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Download patch

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}