Added Curve25519-donna changes.

Added a wrapper class that implements the following API calls which for
Curve25519.
+ ScalarMult to compute the shared key.
+ ScalarBaseMult to get public key.
+ ConvertToPrivateKey returns a private key from random bytes.

Per agl/wtc, grabbed the rev 234205ff from the git repo
(https://github.com/agl/curve25519-donna/tree/234205ff1ecaf6b3c1dc76798a462c4293f31fdb)
and checked it in to crypto/ because that version has pure Google copyright.

R=wtc@chromium.org,agl@chromium.org,rsleevi@chromium.org
TEST=crypto unit tests

Review URL: https://chromiumcodereview.appspot.com/12457004

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@187074 0039d316-1c4b-4281-b951-d872f2087c98

1 files changed, 592 insertions, 0 deletions

diff --git a/crypto/curve25519-donna.c b/crypto/curve25519-donna.c
new file mode 100644
index 0000000..f141ac0
--- /dev/null
+++ b/crypto/curve25519-donna.c
@@ -0,0 +1,592 @@
+// Copyright (c) 2013 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+/*
+ * 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 my 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];
+}
+
+/* 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;
+  do {
+    output[10] = 0;
+
+    for (i = 0; i < 10; i += 2) {
+      limb over = output[i] / 0x4000000l;
+      output[i+1] += over;
+      output[i] -= over * 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(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
+}
+
+/* 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;
+
+  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(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);
+  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(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) {
+      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(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[10], 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;
+}