_2_26(const limb v)
+{
+ /* High word of v; no shift needed. */
+ const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
+ /* Set to all 1s if v was negative; else set to 0s. */
+ const int32_t sign = ((int32_t) highword) >> 31;
+ /* Set to 0x3ffffff if v was negative; else set to 0. */
+ const int32_t roundoff = ((uint32_t) sign) >> 6;
+ /* Should return v / (1<<26) */
+ return (v + roundoff) >> 26;
+}
+
+/* return v / (2^25), using only shifts and adds.
+ *
+ * On entry: v can take any value. */
+static inline limb
+div_by_2_25(const limb v)
+{
+ /* High word of v; no shift needed*/
+ const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
+ /* Set to all 1s if v was negative; else set to 0s. */
+ const int32_t sign = ((int32_t) highword) >> 31;
+ /* Set to 0x1ffffff if v was negative; else set to 0. */
+ const int32_t roundoff = ((uint32_t) sign) >> 7;
+ /* Should return v / (1<<25) */
+ return (v + roundoff) >> 25;
+}
+
+/* return v / (2^25), using only shifts and adds.
+ *
+ * On entry: v can take any value. */
+static inline s32
+div_s32_by_2_25(const s32 v)
+{
+ const s32 roundoff = ((uint32_t)(v >> 31)) >> 7;
+ return (v + roundoff) >> 25;
+}
+
+/* Reduce all coefficients of the short form input so that |x| < 2^26.
+ *
+ * On entry: |output[i]| < 280*2^54 */
+static void freduce_coefficients(limb *output) {
+ unsigned i;
+
+ output[10] = 0;
+
+ for (i = 0; i < 10; i += 2) {
+ limb over = div_by_2_26(output[i]);
+ /* The entry condition (that |output[i]| < 280*2^54) means that over is, at
+ * most, 280*2^28 in the first iteration of this loop. This is added to the
+ * next limb and we can approximate the resulting bound of that limb by
+ * 281*2^54. */
+ output[i] -= over << 26;
+ output[i+1] += over;
+
+ /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
+ * 281*2^29. When this is added to the next limb, the resulting bound can
+ * be approximated as 281*2^54.
+ *
+ * For subsequent iterations of the loop, 281*2^54 remains a conservative
+ * bound and no overflow occurs. */
+ over = div_by_2_25(output[i+1]);
+ output[i+1] -= over << 25;
+ output[i+2] += over;
+ }
+ /* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
+ output[0] += output[10] << 4;
+ output[0] += output[10] << 1;
+ output[0] += output[10];
+
+ output[10] = 0;
+
+ /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
+ * So |over| will be no more than 2^16. */
+ {
+ limb over = div_by_2_26(output[0]);
+ output[0] -= over << 26;
+ output[1] += over;
+ }
+
+ /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
+ * bound on |output[1]| is sufficient to meet our needs. */
+}
+
+/* A helpful wrapper around fproduct: output = in * in2.
+ *
+ * On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
+ *
+ * output must be distinct to both inputs. The output is reduced degree
+ * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */
+static void
+fmul(limb *output, const limb *in, const limb *in2) {
+ limb t[19];
+ fproduct(t, in, in2);
+ /* |t[i]| < 14*2^54 */
+ freduce_degree(t);
+ freduce_coefficients(t);
+ /* |t[i]| < 2^26 */
+ memcpy(output, t, sizeof(limb) * 10);
+}
+
+/* Square a number: output = in**2
+ *
+ * output must be distinct from the input. The inputs are reduced coefficient
+ * form, the output is not.
+ *
+ * output[x] <= 14 * the largest product of the input limbs. */
+static void fsquare_inner(limb *output, const limb *in) {
+ output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
+ output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
+ output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
+ ((limb) ((s32) in[0])) * ((s32) in[2]));
+ output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
+ ((limb) ((s32) in[0])) * ((s32) in[3]));
+ output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
+ 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
+ 2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
+ output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
+ ((limb) ((s32) in[1])) * ((s32) in[4]) +
+ ((limb) ((s32) in[0])) * ((s32) in[5]));
+ output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
+ ((limb) ((s32) in[2])) * ((s32) in[4]) +
+ ((limb) ((s32) in[0])) * ((s32) in[6]) +
+ 2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
+ output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
+ ((limb) ((s32) in[2])) * ((s32) in[5]) +
+ ((limb) ((s32) in[1])) * ((s32) in[6]) +
+ ((limb) ((s32) in[0])) * ((s32) in[7]));
+ output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
+ 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
+ ((limb) ((s32) in[0])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[5])));
+ output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
+ ((limb) ((s32) in[3])) * ((s32) in[6]) +
+ ((limb) ((s32) in[2])) * ((s32) in[7]) +
+ ((limb) ((s32) in[1])) * ((s32) in[8]) +
+ ((limb) ((s32) in[0])) * ((s32) in[9]));
+ output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
+ ((limb) ((s32) in[4])) * ((s32) in[6]) +
+ ((limb) ((s32) in[2])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
+ ((limb) ((s32) in[1])) * ((s32) in[9])));
+ output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
+ ((limb) ((s32) in[4])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[8]) +
+ ((limb) ((s32) in[2])) * ((s32) in[9]));
+ output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
+ 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
+ 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
+ ((limb) ((s32) in[3])) * ((s32) in[9])));
+ output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
+ ((limb) ((s32) in[5])) * ((s32) in[8]) +
+ ((limb) ((s32) in[4])) * ((s32) in[9]));
+ output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
+ ((limb) ((s32) in[6])) * ((s32) in[8]) +
+ 2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
+ output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
+ ((limb) ((s32) in[6])) * ((s32) in[9]));
+ output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
+ 4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
+ output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
+ output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]);
+}
+
+/* fsquare sets output = in^2.
+ *
+ * On entry: The |in| argument is in reduced coefficients form and |in[i]| <
+ * 2^27.
+ *
+ * On exit: The |output| argument is in reduced coefficients form (indeed, one
+ * need only provide storage for 10 limbs) and |out[i]| < 2^26. */
+static void
+fsquare(limb *output, const limb *in) {
+ limb t[19];
+ fsquare_inner(t, in);
+ /* |t[i]| < 14*2^54 because the largest product of two limbs will be <
+ * 2^(27+27) and fsquare_inner adds together, at most, 14 of those
+ * products. */
+ freduce_degree(t);
+ freduce_coefficients(t);
+ /* |t[i]| < 2^26 */
+ memcpy(output, t, sizeof(limb) * 10);
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static void
+fexpand(limb *output, const u8 *input) {
+#define F(n,start,shift,mask) \
+ output[n] = ((((limb) input[start + 0]) | \
+ ((limb) input[start + 1]) << 8 | \
+ ((limb) input[start + 2]) << 16 | \
+ ((limb) input[start + 3]) << 24) >> shift) & mask;
+ F(0, 0, 0, 0x3ffffff);
+ F(1, 3, 2, 0x1ffffff);
+ F(2, 6, 3, 0x3ffffff);
+ F(3, 9, 5, 0x1ffffff);
+ F(4, 12, 6, 0x3ffffff);
+ F(5, 16, 0, 0x1ffffff);
+ F(6, 19, 1, 0x3ffffff);
+ F(7, 22, 3, 0x1ffffff);
+ F(8, 25, 4, 0x3ffffff);
+ F(9, 28, 6, 0x1ffffff);
+#undef F
+}
+
+#if (-32 >> 1) != -16
+#error "This code only works when >> does sign-extension on negative numbers"
+#endif
+
+/* s32_eq returns 0xffffffff iff a == b and zero otherwise. */
+static s32 s32_eq(s32 a, s32 b) {
+ a = ~(a ^ b);
+ a &= a << 16;
+ a &= a << 8;
+ a &= a << 4;
+ a &= a << 2;
+ a &= a << 1;
+ return a >> 31;
+}
+
+/* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
+ * both non-negative. */
+static s32 s32_gte(s32 a, s32 b) {
+ a -= b;
+ /* a >= 0 iff a >= b. */
+ return ~(a >> 31);
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array.
+ *
+ * On entry: |input_limbs[i]| < 2^26 */
+static void
+fcontract(u8 *output, limb *input_limbs) {
+ int i;
+ int j;
+ s32 input[10];
+ s32 mask;
+
+ /* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */
+ for (i = 0; i < 10; i++) {
+ input[i] = input_limbs[i];
+ }
+
+ for (j = 0; j < 2; ++j) {
+ for (i = 0; i < 9; ++i) {
+ if ((i & 1) == 1) {
+ /* This calculation is a time-invariant way to make input[i]
+ * non-negative by borrowing from the next-larger limb. */
+ const s32 mask = input[i] >> 31;
+ const s32 carry = -((input[i] & mask) >> 25);
+ input[i] = input[i] + (carry << 25);
+ input[i+1] = input[i+1] - carry;
+ } else {
+ const s32 mask = input[i] >> 31;
+ const s32 carry = -((input[i] & mask) >> 26);
+ input[i] = input[i] + (carry << 26);
+ input[i+1] = input[i+1] - carry;
+ }
+ }
+
+ /* There's no greater limb for input[9] to borrow from, but we can multiply
+ * by 19 and borrow from input[0], which is valid mod 2^255-19. */
+ {
+ const s32 mask = input[9] >> 31;
+ const s32 carry = -((input[9] & mask) >> 25);
+ input[9] = input[9] + (carry << 25);
+ input[0] = input[0] - (carry * 19);
+ }
+
+ /* After the first iteration, input[1..9] are non-negative and fit within
+ * 25 or 26 bits, depending on position. However, input[0] may be
+ * negative. */
+ }
+
+ /* The first borrow-propagation pass above ended with every limb
+ except (possibly) input[0] non-negative.
+
+ If input[0] was negative after the first pass, then it was because of a
+ carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
+ one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
+
+ In the second pass, each limb is decreased by at most one. Thus the second
+ borrow-propagation pass could only have wrapped around to decrease
+ input[0] again if the first pass left input[0] negative *and* input[1]
+ through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
+ and this last borrow-propagation step will leave input[1] non-negative. */
+ {
+ const s32 mask = input[0] >> 31;
+ const s32 carry = -((input[0] & mask) >> 26);
+ input[0] = input[0] + (carry << 26);
+ input[1] = input[1] - carry;
+ }
+
+ /* All input[i] are now non-negative. However, there might be values between
+ * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */
+ for (j = 0; j < 2; j++) {
+ for (i = 0; i < 9; i++) {
+ if ((i & 1) == 1) {
+ const s32 carry = input[i] >> 25;
+ input[i] &= 0x1ffffff;
+ input[i+1] += carry;
+ } else {
+ const s32 carry = input[i] >> 26;
+ input[i] &= 0x3ffffff;
+ input[i+1] += carry;
+ }
+ }
+
+ {
+ const s32 carry = input[9] >> 25;
+ input[9] &= 0x1ffffff;
+ input[0] += 19*carry;
+ }
+ }
+
+ /* If the first carry-chain pass, just above, ended up with a carry from
+ * input[9], and that caused input[0] to be out-of-bounds, then input[0] was
+ * < 2^26 + 2*19, because the carry was, at most, two.
+ *
+ * If the second pass carried from input[9] again then input[0] is < 2*19 and
+ * the input[9] -> input[0] carry didn't push input[0] out of bounds. */
+
+ /* It still remains the case that input might be between 2^255-19 and 2^255.
+ * In this case, input[1..9] must take their maximum value and input[0] must
+ * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */
+ mask = s32_gte(input[0], 0x3ffffed);
+ for (i = 1; i < 10; i++) {
+ if ((i & 1) == 1) {
+ mask &= s32_eq(input[i], 0x1ffffff);
+ } else {
+ mask &= s32_eq(input[i], 0x3ffffff);
+ }
+ }
+
+ /* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
+ * this conditionally subtracts 2^255-19. */
+ input[0] -= mask & 0x3ffffed;
+
+ for (i = 1; i < 10; i++) {
+ if ((i & 1) == 1) {
+ input[i] -= mask & 0x1ffffff;
+ } else {
+ input[i] -= mask & 0x3ffffff;
+ }
+ }
+
+ input[1] <<= 2;
+ input[2] <<= 3;
+ input[3] <<= 5;
+ input[4] <<= 6;
+ input[6] <<= 1;
+ input[7] <<= 3;
+ input[8] <<= 4;
+ input[9] <<= 6;
+#define F(i, s) \
+ output[s+0] |= input[i] & 0xff; \
+ output[s+1] = (input[i] >> 8) & 0xff; \
+ output[s+2] = (input[i] >> 16) & 0xff; \
+ output[s+3] = (input[i] >> 24) & 0xff;
+ output[0] = 0;
+ output[16] = 0;
+ F(0,0);
+ F(1,3);
+ F(2,6);
+ F(3,9);
+ F(4,12);
+ F(5,16);
+ F(6,19);
+ F(7,22);
+ F(8,25);
+ F(9,28);
+#undef F
+}
+
+/* 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
+ *
+ * On entry and exit, the absolute value of the limbs of all inputs and outputs
+ * are < 2^26. */
+static void fmonty(limb *x2, limb *z2, /* output 2Q */
+ limb *x3, limb *z3, /* output Q + Q' */
+ limb *x, limb *z, /* input Q */
+ limb *xprime, limb *zprime, /* input Q' */
+ const limb *qmqp /* input Q - Q' */) {
+ limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
+ zzprime[19], zzzprime[19], xxxprime[19];
+
+ memcpy(origx, x, 10 * sizeof(limb));
+ fsum(x, z);
+ /* |x[i]| < 2^27 */
+ fdifference(z, origx); /* does x - z */
+ /* |z[i]| < 2^27 */
+
+ memcpy(origxprime, xprime, sizeof(limb) * 10);
+ fsum(xprime, zprime);
+ /* |xprime[i]| < 2^27 */
+ fdifference(zprime, origxprime);
+ /* |zprime[i]| < 2^27 */
+ fproduct(xxprime, xprime, z);
+ /* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
+ * 2^(27+27) and fproduct adds together, at most, 14 of those products.
+ * (Approximating that to 2^58 doesn't work out.) */
+ fproduct(zzprime, x, zprime);
+ /* |zzprime[i]| < 14*2^54 */
+ freduce_degree(xxprime);
+ freduce_coefficients(xxprime);
+ /* |xxprime[i]| < 2^26 */
+ freduce_degree(zzprime);
+ freduce_coefficients(zzprime);
+ /* |zzprime[i]| < 2^26 */
+ memcpy(origxprime, xxprime, sizeof(limb) * 10);
+ fsum(xxprime, zzprime);
+ /* |xxprime[i]| < 2^27 */
+ fdifference(zzprime, origxprime);
+ /* |zzprime[i]| < 2^27 */
+ fsquare(xxxprime, xxprime);
+ /* |xxxprime[i]| < 2^26 */
+ fsquare(zzzprime, zzprime);
+ /* |zzzprime[i]| < 2^26 */
+ fproduct(zzprime, zzzprime, qmqp);
+ /* |zzprime[i]| < 14*2^52 */
+ freduce_degree(zzprime);
+ freduce_coefficients(zzprime);
+ /* |zzprime[i]| < 2^26 */
+ memcpy(x3, xxxprime, sizeof(limb) * 10);
+ memcpy(z3, zzprime, sizeof(limb) * 10);
+
+ fsquare(xx, x);
+ /* |xx[i]| < 2^26 */
+ fsquare(zz, z);
+ /* |zz[i]| < 2^26 */
+ fproduct(x2, xx, zz);
+ /* |x2[i]| < 14*2^52 */
+ freduce_degree(x2);
+ freduce_coefficients(x2);
+ /* |x2[i]| < 2^26 */
+ fdifference(zz, xx); // does zz = xx - zz
+ /* |zz[i]| < 2^27 */
+ memset(zzz + 10, 0, sizeof(limb) * 9);
+ fscalar_product(zzz, zz, 121665);
+ /* |zzz[i]| < 2^(27+17) */
+ /* No need to call freduce_degree here:
+ fscalar_product doesn't increase the degree of its input. */
+ freduce_coefficients(zzz);
+ /* |zzz[i]| < 2^26 */
+ fsum(zzz, xx);
+ /* |zzz[i]| < 2^27 */
+ fproduct(z2, zz, zzz);
+ /* |z2[i]| < 14*2^(26+27) */
+ freduce_degree(z2);
+ freduce_coefficients(z2);
+ /* |z2|i| < 2^26 */
+}
+
+/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
+ * them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
+ * side-channel attacks.
+ *
+ * NOTE that this function requires that 'iswap' be 1 or 0; other values give
+ * wrong results. Also, the two limb arrays must be in reduced-coefficient,
+ * reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
+ * and all all values in a[0..9],b[0..9] must have magnitude less than
+ * INT32_MAX. */
+static void
+swap_conditional(limb a[19], limb b[19], limb iswap) {
+ unsigned i;
+ const s32 swap = (s32) -iswap;
+
+ for (i = 0; i < 10; ++i) {
+ const s32 x = swap & ( ((s32)a[i]) ^ ((s32)b[i]) );
+ a[i] = ((s32)a[i]) ^ x;
+ b[i] = ((s32)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 little endian, 32-byte number
+ * q: a point of the curve (short form) */
+static void
+cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) {
+ limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
+ limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
+ limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
+ limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
+
+ unsigned i, j;
+
+ memcpy(nqpqx, q, sizeof(limb) * 10);
+
+ for (i = 0; i < 32; ++i) {
+ u8 byte = n[31 - i];
+ for (j = 0; j < 8; ++j) {
+ const limb bit = byte >> 7;
+
+ swap_conditional(nqx, nqpqx, bit);
+ swap_conditional(nqz, nqpqz, bit);
+ fmonty(nqx2, nqz2,
+ nqpqx2, nqpqz2,
+ nqx, nqz,
+ nqpqx, nqpqz,
+ q);
+ swap_conditional(nqx2, nqpqx2, bit);
+ swap_conditional(nqz2, nqpqz2, 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(limb) * 10);
+ memcpy(resultz, nqz, sizeof(limb) * 10);
+}
+
+// -----------------------------------------------------------------------------
+// Shamelessly copied from djb's code
+// -----------------------------------------------------------------------------
+static void
+crecip(limb *out, const limb *z) {
+ limb z2[10];
+ limb z9[10];
+ limb z11[10];
+ limb z2_5_0[10];
+ limb z2_10_0[10];
+ limb z2_20_0[10];
+ limb z2_50_0[10];
+ limb z2_100_0[10];
+ limb t0[10];
+ limb t1[10];
+ 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);
+}
+
+int
+curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) {
+ limb bp[10], x[10], z[11], zmone[10];
+ 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;
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-11 15:37:50 +0000