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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);
|
|
|
+}
|