ref: a2644d1d980e0f1c5439dce7764f0d051cf4cc41
parent: 330b2e6a59402d3a290629f409d77c2692973f3c
author: Ori Bernstein <[email protected]>
date: Sun Jan 6 18:13:53 EST 2019
Add start of x25519 code. Not yet tested, so not enabled.
--- /dev/null
+++ b/lib/crypto/x25519.myr
@@ -1,0 +1,642 @@
+/* Copyright 2008, Google Inc.
+ * Translated to Myrddin by Ori Bernstein in 2018
+ * 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.
+ */
+
+use std
+
+pkg crypto =
+ const fdiff : (out : felem[:], in : felem[:] -> void)
+;;
+
+type felem = uint64
+
+/* Sum two numbers: out += in */
+const fsum = {out, in+ for var i = 0; i < 10; i += 2
+ out[0 + i] = out[0 + i] + in[0 + i]
+ out[1 + i] = out[1 + i] + in[1 + i]
+ ;;
+}
+
+/* Find the difference of two numbers: out = in - out
+ * (note the order of the arguments!)
+ */
+const fdiff = {out, in+ for var i = 0; i < 10; i++
+ out[i] = (in[i] - out[i])
+ ;;
+}
+
+/* Multiply a number my a scalar: out = in * scalar */
+const fscalarproduct = {out, in, scalar+ for var i = 0; i < 10; i++
+ out[i] = in[i] * scalar
+ ;;
+}
+
+/* Multiply two numbers: out = in2 * in
+ *
+ * out must be distinct to both ins. The ins are reduced coefficient
+ * form, the out is not.
+ */
+const fproduct = {out, in, in2+ out[0] = in2[0] * in[0]
+ out[1] = in2[0] * in[1] + \
+ in2[1] * in[0]
+ out[2] = 2 * in2[1] * in[1] + \
+ in2[0] * in[2] + \
+ in2[2] * in[0]
+ out[3] = in2[1] * in[2] + \
+ in2[2] * in[1] + \
+ in2[0] * in[3] + \
+ in2[3] * in[0]
+ out[4] = in2[2] * in[2] + \
+ 2 * (in2[1] * in[3] + \
+ in2[3] * in[1]) + \
+ in2[0] * in[4] + \
+ in2[4] * in[0]
+ out[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]
+ out[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]
+ out[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]
+ out[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]
+ out[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]
+ out[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]
+ out[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]
+ out[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]
+ out[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]
+ out[14] = 2 * (in2[7] * in[7] + \
+ in2[5] * in[9] + \
+ in2[9] * in[5]) + \
+ in2[6] * in[8] + \
+ in2[8] * in[6]
+ out[15] = in2[7] * in[8] + \
+ in2[8] * in[7] + \
+ in2[6] * in[9] + \
+ in2[9] * in[6]
+ out[16] = in2[8] * in[8] + \
+ 2 * (in2[7] * in[9] + \
+ in2[9] * in[7])
+ out[17] = in2[8] * in[9] + \
+ in2[9] * in[8]
+ out[18] = 2 * in2[9] * in[9]
+}
+
+
+/* Reduce a long form to a short form by taking the input mod 2^255 - 19. */
+const freducedegree= {out+ out[8] += 19 * out[18];
+ out[7] += 19 * out[17];
+ out[6] += 19 * out[16];
+ out[5] += 19 * out[15];
+ out[4] += 19 * out[14];
+ out[3] += 19 * out[13];
+ out[2] += 19 * out[12];
+ out[1] += 19 * out[11];
+ out[0] += 19 * out[10];
+}
+
+/* Reduce all coeff of the short form in to be -2**25 <= x <= 2**25
+ */
+const freducecoeff = {out+ var over, over2
+
+ while true
+ out[10] = 0
+
+ for var i = 0; i < 10; i += 2
+ over = out[i] / (0x2000000l : felem)
+ over2 = (over + ((over >> 63) * 2) + 1) / 2
+ out[i+1] += over2
+ out[i] -= over2 * (0x4000000l : felem)
+
+ over = out[i+1] / 0x2000000
+ out[i+2] += over
+ out[i+1] -= over * 0x2000000
+ ;;
+ out[0] += 19 * out[10]
+ if out[10] == 0
+ break
+ ;;
+ ;;
+}
+
+/* A helpful wrapper around fproduct: out = in * in2.
+ *
+ * out must be distinct to both ins. The out is reduced degree and
+ * reduced coefficient.
+ */
+const fmul = {out, in, in2+ var t : felem[19]
+
+ fproduct(t[:], in, in2)
+ freducedegree(t[:])
+ freducecoeff(t[:])
+ std.slcp(out, t[:10])
+}
+
+const fsquareinner = {out, in+ var tmp : felem
+
+ out[0] = in[0] * in[0]
+ out[1] = 2 * in[0] * in[1]
+ out[2] = 2 * (in[1] * in[1] + \
+ in[0] * in[2])
+ out[3] = 2 * (in[1] * in[2] + \
+ in[0] * in[3])
+ out[4] = in[2] * in[2] + \
+ 4 * in[1] * in[3] + \
+ 2 * in[0] * in[4]
+ out[5] = 2 * (in[2] * in[3] + \
+ in[1] * in[4] + \
+ in[0] * in[5])
+ out[6] = 2 * (in[3] * in[3] + \
+ in[2] * in[4] + \
+ in[0] * in[6] + \
+ 2 * in[1] * in[5])
+ out[7] = 2 * (in[3] * in[4] + \
+ in[2] * in[5] + \
+ in[1] * in[6] + \
+ in[0] * in[7])
+ tmp = in[1] * in[7] + in[3] * in[5]
+ out[8] = in[4] * in[4] + \
+ 2 * (in[2] * in[6] + \
+ in[0] * in[8] + \
+ 2 * tmp)
+ out[9] = 2 * (in[4] * in[5] + \
+ in[3] * in[6] + \
+ in[2] * in[7] + \
+ in[1] * in[8] + \
+ in[0] * in[9])
+ tmp = in[3] * in[7] + in[1] * in[9]
+ out[10] = 2 * (in[5] * in[5] + \
+ in[4] * in[6] + \
+ in[2] * in[8] + \
+ 2 * tmp)
+ out[11] = 2 * (in[5] * in[6] + \
+ in[4] * in[7] + \
+ in[3] * in[8] + \
+ in[2] * in[9])
+ out[12] = in[6] * in[6] + \
+ 2 * (in[4] * in[8] + \
+ 2 * (in[5] * in[7] + \
+ in[3] * in[9]))
+ out[13] = 2 * (in[6] * in[7] + \
+ in[5] * in[8] + \
+ in[4] * in[9])
+ out[14] = 2 * (in[7] * in[7] + \
+ in[6] * in[8] + \
+ 2 * in[5] * in[9])
+ out[15] = 2 * (in[7] * in[8] + \
+ in[6] * in[9])
+ out[16] = in[8] * in[8] + \
+ 4 * in[7] * in[9]
+ out[17] = 2 * in[8] * in[9]
+ out[18] = 2 * in[9] * in[9]
+}
+
+const fsquare = {out, in+ var t : felem[19]
+ fsquareinner(t[:], in)
+ freducedegree(t[:])
+ freducecoeff(t[:])
+ std.slcp(out, t[:10])
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+const fexpand = {out, in+ /*
+ * #define F(n,start,shift,mask) \
+ * out[n] = (((in[start + 0] : felem) | \
+ * (in[start + 1] : felem) << 8 | \
+ * (in[start + 2] : felem) << 16 | \
+ * (in[start + 3] : felem) << 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
+ */
+ out[0] = (((in[0 + 0] : felem) | (in[0 + 1] : felem) << 8 | (in[0 + 2] : felem) << 16 | (in[0 + 3] : felem) << 24) >> 0) & 0x3ffffff
+ out[1] = (((in[3 + 0] : felem) | (in[3 + 1] : felem) << 8 | (in[3 + 2] : felem) << 16 | (in[3 + 3] : felem) << 24) >> 2) & 0x1ffffff
+ out[2] = (((in[6 + 0] : felem) | (in[6 + 1] : felem) << 8 | (in[6 + 2] : felem) << 16 | (in[6 + 3] : felem) << 24) >> 3) & 0x3ffffff
+ out[3] = (((in[9 + 0] : felem) | (in[9 + 1] : felem) << 8 | (in[9 + 2] : felem) << 16 | (in[9 + 3] : felem) << 24) >> 5) & 0x1ffffff
+ out[4] = (((in[12 + 0] : felem) | (in[12 + 1] : felem) << 8 | (in[12 + 2] : felem) << 16 | (in[12 + 3] : felem) << 24) >> 6) & 0x3ffffff
+ out[5] = (((in[16 + 0] : felem) | (in[16 + 1] : felem) << 8 | (in[16 + 2] : felem) << 16 | (in[16 + 3] : felem) << 24) >> 0) & 0x1ffffff
+ out[6] = (((in[19 + 0] : felem) | (in[19 + 1] : felem) << 8 | (in[19 + 2] : felem) << 16 | (in[19 + 3] : felem) << 24) >> 1) & 0x3ffffff
+ out[7] = (((in[22 + 0] : felem) | (in[22 + 1] : felem) << 8 | (in[22 + 2] : felem) << 16 | (in[22 + 3] : felem) << 24) >> 3) & 0x1ffffff
+ out[8] = (((in[25 + 0] : felem) | (in[25 + 1] : felem) << 8 | (in[25 + 2] : felem) << 16 | (in[25 + 3] : felem) << 24) >> 4) & 0x3ffffff
+ out[9] = (((in[28 + 0] : felem) | (in[28 + 1] : felem) << 8 | (in[28 + 2] : felem) << 16 | (in[28 + 3] : felem) << 24) >> 6) & 0x1ffffff
+
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+const fcontract = {out, in+ while true
+ for var i = 0; i < 9; ++i
+ if (i & 1) == 1
+ while in[i] < 0
+ in[i] += 0x2000000
+ in[i + 1]--
+ ;;
+ else
+ while in[i] < 0
+ in[i] += 0x4000000
+ in[i + 1]--
+ ;;
+ ;;
+ ;;
+ while in[9] < 0
+ in[9] += 0x2000000
+ in[0] -= 19
+ ;;
+ if in[0] >= 0
+ break
+ ;;
+ ;;
+
+ in[1] <<= 2
+ in[2] <<= 3
+ in[3] <<= 5
+ in[4] <<= 6
+ in[6] <<= 1
+ in[7] <<= 3
+ in[8] <<= 4
+ in[9] <<= 6
+ /*
+ * #define F(i, s) \
+ * out[s+0] |= in[i] & 0xff; \
+ * out[s+1] = (in[i] >> 8) & 0xff; \
+ * out[s+2] = (in[i] >> 16) & 0xff; \
+ * out[s+3] = (in[i] >> 24) & 0xff
+ * out[0] = 0
+ * out[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
+ */
+ out[0] = 0
+ out[16] = 0
+ out[ 0 + 0] |= (in[0] : byte); out[ 0 +1] = (in[0] >> 8 : byte); out[ 0 +2] = (in[0] >> 16 : byte); out[ 0 +3] = (in[0] >> 24 : byte)
+ out[ 3 + 0] |= (in[1] : byte); out[ 3 +1] = (in[1] >> 8 : byte); out[ 3 +2] = (in[1] >> 16 : byte); out[ 3 +3] = (in[1] >> 24 : byte)
+ out[ 6 + 0] |= (in[2] : byte); out[ 6 +1] = (in[2] >> 8 : byte); out[ 6 +2] = (in[2] >> 16 : byte); out[ 6 +3] = (in[2] >> 24 : byte)
+ out[ 9 + 0] |= (in[3] : byte); out[ 9 +1] = (in[3] >> 8 : byte); out[ 9 +2] = (in[3] >> 16 : byte); out[ 9 +3] = (in[3] >> 24 : byte)
+ out[12 + 0] |= (in[4] : byte); out[12 +1] = (in[4] >> 8 : byte); out[12 +2] = (in[4] >> 16 : byte); out[12 +3] = (in[4] >> 24 : byte)
+ out[16 + 0] |= (in[5] : byte); out[16 +1] = (in[5] >> 8 : byte); out[16 +2] = (in[5] >> 16 : byte); out[16 +3] = (in[5] >> 24 : byte)
+ out[19 + 0] |= (in[6] : byte); out[19 +1] = (in[6] >> 8 : byte); out[19 +2] = (in[6] >> 16 : byte); out[19 +3] = (in[6] >> 24 : byte)
+ out[22 + 0] |= (in[7] : byte); out[22 +1] = (in[7] >> 8 : byte); out[22 +2] = (in[7] >> 16 : byte); out[22 +3] = (in[7] >> 24 : byte)
+ out[25 + 0] |= (in[8] : byte); out[25 +1] = (in[8] >> 8 : byte); out[25 +2] = (in[8] >> 16 : byte); out[25 +3] = (in[8] >> 24 : byte)
+ out[28 + 0] |= (in[9] : byte); out[28 +1] = (in[9] >> 8 : byte); out[28 +2] = (in[9] >> 16 : byte); out[28 +3] = (in[9] >> 24 : byte)
+}
+
+/* Input: Q, Q', Q-Q'
+ * Output: 2Q, Q+Q'
+ *
+ * x2 z3: long form, out 2Q
+ * x3 z3: long form, out Q + Q'
+ * x z: short form, destroyed, in Q
+ * xprime zprime: short form, destroyed, in Q'
+ * qmqp: short form, preserved, in Q - Q'
+ */
+const fmonty = {x2, z2, x3, z3, x, z, xprime, zprime, qmqp+ var origx : felem[10]
+ var origxprime : felem[10]
+ var zzz : felem [19]
+ var xx : felem[19]
+ var zz : felem[19]
+ var xxprime : felem[19]
+ var zzprime : felem[19]
+ var zzzprime : felem[19]
+ var xxxprime : felem[19]
+
+ std.slcp(origx[:], x[:10])
+ fsum(x, z)
+ fdiff(z, origx[:]); // does x - z
+
+ std.slcp(origxprime[:], xprime[:10])
+ fsum(xprime, zprime)
+ fdiff(zprime, origxprime[:])
+ fproduct(xxprime[:], xprime, z)
+ fproduct(zzprime[:], x, zprime)
+ freducedegree(xxprime[:])
+ freducecoeff(xxprime[:])
+ freducedegree(zzprime[:])
+ freducecoeff(zzprime[:])
+ std.slcp(origxprime[:], xxprime[:10])
+ fsum(xxprime[:], zzprime[:])
+ fdiff(zzprime[:], origxprime[:])
+ fsquare(xxxprime[:], xxprime[:])
+ fsquare(zzzprime[:], zzprime[:])
+ fproduct(zzprime[:], zzzprime[:], qmqp)
+ freducedegree(zzprime[:])
+ freducecoeff(zzprime[:])
+ std.slcp(x3, xxxprime[:10])
+ std.slcp(z3, zzprime[:10])
+
+ fsquare(xx[:], x)
+ fsquare(zz[:], z)
+ fproduct(x2, xx[:], zz[:])
+ freducedegree(x2)
+ freducecoeff(x2)
+ fdiff(zz[:], xx[:]); // does zz = xx - zz
+ std.slfill(zzz[10:], 0)
+ fscalarproduct(zzz, zz, 121665)
+ freducedegree(zzz[:])
+ freducecoeff(zzz[:])
+ fsum(zzz[:], xx[:])
+ fproduct(z2, zz[:], zzz[:])
+ freducedegree(z2)
+ freducecoeff(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)
+ */
+const cmult = {resultx, resultz, n, q+ var a : felem[19] = [0:0, 18:0]
+ var b : felem[19] = [0:1, 18:0]
+ var c : felem[19] = [0:1, 18:0]
+ var d : felem[19] = [0:0, 18:0]
+ var e : felem[19] = [0:0, 18:0]
+ var f : felem[19] = [0:1, 18:0]
+ var g : felem[19] = [0:0, 18:0]
+ var h : felem[19] = [0:1, 18:0]
+ var nqpqx = a[:]
+ var nqpqz = b[:]
+ var nqx = c[:]
+ var nqz = d[:]
+ var nqpqx2 = e[:]
+ var nqpqz2 = f[:]
+ var nqx2 = g[:]
+ var nqz2 = h[:]
+ var t
+
+ std.slcp(nqpqx[:10], q[:10])
+ for var i = 0; i < 32; ++i
+ var byte = n[31 - i]
+ for var j = 0; j < 8; ++j
+ if byte & 0x80 != 0
+ 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
+ ;;
+ ;;
+
+ std.slcp(resultx, nqx[:10])
+ std.slcp(resultz, nqz[:10])
+}
+
+// -----------------------------------------------------------------------------
+// Shamelessly copied from djb's code
+// -----------------------------------------------------------------------------
+const crecip = {out, z+ var z2 : felem[10]
+ var z9 : felem[10]
+ var z11 : felem[10]
+ var z2_5_0 : felem[10]
+ var z2_10_0 : felem[10]
+ var z2_20_0 : felem[10]
+ var z2_50_0 : felem[10]
+ var z2_100_0 : felem[10]
+ var t0 : felem[10]
+ var t1 : felem[10]
+ var 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 var 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 var 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[:])
+}
+
+const curve25519 = {pub : byte[:/*32*/], secret : byte[:/*32*/], basepoint : byte[:/*32*/]+ var bp : felem[10]
+ var x : felem[10]
+ var z : felem[10]
+ var zmone : felem[10]
+
+ std.assert(pub.len == 32 && secret.len == 32 && basepoint.len == 32, "wrong key sizes")
+ fexpand(bp[:], basepoint[:])
+ cmult(x[:], z[:], secret[:], bp[:])
+ crecip(zmone[:], z[:])
+ fmul(z[:], x[:], zmone[:])
+ fcontract(pub[:], z[:])
+}