diff options
Diffstat (limited to 'fpga_curve.cpp')
| -rw-r--r-- | fpga_curve.cpp | 340 |
1 files changed, 0 insertions, 340 deletions
diff --git a/fpga_curve.cpp b/fpga_curve.cpp deleted file mode 100644 index 9cc8ec0..0000000 --- a/fpga_curve.cpp +++ /dev/null @@ -1,340 +0,0 @@ -//------------------------------------------------------------------------------
-//
-// fpga_curve.cpp
-// ------------------------------------
-// Elliptic curve arithmetic procedures
-//
-// Authors: Pavel Shatov
-//
-// Copyright (c) 2015-2016, 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 <stdint.h>
-#include "ecdsa_model.h"
-#include "fpga_lowlevel.h"
-#include "fpga_modular.h"
-#include "fpga_curve.h"
-#include "fpga_util.h"
-
-
-//------------------------------------------------------------------------------
-// Globals
-//------------------------------------------------------------------------------
-FPGA_BUFFER ecdsa_g_x, ecdsa_g_y;
-FPGA_BUFFER ecdsa_h_x, ecdsa_h_y;
-FPGA_BUFFER ecdsa_q_x, ecdsa_q_y;
-FPGA_BUFFER ecdsa_r_x, ecdsa_r_y;
-
-
-//------------------------------------------------------------------------------
-void fpga_curve_init()
-//------------------------------------------------------------------------------
-{
- int w; // word counter
-
- FPGA_BUFFER tmp_g_x = ECDSA_G_X, tmp_g_y = ECDSA_G_Y;
- FPGA_BUFFER tmp_h_x = ECDSA_H_X, tmp_h_y = ECDSA_H_Y;
- FPGA_BUFFER tmp_q_x = ECDSA_Q_X, tmp_q_y = ECDSA_Q_Y;
- FPGA_BUFFER tmp_r_x = ECDSA_R_X, tmp_r_y = ECDSA_R_Y;
-
- /* fill buffers for large multi-word integers */
- for (w=0; w<OPERAND_NUM_WORDS; w++)
- { ecdsa_g_x.words[w] = tmp_g_x.words[OPERAND_NUM_WORDS - (w+1)];
- ecdsa_g_y.words[w] = tmp_g_y.words[OPERAND_NUM_WORDS - (w+1)];
- ecdsa_h_x.words[w] = tmp_h_x.words[OPERAND_NUM_WORDS - (w+1)];
- ecdsa_h_y.words[w] = tmp_h_y.words[OPERAND_NUM_WORDS - (w+1)];
- ecdsa_r_x.words[w] = tmp_r_x.words[OPERAND_NUM_WORDS - (w+1)];
- ecdsa_r_y.words[w] = tmp_r_y.words[OPERAND_NUM_WORDS - (w+1)];
- ecdsa_q_x.words[w] = tmp_q_x.words[OPERAND_NUM_WORDS - (w+1)];
- ecdsa_q_y.words[w] = tmp_q_y.words[OPERAND_NUM_WORDS - (w+1)];
- }
-}
-
-
-//------------------------------------------------------------------------------
-//
-// Elliptic curve point doubling routine.
-//
-// R(rx,ry,rz) = 2 * P(px,py,pz)
-//
-// Note, that P(px,py,pz) is supposed to be in projective Jacobian coordinates,
-// R will be in projective Jacobian coordinates.
-//
-// This routine implements algorithm 3.21 from "Guide to Elliptic Curve
-// Cryptography", the only difference is that step 6. does T1 = T2 + T2 and
-// then T2 = T2 + T1 instead of T2 = 3 * T2, because our addition is much
-// faster, than multiplication.
-//
-// Note, that this routine also handles one special case, namely when P is at
-// infinity.
-//
-// Instead of actual modular division, multiplication by pre-computed constant
-// (2^-1 mod q) is done.
-//
-// Note, that FPGA modular multiplier can't multiply a given buffer by itself,
-// this way it's impossible to do eg. fpga_modular_mul(pz, pz, &t1). To overcome
-// the problem the algorithm was modified to do fpga_buffer_copy(pz, &t1) and
-// then fpga_modular_mul(pz, &t1, &t1) instead.
-//
-// WARNING: Though this procedure always does doubling steps, it does not take
-// any active measures to keep run-time constant. The main purpose of this
-// model is to help debug Verilog code for FPGA, so *DO NOT* use is anywhere
-// near production!
-//
-//------------------------------------------------------------------------------
-void fpga_curve_double_jacobian(FPGA_BUFFER *px, FPGA_BUFFER *py, FPGA_BUFFER *pz, FPGA_BUFFER *rx, FPGA_BUFFER *ry, FPGA_BUFFER *rz)
-//------------------------------------------------------------------------------
-{
- FPGA_BUFFER t1, t2, t3; // temporary variables
-
- // check, whether P is at infinity
- bool pz_is_zero = fpga_buffer_is_zero(pz);
-
- /* 2. */ fpga_buffer_copy(pz, &t1);
- fpga_modular_mul(pz, &t1, &t1);
- /* 3. */ fpga_modular_sub(px, &t1, &t2);
- /* 4. */ fpga_modular_add(px, &t1, &t1);
- /* 5. */ fpga_modular_mul(&t1, &t2, &t2);
- /* 6. */ fpga_modular_add(&t2, &t2, &t1);
- /* */ fpga_modular_add(&t1, &t2, &t2);
- /* 7. */ fpga_modular_add(py, py, ry);
- /* 8. */ fpga_modular_mul(pz, ry, rz);
- /* 9. */ fpga_buffer_copy(ry, &t1);
- fpga_buffer_copy(ry, &t3);
- fpga_modular_mul(&t1, &t3, ry);
- /* 10. */ fpga_modular_mul(px, ry, &t3);
- /* 11. */ fpga_buffer_copy(ry, &t1);
- fpga_modular_mul(ry, &t1, &t1);
- /* 12. */ fpga_modular_mul(&t1, &ecdsa_delta, ry);
- /* 13. */ fpga_buffer_copy(&t2, &t1);
- fpga_modular_mul(&t1, &t2, rx);
- /* 14. */ fpga_modular_add(&t3, &t3, &t1);
- /* 15. */ fpga_modular_sub(rx, &t1, rx);
- /* 16. */ fpga_modular_sub(&t3, rx, &t1);
- /* 17. */ fpga_modular_mul(&t1, &t2, &t1);
- /* 18. */ fpga_modular_sub(&t1, ry, ry);
-
- // handle special case (input point is at infinity)
- if (pz_is_zero)
- { fpga_buffer_copy(&ecdsa_one, rx);
- fpga_buffer_copy(&ecdsa_one, ry);
- fpga_buffer_copy(&ecdsa_zero, rz);
- }
-}
-
-
-//------------------------------------------------------------------------------
-//
-// Elliptic curve point addition routine.
-//
-// R(rx,ry,rz) = P(px,py,pz) + Q(qx,qy)
-//
-// Note, that P(px, py, pz) is supposed to be in projective Jacobian
-// coordinates, while Q(qx,qy) is supposed to be in affine coordinates,
-// R(rx, ry, rz) will be in projective Jacobian coordinates. Moreover, in this
-// particular implementation Q is always the base point G.
-//
-// This routine implements algorithm 3.22 from "Guide to Elliptic Curve
-// Cryptography". Differences from the original algorithm:
-//
-// 1) Step 1. is omitted, because point Q is always the base point, which is
-// not at infinity by definition.
-//
-// 2) Step 9.1 just returns the pre-computed double of the base point instead
-// of actually doubling it.
-//
-// Note, that this routine also handles three special cases:
-//
-// 1) P is at infinity
-// 2) P == Q
-// 3) P == -Q
-//
-// Note, that FPGA modular multiplier can't multiply a given buffer by itself,
-// this way it's impossible to do eg. fpga_modular_mul(pz, pz, &t1). To overcome
-// the problem the algorithm was modified to do fpga_buffer_copy(pz, &t1) and
-// then fpga_modular_mul(pz, &t1, &t1) instead.
-//
-// WARNING: This procedure does not take any active measures to keep run-time
-// constant. The main purpose of this model is to help debug Verilog code for
-// FPGA, so *DO NOT* use is anywhere near production!
-//
-//------------------------------------------------------------------------------
-void fpga_curve_add_jacobian(FPGA_BUFFER *px, FPGA_BUFFER *py, FPGA_BUFFER *pz, FPGA_BUFFER *rx, FPGA_BUFFER *ry, FPGA_BUFFER *rz)
-//------------------------------------------------------------------------------
-{
- FPGA_BUFFER t1, t2, t3, t4; // temporary variables
-
- bool pz_is_zero = fpga_buffer_is_zero(pz); // Step 2.
-
- /* 3. */ fpga_buffer_copy(pz, &t1);
- fpga_modular_mul(pz, &t1, &t1);
- /* 4. */ fpga_modular_mul(pz, &t1, &t2);
- /* 5. */ fpga_modular_mul(&t1, &ecdsa_g_x, &t1);
- /* 6. */ fpga_modular_mul(&t2, &ecdsa_g_y, &t2);
- /* 7. */ fpga_modular_sub(&t1, px, &t1);
- /* 8. */ fpga_modular_sub(&t2, py, &t2);
-
- bool t1_is_zero = fpga_buffer_is_zero(&t1); // | Step 9.
- bool t2_is_zero = fpga_buffer_is_zero(&t2); // |
-
- /* 10. */ fpga_modular_mul(pz, &t1, rz);
- /* 11. */ fpga_buffer_copy(&t1, &t3);
- fpga_modular_mul(&t1, &t3, &t3);
- /* 12. */ fpga_modular_mul(&t1, &t3, &t4);
- /* 13. */ fpga_modular_mul(px, &t3, &t3);
- /* 14. */ fpga_modular_add(&t3, &t3, &t1);
- /* 15. */ fpga_buffer_copy(&t2, rx);
- fpga_modular_mul(rx, &t2, rx);
- /* 16. */ fpga_modular_sub(rx, &t1, rx);
- /* 17. */ fpga_modular_sub(rx, &t4, rx);
- /* 18. */ fpga_modular_sub(&t3, rx, &t3);
- /* 19. */ fpga_modular_mul(&t2, &t3, &t3);
- /* 20. */ fpga_modular_mul(py, &t4, &t4);
- /* 21. */ fpga_modular_sub(&t3, &t4, ry);
-
- //
- // final selection
- //
- if (pz_is_zero) // P at infinity ?
- { fpga_buffer_copy(&ecdsa_g_x, rx);
- fpga_buffer_copy(&ecdsa_g_y, ry);
- fpga_buffer_copy(&ecdsa_one, rz);
- }
- else if (t1_is_zero) // same x for P and Q ?
- {
- fpga_buffer_copy(t2_is_zero ? &ecdsa_h_x : &ecdsa_one, rx); // | same y ? (P==Q => R=2*G) : (P==-Q => R=O)
- fpga_buffer_copy(t2_is_zero ? &ecdsa_h_y : &ecdsa_one, ry); // |
- fpga_buffer_copy(t2_is_zero ? &ecdsa_one : &ecdsa_zero, rz); // |
- }
-}
-
-
-//------------------------------------------------------------------------------
-//
-// Conversion from projective Jacobian to affine coordinates.
-//
-// P(px,py,pz) -> Q(qx,qy)
-//
-// Note, that qx = px / Z^2 and qy = py / Z^3. Division in modular arithmetic
-// is equivalent to multiplication by the inverse value of divisor, so
-// qx = px * (pz^-1)^2 and qy = py * (pz^-1)^3.
-//
-// Note, that this procedure does *NOT* handle points at infinity correctly. It
-// can only be called from the base point multiplication routine, that
-// specifically makes sure that P is not at infinity, so pz will always be
-// non-zero value.
-//
-//------------------------------------------------------------------------------
-void fpga_curve_point_to_affine(FPGA_BUFFER *px, FPGA_BUFFER *py, FPGA_BUFFER *pz, FPGA_BUFFER *qx, FPGA_BUFFER *qy)
-//------------------------------------------------------------------------------
-{
- FPGA_BUFFER pz1; // inverse value of pz
- FPGA_BUFFER t2, t3; // intermediate values
-
- fpga_modular_inv(pz, &pz1); // pz1 = pz^-1 (mod q)
-
- fpga_modular_mul(&pz1, &pz1, &t2); // t2 = pz1 ^ 2 (mod q)
- fpga_modular_mul(&pz1, &t2, &t3); // t3 = tz1 ^ 3 (mod q)
-
- fpga_modular_mul(px, &t2, qx); // qx = px * (pz^-1)^2 (mod q)
- fpga_modular_mul(py, &t3, qy); // qy = py * (pz^-1)^3 (mod q)
-}
-
-
-//------------------------------------------------------------------------------
-//
-// Elliptic curve base point scalar multiplication routine.
-//
-// Q(qx,qy) = k * G(px,py)
-//
-// Note, that Q is supposed to be in affine coordinates. Multiplication is done
-// using the double-and-add algorithm 3.27 from "Guide to Elliptic Curve
-// Cryptography".
-//
-// WARNING: Though this procedure always does the addition step, it only
-// updates the result when current bit of k is set. It does not take any
-// active measures to keep run-time constant. The main purpose of this model
-// is to help debug Verilog code for FPGA, so *DO NOT* use it anywhere near
-// production!
-//
-//------------------------------------------------------------------------------
-void fpga_curve_scalar_multiply(FPGA_BUFFER *k, FPGA_BUFFER *qx, FPGA_BUFFER *qy)
-//------------------------------------------------------------------------------
-{
- int word_count, bit_count; // counters
-
- FPGA_BUFFER rx, ry, rz; // intermediate result
- FPGA_BUFFER tx, ty, tz; // temporary variable
-
- /* set initial value of R to point at infinity */
- fpga_buffer_copy(&ecdsa_one, &rx);
- fpga_buffer_copy(&ecdsa_one, &ry);
- fpga_buffer_copy(&ecdsa_zero, &rz);
-
- /* process bits of k left-to-right */
- for (word_count=OPERAND_NUM_WORDS; word_count>0; word_count--)
- for (bit_count=FPGA_WORD_WIDTH; bit_count>0; bit_count--)
- {
- /* calculate T = 2 * R */
- fpga_curve_double_jacobian(&rx, &ry, &rz, &tx, &ty, &tz);
-
- /* always calculate R = T + P for constant-time */
- fpga_curve_add_jacobian(&tx, &ty, &tz, &rx, &ry, &rz);
-
- /* revert to the value of T before addition if the current bit of k is not set */
- if (!((k->words[word_count-1] >> (bit_count-1)) & 1))
- { fpga_buffer_copy(&tx, &rx);
- fpga_buffer_copy(&ty, &ry);
- fpga_buffer_copy(&tz, &rz);
- }
-
- }
-
- // convert result to affine coordinates anyway
- fpga_curve_point_to_affine(&rx, &ry, &rz, qx, qy);
-
- // check, that rz is non-zero (not point at infinity)
- bool rz_is_zero = fpga_buffer_is_zero(&rz);
-
- // handle special case (result is point at infinity)
- if (rz_is_zero)
- { fpga_buffer_copy(&ecdsa_zero, qx);
- fpga_buffer_copy(&ecdsa_zero, qy);
- }
-}
-
-
-//------------------------------------------------------------------------------
-// End-of-File
-//------------------------------------------------------------------------------
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