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-rw-r--r--src/ext/curve25519_donna/README44
-rw-r--r--src/ext/curve25519_donna/curve25519-donna-c64.c449
-rw-r--r--src/ext/curve25519_donna/curve25519-donna.c730
3 files changed, 1223 insertions, 0 deletions
diff --git a/src/ext/curve25519_donna/README b/src/ext/curve25519_donna/README
new file mode 100644
index 000000000..9f77bd7d9
--- /dev/null
+++ b/src/ext/curve25519_donna/README
@@ -0,0 +1,44 @@
+See http://code.google.com/p/curve25519-donna/ for details.
+
+BUILDING:
+
+If you run `make`, two .a archives will be built, similar to djb's curve25519
+code. Alternatively, read on:
+
+The C implementation is contained within curve25519-donna.c. It has no external
+dependancies and is BSD licenced. You can copy/include/link it directly in with
+your program. Recommended C flags: -O2
+
+The x86-64 bit implementation is contained within curve25519-donna-x86-64.c and
+curve25519-donna-x86-64.s. Build like this:
+
+% cpp curve25519-donna-x86-64.s > curve25519-donna-x86-64.s.pp
+% as -o curve25519-donna-x86-64.s.o curve25519-donna-x86-64.s.pp
+% gcc -O2 -c curve25519-donna-x86-64.c
+
+Then the two .o files can be linked in
+
+USAGE:
+
+The usage is exactly the same as djb's code (as described at
+http://cr.yp.to/ecdh.html) expect that the function is called curve25519_donna.
+
+In short,
+
+To generate a private key, generate 32 random bytes and:
+
+ mysecret[0] &= 248;
+ mysecret[31] &= 127;
+ mysecret[31] |= 64;
+
+To generate the public key, just do
+
+ static const uint8_t basepoint[32] = {9};
+ curve25519_donna(mypublic, mysecret, basepoint);
+
+To generate an agreed key do:
+ uint8_t shared_key[32];
+ curve25519_donna(shared_key, mysecret, theirpublic);
+
+And hash the shared_key with a cryptographic hash function before using.
+
diff --git a/src/ext/curve25519_donna/curve25519-donna-c64.c b/src/ext/curve25519_donna/curve25519-donna-c64.c
new file mode 100644
index 000000000..9ebd8a12d
--- /dev/null
+++ b/src/ext/curve25519_donna/curve25519-donna-c64.c
@@ -0,0 +1,449 @@
+/* Copyright 2008, Google Inc.
+ * All rights reserved.
+ *
+ * Code released into the public domain.
+ *
+ * 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>
+
+typedef uint8_t u8;
+typedef uint64_t limb;
+typedef limb felem[5];
+// This is a special gcc mode for 128-bit integers. It's implemented on 64-bit
+// platforms only as far as I know.
+typedef unsigned uint128_t __attribute__((mode(TI)));
+
+#undef force_inline
+#define force_inline __attribute__((always_inline))
+
+/* Sum two numbers: output += in */
+static inline void force_inline
+fsum(limb *output, const limb *in) {
+ output[0] += in[0];
+ output[1] += in[1];
+ output[2] += in[2];
+ output[3] += in[3];
+ output[4] += in[4];
+}
+
+/* Find the difference of two numbers: output = in - output
+ * (note the order of the arguments!)
+ *
+ * Assumes that out[i] < 2**52
+ * On return, out[i] < 2**55
+ */
+static inline void force_inline
+fdifference_backwards(felem out, const felem in) {
+ /* 152 is 19 << 3 */
+ static const limb two54m152 = (((limb)1) << 54) - 152;
+ static const limb two54m8 = (((limb)1) << 54) - 8;
+
+ out[0] = in[0] + two54m152 - out[0];
+ out[1] = in[1] + two54m8 - out[1];
+ out[2] = in[2] + two54m8 - out[2];
+ out[3] = in[3] + two54m8 - out[3];
+ out[4] = in[4] + two54m8 - out[4];
+}
+
+/* Multiply a number by a scalar: output = in * scalar */
+static inline void force_inline
+fscalar_product(felem output, const felem in, const limb scalar) {
+ uint128_t a;
+
+ a = ((uint128_t) in[0]) * scalar;
+ output[0] = ((limb)a) & 0x7ffffffffffff;
+
+ a = ((uint128_t) in[1]) * scalar + ((limb) (a >> 51));
+ output[1] = ((limb)a) & 0x7ffffffffffff;
+
+ a = ((uint128_t) in[2]) * scalar + ((limb) (a >> 51));
+ output[2] = ((limb)a) & 0x7ffffffffffff;
+
+ a = ((uint128_t) in[3]) * scalar + ((limb) (a >> 51));
+ output[3] = ((limb)a) & 0x7ffffffffffff;
+
+ a = ((uint128_t) in[4]) * scalar + ((limb) (a >> 51));
+ output[4] = ((limb)a) & 0x7ffffffffffff;
+
+ output[0] += (a >> 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.
+ *
+ * Assumes that in[i] < 2**55 and likewise for in2.
+ * On return, output[i] < 2**52
+ */
+static inline void force_inline
+fmul(felem output, const felem in2, const felem in) {
+ uint128_t t[5];
+ limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
+
+ r0 = in[0];
+ r1 = in[1];
+ r2 = in[2];
+ r3 = in[3];
+ r4 = in[4];
+
+ s0 = in2[0];
+ s1 = in2[1];
+ s2 = in2[2];
+ s3 = in2[3];
+ s4 = in2[4];
+
+ t[0] = ((uint128_t) r0) * s0;
+ t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
+ t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
+ t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
+ t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
+
+ r4 *= 19;
+ r1 *= 19;
+ r2 *= 19;
+ r3 *= 19;
+
+ t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
+ t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
+ t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
+ t[3] += ((uint128_t) r4) * s4;
+
+ r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
+ t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
+ t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
+ t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
+ t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
+ r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
+ r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
+ r2 += c;
+
+ output[0] = r0;
+ output[1] = r1;
+ output[2] = r2;
+ output[3] = r3;
+ output[4] = r4;
+}
+
+static inline void force_inline
+fsquare_times(felem output, const felem in, limb count) {
+ uint128_t t[5];
+ limb r0,r1,r2,r3,r4,c;
+ limb d0,d1,d2,d4,d419;
+
+ r0 = in[0];
+ r1 = in[1];
+ r2 = in[2];
+ r3 = in[3];
+ r4 = in[4];
+
+ do {
+ d0 = r0 * 2;
+ d1 = r1 * 2;
+ d2 = r2 * 2 * 19;
+ d419 = r4 * 19;
+ d4 = d419 * 2;
+
+ t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
+ t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
+ t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
+ t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
+ t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
+
+ r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
+ t[1] += c; r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
+ t[2] += c; r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
+ t[3] += c; r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
+ t[4] += c; r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
+ r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
+ r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
+ r2 += c;
+ } while(--count);
+
+ output[0] = r0;
+ output[1] = r1;
+ output[2] = r2;
+ output[3] = r3;
+ output[4] = r4;
+}
+
+/* Load a little-endian 64-bit number */
+static limb
+load_limb(const u8 *in) {
+ return
+ ((limb)in[0]) |
+ (((limb)in[1]) << 8) |
+ (((limb)in[2]) << 16) |
+ (((limb)in[3]) << 24) |
+ (((limb)in[4]) << 32) |
+ (((limb)in[5]) << 40) |
+ (((limb)in[6]) << 48) |
+ (((limb)in[7]) << 56);
+}
+
+static void
+store_limb(u8 *out, limb in) {
+ out[0] = in & 0xff;
+ out[1] = (in >> 8) & 0xff;
+ out[2] = (in >> 16) & 0xff;
+ out[3] = (in >> 24) & 0xff;
+ out[4] = (in >> 32) & 0xff;
+ out[5] = (in >> 40) & 0xff;
+ out[6] = (in >> 48) & 0xff;
+ out[7] = (in >> 56) & 0xff;
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static void
+fexpand(limb *output, const u8 *in) {
+ output[0] = load_limb(in) & 0x7ffffffffffff;
+ output[1] = (load_limb(in+6) >> 3) & 0x7ffffffffffff;
+ output[2] = (load_limb(in+12) >> 6) & 0x7ffffffffffff;
+ output[3] = (load_limb(in+19) >> 1) & 0x7ffffffffffff;
+ output[4] = (load_limb(in+24) >> 12) & 0x7ffffffffffff;
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+static void
+fcontract(u8 *output, const felem input) {
+ uint128_t t[5];
+
+ t[0] = input[0];
+ t[1] = input[1];
+ t[2] = input[2];
+ t[3] = input[3];
+ t[4] = input[4];
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
+
+ /* 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. */
+
+ t[0] += 19;
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
+ t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
+
+ /* now between 19 and 2^255-1 in both cases, and offset by 19. */
+
+ t[0] += 0x8000000000000 - 19;
+ t[1] += 0x8000000000000 - 1;
+ t[2] += 0x8000000000000 - 1;
+ t[3] += 0x8000000000000 - 1;
+ t[4] += 0x8000000000000 - 1;
+
+ /* now between 2^255 and 2^256-20, and offset by 2^255. */
+
+ t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
+ t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
+ t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
+ t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
+ t[4] &= 0x7ffffffffffff;
+
+ store_limb(output, t[0] | (t[1] << 51));
+ store_limb(output+8, (t[1] >> 13) | (t[2] << 38));
+ store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
+ store_limb(output+24, (t[3] >> 39) | (t[4] << 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(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[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5],
+ zzprime[5], zzzprime[5];
+
+ memcpy(origx, x, 5 * sizeof(limb));
+ fsum(x, z);
+ fdifference_backwards(z, origx); // does x - z
+
+ memcpy(origxprime, xprime, sizeof(limb) * 5);
+ fsum(xprime, zprime);
+ fdifference_backwards(zprime, origxprime);
+ fmul(xxprime, xprime, z);
+ fmul(zzprime, x, zprime);
+ memcpy(origxprime, xxprime, sizeof(limb) * 5);
+ fsum(xxprime, zzprime);
+ fdifference_backwards(zzprime, origxprime);
+ fsquare_times(x3, xxprime, 1);
+ fsquare_times(zzzprime, zzprime, 1);
+ fmul(z3, zzzprime, qmqp);
+
+ fsquare_times(xx, x, 1);
+ fsquare_times(zz, z, 1);
+ 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 limb 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(limb a[5], limb b[5], limb iswap) {
+ unsigned i;
+ const limb swap = -iswap;
+
+ for (i = 0; i < 5; ++i) {
+ const limb 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 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[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
+ limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
+ limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
+ limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
+
+ unsigned i, j;
+
+ memcpy(nqpqx, q, sizeof(limb) * 5);
+
+ 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) * 5);
+ memcpy(resultz, nqz, sizeof(limb) * 5);
+}
+
+
+// -----------------------------------------------------------------------------
+// Shamelessly copied from djb's code, tightened a little
+// -----------------------------------------------------------------------------
+static void
+crecip(felem out, const felem z) {
+ felem a,t0,b,c;
+
+ /* 2 */ fsquare_times(a, z, 1); // a = 2
+ /* 8 */ fsquare_times(t0, a, 2);
+ /* 9 */ fmul(b, t0, z); // b = 9
+ /* 11 */ fmul(a, b, a); // a = 11
+ /* 22 */ fsquare_times(t0, a, 1);
+ /* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
+ /* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
+ /* 2^10 - 2^0 */ fmul(b, t0, b);
+ /* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
+ /* 2^20 - 2^0 */ fmul(c, t0, b);
+ /* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
+ /* 2^40 - 2^0 */ fmul(t0, t0, c);
+ /* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
+ /* 2^50 - 2^0 */ fmul(b, t0, b);
+ /* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
+ /* 2^100 - 2^0 */ fmul(c, t0, b);
+ /* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
+ /* 2^200 - 2^0 */ fmul(t0, t0, c);
+ /* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
+ /* 2^250 - 2^0 */ fmul(t0, t0, b);
+ /* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
+ /* 2^255 - 21 */ fmul(out, t0, a);
+}
+
+int curve25519_donna(u8 *, const u8 *, const u8 *);
+
+int
+curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) {
+ limb 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;
+}
diff --git a/src/ext/curve25519_donna/curve25519-donna.c b/src/ext/curve25519_donna/curve25519-donna.c
new file mode 100644
index 000000000..80e4594ee
--- /dev/null
+++ b/src/ext/curve25519_donna/curve25519-donna.c
@@ -0,0 +1,730 @@
+/* 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>
+
+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.
+ */
+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. */
+static void freduce_degree(limb *output) {
+ /* Each of these shifts and adds ends up multiplying the value by 19. */
+ 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. */
+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. */
+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;
+}
+
+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]| < 2^62
+ */
+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]);
+ output[i] -= over << 26;
+ output[i+1] += over;
+
+ over = div_by_2_25(output[i+1]);
+ output[i+1] -= over << 25;
+ output[i+2] += over;
+ }
+ /* Now |output[10]| < 2 ^ 38 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 * 2^38
+ * So |over| will be no more than 77825 */
+ {
+ 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 + 77825
+ * So |over| will be no more than 1. */
+ {
+ /* output[1] fits in 32 bits, so we can use div_s32_by_2_25 here. */
+ s32 over32 = div_s32_by_2_25((s32) output[1]);
+ output[1] -= over32 << 25;
+ output[2] += over32;
+ }
+
+ /* Finally, output[0,1,3..9] are reduced, and output[2] is "nearly reduced":
+ * we have |output[2]| <= 2^26. This is good enough for all of our math,
+ * but it will require an extra freduce_coefficients before fcontract. */
+}
+
+/* A helpful wrapper around fproduct: output = in * in2.
+ *
+ * output must be distinct to both inputs. The output is reduced degree and
+ * reduced coefficient.
+ */
+static void
+fmul(limb *output, const limb *in, const limb *in2) {
+ limb t[19];
+ fproduct(t, in, in2);
+ freduce_degree(t);
+ freduce_coefficients(t);
+ memcpy(output, t, sizeof(limb) * 10);
+}
+
+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]);
+}
+
+static void
+fsquare(limb *output, const limb *in) {
+ limb t[19];
+ fsquare_inner(t, in);
+ freduce_degree(t);
+ freduce_coefficients(t);
+ 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
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+static void
+fcontract(u8 *output, limb *input) {
+ int i;
+ int j;
+
+ 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] positive
+ by borrowing from the next-larger limb.
+ */
+ const s32 mask = (s32)(input[i]) >> 31;
+ const s32 carry = -(((s32)(input[i]) & mask) >> 25);
+ input[i] = (s32)(input[i]) + (carry << 25);
+ input[i+1] = (s32)(input[i+1]) - carry;
+ } else {
+ const s32 mask = (s32)(input[i]) >> 31;
+ const s32 carry = -(((s32)(input[i]) & mask) >> 26);
+ input[i] = (s32)(input[i]) + (carry << 26);
+ input[i+1] = (s32)(input[i+1]) - carry;
+ }
+ }
+ {
+ const s32 mask = (s32)(input[9]) >> 31;
+ const s32 carry = -(((s32)(input[9]) & mask) >> 25);
+ input[9] = (s32)(input[9]) + (carry << 25);
+ input[0] = (s32)(input[0]) - (carry * 19);
+ }
+ }
+
+ /* The first borrow-propagation pass above ended with every limb
+ except (possibly) input[0] non-negative.
+
+ Since each input limb except input[0] is decreased by at most 1
+ by a borrow-propagation pass, 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 = (s32)(input[0]) >> 31;
+ const s32 carry = -(((s32)(input[0]) & mask) >> 26);
+ input[0] = (s32)(input[0]) + (carry << 26);
+ input[1] = (s32)(input[1]) - carry;
+ }
+
+ /* Both passes through the above loop, plus the last 0-to-1 step, are
+ necessary: if input[9] is -1 and input[0] through input[8] are 0,
+ negative values will remain in the array until the end.
+ */
+
+ 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
+ */
+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);
+ fdifference(z, origx); // does x - z
+
+ memcpy(origxprime, xprime, sizeof(limb) * 10);
+ fsum(xprime, zprime);
+ fdifference(zprime, origxprime);
+ fproduct(xxprime, xprime, z);
+ fproduct(zzprime, x, zprime);
+ freduce_degree(xxprime);
+ freduce_coefficients(xxprime);
+ freduce_degree(zzprime);
+ freduce_coefficients(zzprime);
+ memcpy(origxprime, xxprime, sizeof(limb) * 10);
+ fsum(xxprime, zzprime);
+ fdifference(zzprime, origxprime);
+ fsquare(xxxprime, xxprime);
+ fsquare(zzzprime, zzprime);
+ fproduct(zzprime, zzzprime, qmqp);
+ freduce_degree(zzprime);
+ freduce_coefficients(zzprime);
+ memcpy(x3, xxxprime, sizeof(limb) * 10);
+ memcpy(z3, zzprime, sizeof(limb) * 10);
+
+ fsquare(xx, x);
+ fsquare(zz, z);
+ fproduct(x2, xx, zz);
+ freduce_degree(x2);
+ freduce_coefficients(x2);
+ fdifference(zz, xx); // does zz = xx - zz
+ memset(zzz + 10, 0, sizeof(limb) * 9);
+ fscalar_product(zzz, zz, 121665);
+ /* No need to call freduce_degree here:
+ fscalar_product doesn't increase the degree of its input. */
+ freduce_coefficients(zzz);
+ fsum(zzz, xx);
+ fproduct(z2, zz, zzz);
+ freduce_degree(z2);
+ freduce_coefficients(z2);
+}
+
+/* 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 *, const u8 *, const u8 *);
+
+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);
+ freduce_coefficients(z);
+ fcontract(mypublic, z);
+ return 0;
+}
generated by cgit v1.2.3 (git 2.45.0) at 2024-11-20 11:34:58 +0000