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//------------------------------------------------------------------------------
//
// x25519_fpga_curve_abstract.cpp
// -----------------------------------------------
// Elliptic curve arithmetic procedures for X25519
//
// Authors: Pavel Shatov
//
// Copyright (c) 2015-2016, 2018 NORDUnet A/S
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// - Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// - Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// - Neither the name of the NORDUnet nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
// Headers
//------------------------------------------------------------------------------
#include "x25519_fpga_model.h"
//------------------------------------------------------------------------------
// Globals
//------------------------------------------------------------------------------
FPGA_BUFFER X25519_G_X; // x-coordinate of the base point
FPGA_BUFFER X25519_A24; // coefficient (A + 2) / 4
//------------------------------------------------------------------------------
void fpga_curve_x25519_init()
//------------------------------------------------------------------------------
{
int w_src, w_dst; // word counters
FPGA_WORD TMP_G_X[FPGA_OPERAND_NUM_WORDS] = X25519_G_X_INIT;
FPGA_WORD TMP_A24[FPGA_OPERAND_NUM_WORDS] = X25519_A24_INIT;
/* fill buffers for large multi-word integers */
for ( w_src = 0, w_dst = FPGA_OPERAND_NUM_WORDS - 1;
w_src < FPGA_OPERAND_NUM_WORDS;
w_src++, w_dst--)
{
X25519_G_X.words[w_dst] = TMP_G_X[w_src];
X25519_A24.words[w_dst] = TMP_A24[w_src];
}
}
//------------------------------------------------------------------------------
//
// Elliptic curve point scalar multiplication routine.
//
// This uses the Montgomery ladder to do the multiplication and then
// converts the result to affine coordinates.
//
// The algorithm is based on Algorithm 3 from "How to (pre-)compute a ladder"
// https://eprint.iacr.org/2017/264.pdf
//
//------------------------------------------------------------------------------
void fpga_curve_x25519_scalar_multiply_abstract(const FPGA_BUFFER *PX, const FPGA_BUFFER *K, FPGA_BUFFER *QX)
//------------------------------------------------------------------------------
{
int word_count, bit_count; // counters
// temporary buffers
FPGA_BUFFER R0_X;
FPGA_BUFFER R0_Z;
FPGA_BUFFER R1_X;
FPGA_BUFFER R1_Z;
FPGA_BUFFER T0_X;
FPGA_BUFFER T0_Z;
FPGA_BUFFER T1_X;
FPGA_BUFFER T1_Z;
// initialization
fpga_multiword_copy(&CURVE25519_ONE, &R0_X);
fpga_multiword_copy(&CURVE25519_ZERO, &R0_Z);
fpga_multiword_copy(PX, &R1_X);
fpga_multiword_copy(&CURVE25519_ONE, &R1_Z);
// handy vars
FPGA_WORD k_word;
bool k_bit, r_swap = false;
// multiply
for (word_count=FPGA_OPERAND_NUM_WORDS; word_count>0; word_count--)
{
for (bit_count=FPGA_WORD_WIDTH; bit_count>0; bit_count--)
{
// get current bit of K
k_word = K->words[word_count - 1] >> (bit_count - 1);
k_bit = (k_word & (FPGA_WORD)1) == 1;
// we feed either R0, R1 or R1, R0 into the ladder
fpga_multiword_copy(r_swap == k_bit ? &R0_X : &R1_X, &T0_X);
fpga_multiword_copy(r_swap == k_bit ? &R0_Z : &R1_Z, &T0_Z);
fpga_multiword_copy(r_swap == k_bit ? &R1_X : &R0_X, &T1_X);
fpga_multiword_copy(r_swap == k_bit ? &R1_Z : &R0_Z, &T1_Z);
// remember whether we did swapping
r_swap = k_bit;
// montgomery ladder step
fpga_curve_x25519_ladder_step( PX,
&T0_X, &T0_Z, &T1_X, &T1_Z,
&R0_X, &R0_Z, &R1_X, &R1_Z);
}
}
// since the lower three bits of the private key are always ...000,
// the result is in R0_X, R0_Z and
// now conversion to affine coordinates
fpga_curve_x25519_to_affine(&R0_X, &R0_Z, &T0_X);
// so far we've done everything modulo 2*P, we now need
// to do final reduction modulo P, this can be done using
// our modular adder this way:
fpga_modular_add(&T0_X, &CURVE25519_ZERO, QX, &CURVE25519_1P);
}
//------------------------------------------------------------------------------
//
// Montgomery Ladder Step
//
// There are many papers describing Montgomery ladder, this particular
// implementation is based on Algorithm 2 from "Fast elliptic-curve
// cryptography on the Cell Broadband Engine" by Neil Costigan and Peter
// Schwabe
// https://cryptojedi.org/papers/celldh-20090107.pdf
//
//------------------------------------------------------------------------------
void fpga_curve_x25519_ladder_step (const FPGA_BUFFER *PX,
const FPGA_BUFFER *R0X_in, const FPGA_BUFFER *R0Z_in,
const FPGA_BUFFER *R1X_in, const FPGA_BUFFER *R1Z_in,
FPGA_BUFFER *R0X_out, FPGA_BUFFER *R0Z_out,
FPGA_BUFFER *R1X_out, FPGA_BUFFER *R1Z_out)
//------------------------------------------------------------------------------
{
FPGA_BUFFER S0, S1;
FPGA_BUFFER D0, D1;
FPGA_BUFFER QS0, QD0;
FPGA_BUFFER S0D1, S1D0;
FPGA_BUFFER TS, TD;
FPGA_BUFFER QTD;
FPGA_BUFFER T0, TA, T1;
fpga_modular_add(R0X_in, R0Z_in, &S0, &CURVE25519_2P);
fpga_modular_add(R1X_in, R1Z_in, &S1, &CURVE25519_2P);
fpga_modular_sub(R0X_in, R0Z_in, &D0, &CURVE25519_2P);
fpga_modular_sub(R1X_in, R1Z_in, &D1, &CURVE25519_2P);
//
fpga_modular_mul(&S0, &S0, &QS0, &CURVE25519_2P);
fpga_modular_mul(&D0, &D0, &QD0, &CURVE25519_2P);
fpga_modular_mul(&S0, &D1, &S0D1, &CURVE25519_2P);
fpga_modular_mul(&S1, &D0, &S1D0, &CURVE25519_2P);
//
fpga_modular_add(&S1D0, &S0D1, &TS, &CURVE25519_2P);
fpga_modular_sub(&S1D0, &S0D1, &TD, &CURVE25519_2P);
//
fpga_modular_mul(&TD, &TD, &QTD, &CURVE25519_2P);
//
fpga_modular_sub(&QS0, &QD0, &T0, &CURVE25519_2P);
fpga_modular_mul(&T0, &X25519_A24, &TA, &CURVE25519_2P);
fpga_modular_add(&TA, &QD0, &T1, &CURVE25519_2P);
//
fpga_modular_mul(&QS0, &QD0, R0X_out, &CURVE25519_2P);
fpga_modular_mul(&T0, &T1, R0Z_out, &CURVE25519_2P);
fpga_modular_mul(&TS, &TS, R1X_out, &CURVE25519_2P);
fpga_modular_mul(PX, &QTD, R1Z_out, &CURVE25519_2P);
}
//------------------------------------------------------------------------------
//
// Conversion to affine coordinates.
//
// Q_X = P_X / P_Z = P_X * P_Z ^ -1
//
//------------------------------------------------------------------------------
void fpga_curve_x25519_to_affine (const FPGA_BUFFER *P_X,
const FPGA_BUFFER *P_Z,
FPGA_BUFFER *Q_X)
//------------------------------------------------------------------------------
{
FPGA_BUFFER P_Z_1;
fpga_modular_inv_abstract(P_Z, &P_Z_1, &CURVE25519_2P);
fpga_modular_mul(P_X, &P_Z_1, Q_X, &CURVE25519_2P);
}
//------------------------------------------------------------------------------
// End-of-File
//------------------------------------------------------------------------------
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