ref: 0e51046942cb5f7168b24b719761297d100082b0
parent: d8a57c0ae3ebd8da230abf545485cf701ef7df77
author: cinap_lenrek <[email protected]>
date: Fri Aug 28 08:08:54 EDT 2015
libsec: add curve25519() from http://code.google.com/p/curve25519-donna/ this is a portable version of curve25519() by google.
--- a/sys/include/libsec.h
+++ b/sys/include/libsec.h
@@ -460,3 +460,6 @@
/* password-based key derivation function 2 (RFC 2898) */
void pbkdf2_hmac_sha1(uchar *p, ulong plen, uchar *s, ulong slen, ulong rounds, uchar *d, ulong dlen);
+
+/* Curve25519 elliptic curve, public key function */
+void curve25519(uchar mypublic[32], uchar secret[32], uchar basepoint[32]);
--- /dev/null
+++ b/sys/src/libsec/port/curve25519.c
@@ -1,0 +1,570 @@
+/* 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: Curve25519 elliptic curve, public key function
+ *
+ * http://code.google.com/p/curve25519-donna/
+ *
+ * Adam Langley <[email protected]>
+ *
+ * Derived from public domain C code by Daniel J. Bernstein <[email protected]>
+ *
+ * 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 <u.h>
+#include <libc.h>
+#include <libsec.h>
+
+typedef vlong felem;
+
+/* Sum two numbers: output += in */
+static void fsum(felem *output, felem *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(felem *output, felem *in) {+ unsigned i;
+ for (i = 0; i < 10; ++i) {+ output[i] = (in[i] - output[i]);
+ }
+}
+
+/* Multiply a number my a scalar: output = in * scalar */
+static void fscalar_product(felem *output, felem *in, felem 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(felem *output, felem *in2, felem *in) {+ output[0] = in2[0] * in[0];
+ output[1] = in2[0] * in[1] +
+ in2[1] * in[0];
+ output[2] = 2 * in2[1] * in[1] +
+ in2[0] * in[2] +
+ in2[2] * in[0];
+ output[3] = in2[1] * in[2] +
+ in2[2] * in[1] +
+ in2[0] * in[3] +
+ in2[3] * in[0];
+ output[4] = in2[2] * in[2] +
+ 2 * (in2[1] * in[3] +
+ in2[3] * in[1]) +
+ in2[0] * in[4] +
+ in2[4] * in[0];
+ output[5] = in2[2] * in[3] +
+ in2[3] * in[2] +
+ in2[1] * in[4] +
+ in2[4] * in[1] +
+ in2[0] * in[5] +
+ in2[5] * in[0];
+ output[6] = 2 * (in2[3] * in[3] +
+ in2[1] * in[5] +
+ in2[5] * in[1]) +
+ in2[2] * in[4] +
+ in2[4] * in[2] +
+ in2[0] * in[6] +
+ in2[6] * in[0];
+ output[7] = in2[3] * in[4] +
+ in2[4] * in[3] +
+ in2[2] * in[5] +
+ in2[5] * in[2] +
+ in2[1] * in[6] +
+ in2[6] * in[1] +
+ in2[0] * in[7] +
+ in2[7] * in[0];
+ output[8] = in2[4] * in[4] +
+ 2 * (in2[3] * in[5] +
+ in2[5] * in[3] +
+ in2[1] * in[7] +
+ in2[7] * in[1]) +
+ in2[2] * in[6] +
+ in2[6] * in[2] +
+ in2[0] * in[8] +
+ in2[8] * in[0];
+ output[9] = in2[4] * in[5] +
+ in2[5] * in[4] +
+ in2[3] * in[6] +
+ in2[6] * in[3] +
+ in2[2] * in[7] +
+ in2[7] * in[2] +
+ in2[1] * in[8] +
+ in2[8] * in[1] +
+ in2[0] * in[9] +
+ in2[9] * in[0];
+ output[10] = 2 * (in2[5] * in[5] +
+ in2[3] * in[7] +
+ in2[7] * in[3] +
+ in2[1] * in[9] +
+ in2[9] * in[1]) +
+ in2[4] * in[6] +
+ in2[6] * in[4] +
+ in2[2] * in[8] +
+ in2[8] * in[2];
+ output[11] = in2[5] * in[6] +
+ in2[6] * in[5] +
+ in2[4] * in[7] +
+ in2[7] * in[4] +
+ in2[3] * in[8] +
+ in2[8] * in[3] +
+ in2[2] * in[9] +
+ in2[9] * in[2];
+ output[12] = in2[6] * in[6] +
+ 2 * (in2[5] * in[7] +
+ in2[7] * in[5] +
+ in2[3] * in[9] +
+ in2[9] * in[3]) +
+ in2[4] * in[8] +
+ in2[8] * in[4];
+ output[13] = in2[6] * in[7] +
+ in2[7] * in[6] +
+ in2[5] * in[8] +
+ in2[8] * in[5] +
+ in2[4] * in[9] +
+ in2[9] * in[4];
+ output[14] = 2 * (in2[7] * in[7] +
+ in2[5] * in[9] +
+ in2[9] * in[5]) +
+ in2[6] * in[8] +
+ in2[8] * in[6];
+ output[15] = in2[7] * in[8] +
+ in2[8] * in[7] +
+ in2[6] * in[9] +
+ in2[9] * in[6];
+ output[16] = in2[8] * in[8] +
+ 2 * (in2[7] * in[9] +
+ in2[9] * in[7]);
+ output[17] = in2[8] * in[9] +
+ in2[9] * in[8];
+ output[18] = 2 * in2[9] * in[9];
+}
+
+/* Reduce a long form to a short form by taking the input mod 2^255 - 19. */
+static void freduce_degree(felem *output) {+ output[8] += 19 * output[18];
+ output[7] += 19 * output[17];
+ output[6] += 19 * output[16];
+ output[5] += 19 * output[15];
+ output[4] += 19 * output[14];
+ output[3] += 19 * output[13];
+ output[2] += 19 * output[12];
+ output[1] += 19 * output[11];
+ output[0] += 19 * output[10];
+}
+
+/* Reduce all coefficients of the short form input to be -2**25 <= x <= 2**25
+ */
+static void freduce_coefficients(felem *output) {+ unsigned i;
+ do {+ output[10] = 0;
+
+ for (i = 0; i < 10; i += 2) {+ felem over = output[i] / 0x2000000l;
+ felem over2 = (over + ((over >> 63) * 2) + 1) / 2;
+ output[i+1] += over2;
+ output[i] -= over2 * 0x4000000l;
+
+ over = output[i+1] / 0x2000000;
+ output[i+2] += over;
+ output[i+1] -= over * 0x2000000;
+ }
+ output[0] += 19 * output[10];
+ } while (output[10]);
+}
+
+/* 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(felem *output, felem *in, felem *in2) {+ felem t[19];
+ fproduct(t, in, in2);
+ freduce_degree(t);
+ freduce_coefficients(t);
+ memcpy(output, t, sizeof(felem) * 10);
+}
+
+static void fsquare_inner(felem *output, felem *in) {+ output[0] = in[0] * in[0];
+ output[1] = 2 * in[0] * in[1];
+ output[2] = 2 * (in[1] * in[1] +
+ in[0] * in[2]);
+ output[3] = 2 * (in[1] * in[2] +
+ in[0] * in[3]);
+ output[4] = in[2] * in[2] +
+ 4 * in[1] * in[3] +
+ 2 * in[0] * in[4];
+ output[5] = 2 * (in[2] * in[3] +
+ in[1] * in[4] +
+ in[0] * in[5]);
+ output[6] = 2 * (in[3] * in[3] +
+ in[2] * in[4] +
+ in[0] * in[6] +
+ 2 * in[1] * in[5]);
+ output[7] = 2 * (in[3] * in[4] +
+ in[2] * in[5] +
+ in[1] * in[6] +
+ in[0] * in[7]);
+ output[8] = in[4] * in[4] +
+ 2 * (in[2] * in[6] +
+ in[0] * in[8] +
+ 2 * (in[1] * in[7] +
+ in[3] * in[5]));
+ output[9] = 2 * (in[4] * in[5] +
+ in[3] * in[6] +
+ in[2] * in[7] +
+ in[1] * in[8] +
+ in[0] * in[9]);
+ output[10] = 2 * (in[5] * in[5] +
+ in[4] * in[6] +
+ in[2] * in[8] +
+ 2 * (in[3] * in[7] +
+ in[1] * in[9]));
+ output[11] = 2 * (in[5] * in[6] +
+ in[4] * in[7] +
+ in[3] * in[8] +
+ in[2] * in[9]);
+ output[12] = in[6] * in[6] +
+ 2 * (in[4] * in[8] +
+ 2 * (in[5] * in[7] +
+ in[3] * in[9]));
+ output[13] = 2 * (in[6] * in[7] +
+ in[5] * in[8] +
+ in[4] * in[9]);
+ output[14] = 2 * (in[7] * in[7] +
+ in[6] * in[8] +
+ 2 * in[5] * in[9]);
+ output[15] = 2 * (in[7] * in[8] +
+ in[6] * in[9]);
+ output[16] = in[8] * in[8] +
+ 4 * in[7] * in[9];
+ output[17] = 2 * in[8] * in[9];
+ output[18] = 2 * in[9] * in[9];
+}
+
+static void
+fsquare(felem *output, felem *in) {+ felem t[19];
+ fsquare_inner(t, in);
+ freduce_degree(t);
+ freduce_coefficients(t);
+ memcpy(output, t, sizeof(felem) * 10);
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static void
+fexpand(felem *output, uchar *input) {+#define F(n,start,shift,mask) \
+ output[n] = ((((felem) input[start + 0]) | \
+ ((felem) input[start + 1]) << 8 | \
+ ((felem) input[start + 2]) << 16 | \
+ ((felem) 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
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+static void
+fcontract(uchar *output, felem *input) {+ int i;
+
+ do {+ for (i = 0; i < 9; ++i) {+ if ((i & 1) == 1) {+ while (input[i] < 0) {+ input[i] += 0x2000000;
+ input[i + 1]--;
+ }
+ } else {+ while (input[i] < 0) {+ input[i] += 0x4000000;
+ input[i + 1]--;
+ }
+ }
+ }
+ while (input[9] < 0) {+ input[9] += 0x2000000;
+ input[0] -= 19;
+ }
+ } while (input[0] < 0);
+
+ 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(felem *x2, felem *z2, /* output 2Q */
+ felem *x3, felem *z3, /* output Q + Q' */
+ felem *x, felem *z, /* input Q */
+ felem *xprime, felem *zprime, /* input Q' */
+ felem *qmqp /* input Q - Q' */) {+ felem origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
+ zzprime[19], zzzprime[19], xxxprime[19];
+
+ memcpy(origx, x, 10 * sizeof(felem));
+ fsum(x, z);
+ fdifference(z, origx); // does x - z
+
+ memcpy(origxprime, xprime, sizeof(felem) * 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(felem) * 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(felem) * 10);
+ memcpy(z3, zzprime, sizeof(felem) * 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(felem) * 9);
+ fscalar_product(zzz, zz, 121665);
+ freduce_degree(zzz);
+ freduce_coefficients(zzz);
+ fsum(zzz, xx);
+ fproduct(z2, zz, zzz);
+ freduce_degree(z2);
+ freduce_coefficients(z2);
+}
+
+/* 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(felem *resultx, felem *resultz, uchar *n, felem *q) {+ felem a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};+ felem *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
+ felem e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};+ felem *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
+
+ unsigned i, j;
+
+ memcpy(nqpqx, q, sizeof(felem) * 10);
+
+ for (i = 0; i < 32; ++i) {+ uchar byte = n[31 - i];
+ for (j = 0; j < 8; ++j) {+ if (byte & 0x80) {+ fmonty(nqpqx2, nqpqz2,
+ nqx2, nqz2,
+ nqpqx, nqpqz,
+ nqx, nqz,
+ q);
+ } else {+ fmonty(nqx2, nqz2,
+ nqpqx2, nqpqz2,
+ nqx, nqz,
+ nqpqx, nqpqz,
+ q);
+ }
+
+ 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(felem) * 10);
+ memcpy(resultz, nqz, sizeof(felem) * 10);
+}
+
+// -----------------------------------------------------------------------------
+// Shamelessly copied from djb's code
+// -----------------------------------------------------------------------------
+static void
+crecip(felem *out, felem *z) {+ felem z2[10];
+ felem z9[10];
+ felem z11[10];
+ felem z2_5_0[10];
+ felem z2_10_0[10];
+ felem z2_20_0[10];
+ felem z2_50_0[10];
+ felem z2_100_0[10];
+ felem t0[10];
+ felem 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);
+}
+
+void
+curve25519(uchar mypublic[32], uchar secret[32], uchar basepoint[32]) {+ felem bp[10], x[10], z[10], zmone[10];
+ fexpand(bp, basepoint);
+ cmult(x, z, secret, bp);
+ crecip(zmone, z);
+ fmul(z, x, zmone);
+ fcontract(mypublic, z);
+}
--- a/sys/src/libsec/port/mkfile
+++ b/sys/src/libsec/port/mkfile
@@ -22,6 +22,7 @@
ripemd.c\
dh.c\
pbkdf2.c\
+ curve25519.c\
ALLOFILES=${CFILES:%.c=%.$O}