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-/* Copyright 2008, Google Inc.
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- * All rights reserved.
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- *
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- * Redistribution and use in source and binary forms, with or without
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- * modification, are permitted provided that the following conditions are
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- * met:
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- *
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- * * Redistributions of source code must retain the above copyright
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- * notice, this list of conditions and the following disclaimer.
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- * * Redistributions in binary form must reproduce the above
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- * copyright notice, this list of conditions and the following disclaimer
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- * in the documentation and/or other materials provided with the
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- * distribution.
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- * * Neither the name of Google Inc. nor the names of its
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- * contributors may be used to endorse or promote products derived from
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- * this software without specific prior written permission.
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- *
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- * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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- * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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- * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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- * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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- * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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- * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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- * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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- * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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- * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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- * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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- * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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- *
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- * curve25519-donna: Curve25519 elliptic curve, public key function
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- *
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- * http://code.google.com/p/curve25519-donna/
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- *
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- * Adam Langley <agl@imperialviolet.org>
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- *
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- * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
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- *
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- * More information about curve25519 can be found here
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- * http://cr.yp.to/ecdh.html
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- *
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- * djb's sample implementation of curve25519 is written in a special assembly
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- * language called qhasm and uses the floating point registers.
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- *
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- * This is, almost, a clean room reimplementation from the curve25519 paper. It
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- * uses many of the tricks described therein. Only the crecip function is taken
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- * from the sample implementation.
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- */
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-
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-#include <string.h>
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-#include <stdint.h>
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-#include <stdlib.h>
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-#include <stdio.h>
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-#include <errno.h>
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-
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-#ifdef _MSC_VER
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-#define inline __inline
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-#endif
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-
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-typedef uint8_t u8;
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-typedef int32_t s32;
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-typedef int64_t limb;
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-
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-/* Field element representation:
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- *
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- * Field elements are written as an array of signed, 64-bit limbs, least
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- * significant first. The value of the field element is:
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- * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
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- *
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- * i.e. the limbs are 26, 25, 26, 25, ... bits wide.
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- */
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-
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-/* Sum two numbers: output += in */
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-static void fsum(limb *output, const limb *in)
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-{
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- unsigned i;
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- for (i = 0; i < 10; i += 2)
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- {
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- output[0 + i] = (output[0 + i] + in[0 + i]);
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- output[1 + i] = (output[1 + i] + in[1 + i]);
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- }
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-}
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-
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-/* Find the difference of two numbers: output = in - output
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- * (note the order of the arguments!)
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- */
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-static void fdifference(limb *output, const limb *in)
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-{
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- unsigned i;
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- for (i = 0; i < 10; ++i)
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- {
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- output[i] = (in[i] - output[i]);
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- }
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-}
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-
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-/* Multiply a number by a scalar: output = in * scalar */
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-static void fscalar_product(limb *output, const limb *in, const limb scalar)
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-{
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- unsigned i;
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- for (i = 0; i < 10; ++i)
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- {
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- output[i] = in[i] * scalar;
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- }
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-}
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-
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-/* Multiply two numbers: output = in2 * in
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- *
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- * output must be distinct to both inputs. The inputs are reduced coefficient
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- * form, the output is not.
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- */
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-static void fproduct(limb *output, const limb *in2, const limb *in)
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-{
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- output[0] = ((limb)((s32)in2[0])) * ((s32)in[0]);
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- output[1] = ((limb)((s32)in2[0])) * ((s32)in[1]) +
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- ((limb)((s32)in2[1])) * ((s32)in[0]);
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- output[2] = 2 * ((limb)((s32)in2[1])) * ((s32)in[1]) +
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- ((limb)((s32)in2[0])) * ((s32)in[2]) +
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- ((limb)((s32)in2[2])) * ((s32)in[0]);
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- output[3] = ((limb)((s32)in2[1])) * ((s32)in[2]) +
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- ((limb)((s32)in2[2])) * ((s32)in[1]) +
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- ((limb)((s32)in2[0])) * ((s32)in[3]) +
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- ((limb)((s32)in2[3])) * ((s32)in[0]);
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- output[4] = ((limb)((s32)in2[2])) * ((s32)in[2]) +
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- 2 * (((limb)((s32)in2[1])) * ((s32)in[3]) +
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- ((limb)((s32)in2[3])) * ((s32)in[1])) +
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- ((limb)((s32)in2[0])) * ((s32)in[4]) +
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- ((limb)((s32)in2[4])) * ((s32)in[0]);
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- output[5] = ((limb)((s32)in2[2])) * ((s32)in[3]) +
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- ((limb)((s32)in2[3])) * ((s32)in[2]) +
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- ((limb)((s32)in2[1])) * ((s32)in[4]) +
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- ((limb)((s32)in2[4])) * ((s32)in[1]) +
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- ((limb)((s32)in2[0])) * ((s32)in[5]) +
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- ((limb)((s32)in2[5])) * ((s32)in[0]);
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- output[6] = 2 * (((limb)((s32)in2[3])) * ((s32)in[3]) +
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- ((limb)((s32)in2[1])) * ((s32)in[5]) +
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- ((limb)((s32)in2[5])) * ((s32)in[1])) +
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- ((limb)((s32)in2[2])) * ((s32)in[4]) +
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- ((limb)((s32)in2[4])) * ((s32)in[2]) +
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- ((limb)((s32)in2[0])) * ((s32)in[6]) +
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- ((limb)((s32)in2[6])) * ((s32)in[0]);
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- output[7] = ((limb)((s32)in2[3])) * ((s32)in[4]) +
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- ((limb)((s32)in2[4])) * ((s32)in[3]) +
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- ((limb)((s32)in2[2])) * ((s32)in[5]) +
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- ((limb)((s32)in2[5])) * ((s32)in[2]) +
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- ((limb)((s32)in2[1])) * ((s32)in[6]) +
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- ((limb)((s32)in2[6])) * ((s32)in[1]) +
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- ((limb)((s32)in2[0])) * ((s32)in[7]) +
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- ((limb)((s32)in2[7])) * ((s32)in[0]);
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- output[8] = ((limb)((s32)in2[4])) * ((s32)in[4]) +
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- 2 * (((limb)((s32)in2[3])) * ((s32)in[5]) +
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- ((limb)((s32)in2[5])) * ((s32)in[3]) +
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- ((limb)((s32)in2[1])) * ((s32)in[7]) +
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- ((limb)((s32)in2[7])) * ((s32)in[1])) +
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- ((limb)((s32)in2[2])) * ((s32)in[6]) +
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- ((limb)((s32)in2[6])) * ((s32)in[2]) +
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- ((limb)((s32)in2[0])) * ((s32)in[8]) +
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- ((limb)((s32)in2[8])) * ((s32)in[0]);
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- output[9] = ((limb)((s32)in2[4])) * ((s32)in[5]) +
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- ((limb)((s32)in2[5])) * ((s32)in[4]) +
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- ((limb)((s32)in2[3])) * ((s32)in[6]) +
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- ((limb)((s32)in2[6])) * ((s32)in[3]) +
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- ((limb)((s32)in2[2])) * ((s32)in[7]) +
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- ((limb)((s32)in2[7])) * ((s32)in[2]) +
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- ((limb)((s32)in2[1])) * ((s32)in[8]) +
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- ((limb)((s32)in2[8])) * ((s32)in[1]) +
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- ((limb)((s32)in2[0])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[0]);
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- output[10] = 2 * (((limb)((s32)in2[5])) * ((s32)in[5]) +
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- ((limb)((s32)in2[3])) * ((s32)in[7]) +
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- ((limb)((s32)in2[7])) * ((s32)in[3]) +
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- ((limb)((s32)in2[1])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[1])) +
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- ((limb)((s32)in2[4])) * ((s32)in[6]) +
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- ((limb)((s32)in2[6])) * ((s32)in[4]) +
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- ((limb)((s32)in2[2])) * ((s32)in[8]) +
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- ((limb)((s32)in2[8])) * ((s32)in[2]);
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- output[11] = ((limb)((s32)in2[5])) * ((s32)in[6]) +
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- ((limb)((s32)in2[6])) * ((s32)in[5]) +
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- ((limb)((s32)in2[4])) * ((s32)in[7]) +
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- ((limb)((s32)in2[7])) * ((s32)in[4]) +
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- ((limb)((s32)in2[3])) * ((s32)in[8]) +
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- ((limb)((s32)in2[8])) * ((s32)in[3]) +
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- ((limb)((s32)in2[2])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[2]);
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- output[12] = ((limb)((s32)in2[6])) * ((s32)in[6]) +
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- 2 * (((limb)((s32)in2[5])) * ((s32)in[7]) +
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- ((limb)((s32)in2[7])) * ((s32)in[5]) +
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- ((limb)((s32)in2[3])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[3])) +
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- ((limb)((s32)in2[4])) * ((s32)in[8]) +
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- ((limb)((s32)in2[8])) * ((s32)in[4]);
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- output[13] = ((limb)((s32)in2[6])) * ((s32)in[7]) +
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- ((limb)((s32)in2[7])) * ((s32)in[6]) +
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- ((limb)((s32)in2[5])) * ((s32)in[8]) +
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- ((limb)((s32)in2[8])) * ((s32)in[5]) +
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- ((limb)((s32)in2[4])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[4]);
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- output[14] = 2 * (((limb)((s32)in2[7])) * ((s32)in[7]) +
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- ((limb)((s32)in2[5])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[5])) +
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- ((limb)((s32)in2[6])) * ((s32)in[8]) +
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- ((limb)((s32)in2[8])) * ((s32)in[6]);
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- output[15] = ((limb)((s32)in2[7])) * ((s32)in[8]) +
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- ((limb)((s32)in2[8])) * ((s32)in[7]) +
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- ((limb)((s32)in2[6])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[6]);
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- output[16] = ((limb)((s32)in2[8])) * ((s32)in[8]) +
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- 2 * (((limb)((s32)in2[7])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[7]));
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- output[17] = ((limb)((s32)in2[8])) * ((s32)in[9]) +
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- ((limb)((s32)in2[9])) * ((s32)in[8]);
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- output[18] = 2 * ((limb)((s32)in2[9])) * ((s32)in[9]);
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-}
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-
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-/* Reduce a long form to a short form by taking the input mod 2^255 - 19. */
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-static void freduce_degree(limb *output)
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-{
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- /* Each of these shifts and adds ends up multiplying the value by 19. */
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- output[8] += output[18] << 4;
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- output[8] += output[18] << 1;
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- output[8] += output[18];
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- output[7] += output[17] << 4;
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- output[7] += output[17] << 1;
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- output[7] += output[17];
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- output[6] += output[16] << 4;
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- output[6] += output[16] << 1;
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- output[6] += output[16];
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- output[5] += output[15] << 4;
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- output[5] += output[15] << 1;
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- output[5] += output[15];
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- output[4] += output[14] << 4;
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- output[4] += output[14] << 1;
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- output[4] += output[14];
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- output[3] += output[13] << 4;
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- output[3] += output[13] << 1;
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- output[3] += output[13];
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- output[2] += output[12] << 4;
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- output[2] += output[12] << 1;
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- output[2] += output[12];
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- output[1] += output[11] << 4;
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- output[1] += output[11] << 1;
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- output[1] += output[11];
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- output[0] += output[10] << 4;
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- output[0] += output[10] << 1;
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- output[0] += output[10];
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-}
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-
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-#if (-1 & 3) != 3
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-#error "This code only works on a two's complement system"
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-#endif
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-
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-/* return v / 2^26, using only shifts and adds. */
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-static inline limb
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-div_by_2_26(const limb v)
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-{
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- /* High word of v; no shift needed*/
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- const uint32_t highword = (uint32_t)(((uint64_t)v) >> 32);
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- /* Set to all 1s if v was negative; else set to 0s. */
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- const int32_t sign = ((int32_t)highword) >> 31;
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- /* Set to 0x3ffffff if v was negative; else set to 0. */
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- const int32_t roundoff = ((uint32_t)sign) >> 6;
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- /* Should return v / (1<<26) */
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- return (v + roundoff) >> 26;
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-}
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-
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-/* return v / (2^25), using only shifts and adds. */
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-static inline limb
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-div_by_2_25(const limb v)
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-{
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- /* High word of v; no shift needed*/
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- const uint32_t highword = (uint32_t)(((uint64_t)v) >> 32);
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- /* Set to all 1s if v was negative; else set to 0s. */
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- const int32_t sign = ((int32_t)highword) >> 31;
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- /* Set to 0x1ffffff if v was negative; else set to 0. */
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- const int32_t roundoff = ((uint32_t)sign) >> 7;
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- /* Should return v / (1<<25) */
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- return (v + roundoff) >> 25;
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-}
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-
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-static inline s32
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-div_s32_by_2_25(const s32 v)
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-{
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- const s32 roundoff = ((uint32_t)(v >> 31)) >> 7;
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- return (v + roundoff) >> 25;
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-}
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-
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-/* Reduce all coefficients of the short form input so that |x| < 2^26.
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- *
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- * On entry: |output[i]| < 2^62
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- */
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-static void freduce_coefficients(limb *output)
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-{
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- unsigned i;
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-
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- output[10] = 0;
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-
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- for (i = 0; i < 10; i += 2)
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- {
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- limb over = div_by_2_26(output[i]);
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- output[i] -= over << 26;
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- output[i + 1] += over;
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-
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- over = div_by_2_25(output[i + 1]);
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- output[i + 1] -= over << 25;
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- output[i + 2] += over;
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- }
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- /* Now |output[10]| < 2 ^ 38 and all other coefficients are reduced. */
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- output[0] += output[10] << 4;
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- output[0] += output[10] << 1;
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- output[0] += output[10];
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-
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- output[10] = 0;
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-
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- /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19 * 2^38
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- * So |over| will be no more than 77825 */
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- {
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- limb over = div_by_2_26(output[0]);
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- output[0] -= over << 26;
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- output[1] += over;
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- }
|
|
|
-
|
|
|
- /* 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, 0x3ffffff);
|
|
|
-#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;
|
|
|
-}
|
|
|
-
|
|
|
-/// returns 0 for '=' or unrecognized characters, not a problem since PEM is well constrained.
|
|
|
-static int base64_value(int c)
|
|
|
-{
|
|
|
- if (c >= 'A' && c <= 'Z')
|
|
|
- return c - 'A';
|
|
|
- if (c >= 'a' && c <= 'z')
|
|
|
- return 26 + c - 'a';
|
|
|
- if (c >= '0' && c <= '9')
|
|
|
- return 52 + c - '0';
|
|
|
- if (c == '+')
|
|
|
- return 62;
|
|
|
- if (c == '/')
|
|
|
- return 63;
|
|
|
- return 0x1000;
|
|
|
-}
|
|
|
-
|
|
|
-/**
|
|
|
- * @param[in] data the base64 encoded string
|
|
|
- * @param[out] data the decoded result
|
|
|
- * @param[in] len the length of base64 encoded data
|
|
|
- * @param[out] len the length of decoded result
|
|
|
- */
|
|
|
-static void base64_decode(u8 *data, int *len)
|
|
|
-{
|
|
|
- int read = 0;
|
|
|
- int write = 0;
|
|
|
- int state[4];
|
|
|
- while (read < *len)
|
|
|
- {
|
|
|
- state[read % 4] = base64_value(data[read]);
|
|
|
- if (state[read % 4] == 0x1000)
|
|
|
- {
|
|
|
- break;
|
|
|
- }
|
|
|
- if ((read % 4) == 3)
|
|
|
- {
|
|
|
- data[write++] = state[0] << 2 | state[1] >> 4;
|
|
|
- data[write++] = state[1] << 4 | state[2] >> 2;
|
|
|
- data[write++] = state[2] << 6 | state[3] >> 0;
|
|
|
- }
|
|
|
- read++;
|
|
|
- }
|
|
|
- switch (read % 4)
|
|
|
- {
|
|
|
- case 2:
|
|
|
- data[write++] = state[0] << 2 | state[1] >> 4;
|
|
|
- break;
|
|
|
- case 3:
|
|
|
- data[write++] = state[0] << 2 | state[1] >> 4;
|
|
|
- data[write++] = state[1] << 4 | state[2] >> 2;
|
|
|
- }
|
|
|
- *len = write;
|
|
|
-}
|
|
|
-
|
|
|
-/**
|
|
|
- * reads the 32-byte key from a PEM file, takes advantage of the
|
|
|
- * fact that the last 32 bytes of encoded DER data are the key in
|
|
|
- * both the private and public key forms.
|
|
|
- */
|
|
|
-void read_key(const char *filename, u8 *key)
|
|
|
-{
|
|
|
- FILE *f = fopen(filename, "r");
|
|
|
- if (!f)
|
|
|
- {
|
|
|
- fprintf(stderr, "Unable to open %s: %s\n", filename, strerror(errno));
|
|
|
- exit(1);
|
|
|
- }
|
|
|
- char line[512] = {};
|
|
|
- fgets(line, sizeof(line), f);
|
|
|
- if (strncmp(line, "-----BEGIN ", sizeof("-----BEGIN ") - 1) != 0)
|
|
|
- {
|
|
|
- fprintf(stderr, "File %s is not a PEM file\n", filename);
|
|
|
- exit(1);
|
|
|
- }
|
|
|
- fgets(line, sizeof(line), f);
|
|
|
- line[strcspn(line, "\r\n")] = '\0';
|
|
|
- int len = strlen(line);
|
|
|
- base64_decode((u8 *)line, &len);
|
|
|
- if (len < 32)
|
|
|
- {
|
|
|
- fprintf(stderr, "Short read from %s\n", filename);
|
|
|
- exit(1);
|
|
|
- }
|
|
|
- memcpy(key, line + (len - 32), 32);
|
|
|
- fclose(f);
|
|
|
- return;
|
|
|
-}
|
|
|
-
|
|
|
-int main(int argc, char **argv)
|
|
|
-{
|
|
|
- u8 privkey[32];
|
|
|
- u8 pubkey[32];
|
|
|
- u8 result[32];
|
|
|
-
|
|
|
- if (argc != 3)
|
|
|
- {
|
|
|
- fprintf(stderr, "Usage: %s [privkey] [pubkey]\n", argv[0]);
|
|
|
- exit(1);
|
|
|
- }
|
|
|
- read_key(argv[1], privkey);
|
|
|
- read_key(argv[2], pubkey);
|
|
|
- curve25519_donna(result, privkey, pubkey);
|
|
|
- // fwrite(result, 32, 1, stdout);
|
|
|
- for (int i = 0; i < 32; i++)
|
|
|
- {
|
|
|
-
|
|
|
- printf("%d ", result[i]);
|
|
|
- }
|
|
|
- exit(0);
|
|
|
-}
|