Modular math routines

2 files changed, 700 insertions, 0 deletions

diff --git a/curve25519/curve25519_fpga_modular.cpp b/curve25519/curve25519_fpga_modular.cpp
new file mode 100644
index 0000000..7ceb3d2
--- /dev/null
+++ b/curve25519/curve25519_fpga_modular.cpp
@@ -0,0 +1,622 @@
+//------------------------------------------------------------------------------
+//
+// curve25519_fpga_modular.cpp
+// ------------------------------------------
+// Modular arithmetic routines for Curve25519
+//
+// 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 "curve25519_fpga_model.h"
+
+
+//------------------------------------------------------------------------------
+// Globals
+//------------------------------------------------------------------------------
+FPGA_BUFFER CURVE25519_1P;
+FPGA_BUFFER CURVE25519_2P;
+
+
+//------------------------------------------------------------------------------
+void fpga_modular_init()
+//------------------------------------------------------------------------------
+{
+	int w_src, w_dst;	// word counters
+
+		// temporary things
+	FPGA_WORD TMP_1P[FPGA_OPERAND_NUM_WORDS]	= CURVE25519_1P_INIT;
+	FPGA_WORD TMP_2P[FPGA_OPERAND_NUM_WORDS]	= CURVE25519_2P_INIT;
+
+		/* fill buffers for large multi-word integers, we need to fill them in
+		 * reverse order because of the way C arrays are initialized
+		 */
+	for (	w_src = 0, w_dst = FPGA_OPERAND_NUM_WORDS - 1;
+			w_src < FPGA_OPERAND_NUM_WORDS;
+			w_src++, w_dst--)
+	{
+		CURVE25519_1P.words[w_dst]	= TMP_1P[w_src];
+		CURVE25519_2P.words[w_dst]	= TMP_2P[w_src];
+	}
+}
+
+
+//------------------------------------------------------------------------------
+//
+// Modular addition.
+//
+// This routine implements algorithm 3. from "Ultra High Performance ECC over
+// NIST Primes on Commercial FPGAs".
+//
+// s = (a + b) mod q
+//
+// The naive approach is like the following:
+//
+// 1. s = a + b
+// 2. if (s >= q) s -= q
+//
+// The speed-up trick is to simultaneously calculate (a + b) and (a + b - q)
+// and then select the right variant.
+//
+//------------------------------------------------------------------------------
+void fpga_modular_add(const FPGA_BUFFER *A, const FPGA_BUFFER *B, FPGA_BUFFER *S, const FPGA_BUFFER *N)
+//------------------------------------------------------------------------------
+{
+	int w;					// word counter
+	FPGA_BUFFER AB, AB_N;	// intermediate buffers
+	bool c_in, c_out;		// carries
+	bool b_in, b_out;		// borrows
+
+	c_in = false;			// first word has no carry
+	b_in = false;			// first word has no borrow
+	
+		// run parallel addition and subtraction
+	for (w=0; w<FPGA_OPERAND_NUM_WORDS; w++)
+	{
+		fpga_lowlevel_add32(A->words[w], B->words[w], c_in, &AB.words[w],   &c_out);
+		fpga_lowlevel_sub32(AB.words[w], N->words[w], b_in, &AB_N.words[w], &b_out);
+
+		c_in = c_out;	// propagate carry
+		b_in = b_out;	// propagate borrow
+	}
+
+		// now select the right buffer
+
+		/*
+		 * We select the right variant based on borrow and carry flags after
+		 * addition and subtraction of the very last pair of words. Note, that
+		 * we only need to select the first variant (a + b) when (a + b) < q.
+		 * This way if we get negative number after subtraction, we discard it
+		 * and use the output of the adder instead. The subtractor output is
+		 * negative when borrow flag is set *and* carry flag is not set. When
+		 * both borrow and carry are set, the number is non-negative, because
+		 * borrow and carry cancel each other out.
+		 */
+	for (w=0; w<FPGA_OPERAND_NUM_WORDS; w++)
+		S->words[w] = (b_out && !c_out) ? AB.words[w] : AB_N.words[w];
+}
+
+
+//------------------------------------------------------------------------------
+//
+// Modular subtraction.
+//
+// This routine implements algorithm 3. from "Ultra High Performance ECC over
+// NIST Primes on Commercial FPGAs".
+//
+// d = (a - b) mod q
+//
+// The naive approach is like the following:
+//
+// 1. d = a - b
+// 2. if (a < b) d += q
+//
+// The speed-up trick is to simultaneously calculate (a - b) and (a - b + q)
+// and then select the right variant.
+//
+//------------------------------------------------------------------------------
+void fpga_modular_sub(const FPGA_BUFFER *A, const FPGA_BUFFER *B, FPGA_BUFFER *D, const FPGA_BUFFER *N)
+//------------------------------------------------------------------------------
+{
+	int w;					// word counter
+	FPGA_BUFFER AB, AB_N;	// intermediate buffers
+	bool c_in, c_out;		// carries
+	bool b_in, b_out;		// borrows
+
+	c_in = false;			// first word has no carry
+	b_in = false;			// first word has no borrow
+	
+		// run parallel subtraction and addition
+	for (w=0; w<FPGA_OPERAND_NUM_WORDS; w++)
+	{
+		fpga_lowlevel_sub32(A->words[w], B->words[w], b_in, &AB.words[w],   &b_out);
+		fpga_lowlevel_add32(AB.words[w], N->words[w], c_in, &AB_N.words[w], &c_out);
+
+		b_in = b_out;	// propagate borrow
+		c_in = c_out;	// propagate carry
+	}
+
+		// now select the right buffer
+
+		/*
+		 * We select the right variant based on borrow flag after subtraction
+		 * and addition of the very last pair of words. Note, that we only
+		 * need to select the second variant (a - b + q) when a < b. This way
+		 * if we get negative number after subtraction, we discard it
+		 * and use the output of the adder instead. The Subtractor output is
+		 * negative when borrow flag is set.
+		 */
+	for (w=0; w<FPGA_OPERAND_NUM_WORDS; w++)
+		D->words[w] = b_out ? AB_N.words[w] : AB.words[w];
+}
+
+
+//------------------------------------------------------------------------------
+//
+// Modular multiplication for Curve25519.
+//
+// p = (a * b) mod q
+//
+// The complex algorithm is split into three parts:
+//
+// 1. Calculation of partial words
+// 2. Acccumulation of partial words into full-size product
+// 3. Modular reduction of the full-size product
+//
+// See comments for corresponding helper routines for more information.
+//
+//------------------------------------------------------------------------------
+void fpga_modular_mul(const FPGA_BUFFER *A, const FPGA_BUFFER *B, FPGA_BUFFER *P, const FPGA_BUFFER *N)
+//------------------------------------------------------------------------------
+{
+	FPGA_WORD_EXTENDED SI[4*FPGA_OPERAND_NUM_WORDS-1];	// parts of intermediate product
+	FPGA_WORD C[2*FPGA_OPERAND_NUM_WORDS];				// full-size intermediate product
+
+		/* multiply to get partial words */
+	fpga_modular_mul_helper_multiply(A, B, SI);
+
+		/* accumulate partial words into full-size product */
+	fpga_modular_mul_helper_accumulate(SI, C);
+
+		/* reduce full-size product using special routine */
+	fpga_modular_mul_helper_reduce(C, P, N);
+}
+
+
+//------------------------------------------------------------------------------
+//
+// Modular reduction for Curve25519.
+//
+// Note, that this routine reduces 512-bit product modulo 2*P, i.e.
+// 2 * (2^255 -19) = 2^256 - 38. It is computationally more effective to not
+// fully reduce the result until the very end of X25519 calculation.
+//
+// See the "Special Reduction" section of "High-Performance Modular
+// Multiplication on the Cell Processor" by Joppe W. Bos for more information
+// about the math behind reduction: http://joppebos.com/files/waifi09.pdf
+//
+//------------------------------------------------------------------------------
+void fpga_modular_mul_helper_reduce(const FPGA_WORD *C, FPGA_BUFFER *P, const FPGA_BUFFER *N)
+//------------------------------------------------------------------------------
+{
+	int w;	// word counter
+
+		// handy vars
+	FPGA_WORD y;
+	FPGA_WORD x1_msb, x1_lsb;
+	FPGA_WORD x2_msb, x2_lsb;
+	FPGA_WORD x5_msb, x5_lsb;
+	FPGA_WORD n_word;
+
+		// S1 is 262-bit result after the first reduction attempt
+		// S2 is 257-bit result after the second reduction attempt
+	FPGA_WORD S1[FPGA_OPERAND_NUM_WORDS + 1];
+	FPGA_WORD S2[FPGA_OPERAND_NUM_WORDS + 1];
+
+		// carries during the first and the second stages
+	FPGA_WORD_REDUCED t_carry1;
+	FPGA_WORD_EXTENDED t_carry2;
+
+		// borrows for the final stage
+	bool b_in, b_out;
+
+		// temporary result of the final stage
+	FPGA_WORD S2_N[FPGA_OPERAND_NUM_WORDS + 1];
+
+		// outputs of adders
+	FPGA_WORD_EXTENDED T1[FPGA_OPERAND_NUM_WORDS + 1];
+	FPGA_WORD_EXTENDED T2[FPGA_OPERAND_NUM_WORDS + 1];
+	FPGA_WORD_EXTENDED T3[FPGA_OPERAND_NUM_WORDS + 1];
+	FPGA_WORD_EXTENDED T4[FPGA_OPERAND_NUM_WORDS + 1];
+
+		// parts of full input product
+	FPGA_BUFFER P_LO, P_HI;
+
+		// split 512-bit input C into two 256-bit parts
+	for (w=0; w<FPGA_OPERAND_NUM_WORDS; w++)
+	{
+		P_LO.words[w] = C[w];
+		P_HI.words[w] = C[FPGA_OPERAND_NUM_WORDS + w];
+	}
+
+		/* We need to calculate S1 = P_HI * 38 + P_LO, this is done using
+		 * additions instead of multiplications, because our low-level
+		 * multiplier can only process 16 bits at a time, while an adder
+		 * can do 47. This is done by replacing 38 with 32 + 4 + 2 = 
+		 * 2^5 + 2^2 + 2^1, this way:
+		 * S1 = P_LO + (P_HI << 5) + (P_HI << 2) + (P_HI << 1)
+		 */
+
+		/* for every word we need to calculate a sum of five values: three
+		 * shifted copies of P_HI[w], P_LO[w] and carry from the previous word.
+		 * This is done using four adders in a pipelined fashion.
+		 */
+
+	t_carry1 = 0;	// no carry in the very first word
+	for (w=0; w<(FPGA_OPERAND_NUM_WORDS+1); w++)
+	{
+			// upper parts of shifted copies of P_HI[w-i] (from the previous cycle)
+		x1_msb = (w > 0) ? (FPGA_WORD)(P_HI.words[w-1] >> (32 - 1)) : 0;
+		x2_msb = (w > 0) ? (FPGA_WORD)(P_HI.words[w-1] >> (32 - 2)) : 0;
+		x5_msb = (w > 0) ? (FPGA_WORD)(P_HI.words[w-1] >> (32 - 5)) : 0;
+
+			// lower parts of shifted copies of P_HI[w]
+		x1_lsb = (w < FPGA_OPERAND_NUM_WORDS) ? (FPGA_WORD)(P_HI.words[w] << 1) : 0;
+		x2_lsb = (w < FPGA_OPERAND_NUM_WORDS) ? (FPGA_WORD)(P_HI.words[w] << 2) : 0;
+		x5_lsb = (w < FPGA_OPERAND_NUM_WORDS) ? (FPGA_WORD)(P_HI.words[w] << 5) : 0;
+
+			// take care of uppers parts from the previous cycle
+		x1_lsb |= x1_msb;
+		x2_lsb |= x2_msb;
+		x5_lsb |= x5_msb;
+
+			// current word of P_LO
+		y = (w < FPGA_OPERAND_NUM_WORDS) ? P_LO.words[w] : 0;
+
+			// run addition
+		fpga_lowlevel_add47(x1_lsb, x2_lsb,   &T1[w]);	// T1 obtained after clock cycle w
+		fpga_lowlevel_add47(x5_lsb, y,        &T2[w]);	// T2 obtained after clock cycle w
+		fpga_lowlevel_add47(T1[w],  T2[w],    &T3[w]);	// T3 obtained after clock cycle w+1 (when T1 and T2 are available)
+		fpga_lowlevel_add47(T3[w],  t_carry1, &T4[w]);	// T4 obtained after clock cycle w+2 (when T3 is available)
+
+			// store carry
+		t_carry1 = (FPGA_WORD_REDUCED)(T4[w] >> FPGA_WORD_WIDTH);
+
+			// store word of sum
+		S1[w] = (FPGA_WORD)T4[w];
+	}
+
+		/* now repeat what we've just done once again with S1, but this time S1_HI
+		 * is 6-bit wide at most, so we can calculate S1_HI * 38 beforehand,
+		 * add it to the lowest word of S1_LO and then propagate the carry
+		 */
+
+	t_carry2 = 0;
+	t_carry2 += (FPGA_WORD_EXTENDED)S1[FPGA_OPERAND_NUM_WORDS] << 1;
+	t_carry2 += (FPGA_WORD_EXTENDED)S1[FPGA_OPERAND_NUM_WORDS] << 2;
+	t_carry2 += (FPGA_WORD_EXTENDED)S1[FPGA_OPERAND_NUM_WORDS] << 5;
+
+	for (w=0; w<(FPGA_OPERAND_NUM_WORDS+1); w++)
+	{
+			// current word of S1_LO
+		y = (w < FPGA_OPERAND_NUM_WORDS) ? S1[w] : 0;
+
+			// do addition
+		fpga_lowlevel_add47(t_carry2, y, &T1[w]);
+
+			// store carry
+		t_carry2 = (FPGA_WORD_REDUCED)(T1[w] >> FPGA_WORD_WIDTH);
+
+			// store word of sum
+		S2[w] = (FPGA_WORD)T1[w];
+	}
+
+		/* So we've ended up with 257-bit result in S2. Note that there can only be
+		 * two situations, given our modulus N is 2^256 - 38:
+		 *
+		 * a) 0 <= S < N
+		 * b) N <= S < 2*N
+		 *
+		 * This is because we've obtained S2 by adding 256-bit quantity S1_LO and
+		 * 12-bit quantity 38 * S_HI. S1_LO is at most 2^256 - 1 or N + 37, while
+		 * the 12-bit quantity is at most 4095, so the largest possible value of
+		 * S2 is N + 4132, which is obviously less than 2*N.
+		 *
+		 * What we now do is we try subtracting N from S2 to obtain S2_N, if we end up
+		 * with a negative number, we return S2 (reduction was not necessary), otherwise
+		 * we return S2_N.
+		 */
+
+	b_in = false;	// first word has no borrow
+	
+		// run parallel subtraction
+	for (w=0; w<=FPGA_OPERAND_NUM_WORDS; w++)
+	{
+			// current word of N
+		n_word = (w < FPGA_OPERAND_NUM_WORDS) ? N->words[w] : 0;
+
+			// do subtraction
+		fpga_lowlevel_sub32(S2[w], n_word, b_in, &S2_N[w], &b_out);
+
+			// propagate borrow
+		b_in = b_out;
+	}
+	
+		// copy result to output buffer
+	for (w=0; w<FPGA_OPERAND_NUM_WORDS; w++)
+	{
+			// if subtraction of the highest words produced carry, we ended up
+			// with a negative number and S2 must be returned, not S2_N
+		P->words[w] = b_out ? S2[w] : S2_N[w];
+	}
+
+}
+
+
+//------------------------------------------------------------------------------
+//
+// Parallelized multiplication.
+//
+// This routine implements the algorithm in Fig. 3. from "Ultra High
+// Performance ECC over NIST Primes on Commercial FPGAs".
+//
+// Inputs A and B are split into 2*OPERAND_NUM_WORDS words of FPGA_WORD_WIDTH/2
+// bits each, because FPGA multipliers can't handle full FPGA_WORD_WIDTH-wide
+// inputs. These smaller words are multiplied by an array of 2*OPERAND_NUM_WORDS
+// multiplers and accumulated into an array of 4*OPERAND_NUM_WORDS-1 partial
+// output words SI[].
+//
+// The order of loading A and B into the multipliers is a bit complicated,
+// during the first 2*OPERAND_NUM_WORDS-1 cycles one SI word per cycle is
+// obtained, during the very last 2*OPERAND_NUM_WORDS'th cycle all the
+// remaining 2*OPERAND_NUM_WORDS partial words are obtained simultaneously.
+//
+//------------------------------------------------------------------------------
+void fpga_modular_mul_helper_multiply(const FPGA_BUFFER *A, const FPGA_BUFFER *B, FPGA_WORD_EXTENDED *SI)
+//------------------------------------------------------------------------------
+{
+	int w;			// counter
+	int t, x;		// more counters
+	int j, i;		// word indices
+	FPGA_WORD p;	// product
+
+		// buffers for smaller words that multipliers can handle
+	FPGA_WORD_REDUCED AI[2*FPGA_OPERAND_NUM_WORDS];
+	FPGA_WORD_REDUCED BJ[2*FPGA_OPERAND_NUM_WORDS];
+	
+		// split a and b into smaller words
+	for (w=0; w<FPGA_OPERAND_NUM_WORDS; w++)
+		AI[2*w] = (FPGA_WORD_REDUCED)A->words[w], AI[2*w + 1] = (FPGA_WORD_REDUCED)(A->words[w] >> (FPGA_WORD_WIDTH / 2)),
+		BJ[2*w] = (FPGA_WORD_REDUCED)B->words[w], BJ[2*w + 1] = (FPGA_WORD_REDUCED)(B->words[w] >> (FPGA_WORD_WIDTH / 2));
+
+		// accumulators
+	FPGA_WORD_EXTENDED mac[2*FPGA_OPERAND_NUM_WORDS];
+	
+		// clear accumulators
+	for (w=0; w<(2*FPGA_OPERAND_NUM_WORDS); w++) mac[w] = 0;
+
+		// run the crazy algorithm :)
+	for (t=0; t<(2*FPGA_OPERAND_NUM_WORDS); t++)
+	{
+			// save upper half of si[] (one word per cycle)
+		if (t > 0)
+		{	SI[4*FPGA_OPERAND_NUM_WORDS - (t+1)] = mac[t];
+			mac[t] = 0;
+		}
+
+			// update index
+		j = 2*FPGA_OPERAND_NUM_WORDS - (t+1);
+
+			// parallel multiplication
+		for (x=0; x<(2*FPGA_OPERAND_NUM_WORDS); x++)
+		{
+				// update index
+			i = t - x;
+			if (i < 0) i += 2*FPGA_OPERAND_NUM_WORDS;
+
+				// multiply...
+			fpga_lowlevel_mul16(AI[i], BJ[j], &p);
+
+				// ...accumulate
+			mac[x] += p;
+		}
+
+	}
+
+		// now finally save lower half of SI[] (2*OPERAND_NUM_WORDS words at once)
+	for (w=0; w<(2*FPGA_OPERAND_NUM_WORDS); w++)
+		SI[w] = mac[2*FPGA_OPERAND_NUM_WORDS - (w+1)];
+}
+
+
+//------------------------------------------------------------------------------
+//
+// Accumulation of partial words into full-size product.
+//
+// This routine implements the Algorithm 4. from "Ultra High Performance ECC
+// over NIST Primes on Commercial FPGAs".
+//
+// Input words SI[] are accumulated into full-size product C[].
+//
+// The algorithm is a bit tricky, there are 4*OPERAND_NUM_WORDS-1 words in
+// SI[]. Complete operation takes 2*OPERAND_NUM_WORDS cycles, even words are
+// summed in full, odd words are split into two parts. During every cycle the
+// upper part of the previous word and the lower part of the following word are
+// summed too.
+//
+//------------------------------------------------------------------------------
+void fpga_modular_mul_helper_accumulate(const FPGA_WORD_EXTENDED *SI, FPGA_WORD *C)
+//------------------------------------------------------------------------------
+{
+	int w;							// word counter
+	FPGA_WORD_EXTENDED cw0, cw1;	// intermediate sums
+	FPGA_WORD_REDUCED  cw_carry;	// wide carry
+
+		// clear carry
+	cw_carry = 0;
+
+		// execute the algorithm
+	for (w=0; w<(2*FPGA_OPERAND_NUM_WORDS); w++)
+	{
+			// handy flags
+		bool w_is_first = (w == 0);
+		bool w_is_last  = (w == (2*FPGA_OPERAND_NUM_WORDS-1));
+
+			// accumulate full current even word...
+			// ...and also the upper part of the previous odd word (if not the first word)
+		fpga_lowlevel_add47(SI[2*w], w_is_first ? 0 : SI[2*w-1] >> (FPGA_WORD_WIDTH / 2), &cw0);
+
+			// generate another word from "carry" part of the previous even word...
+			// ...and also the lower part of the following odd word (if not the last word)
+		cw1 = w_is_last ? 0 : (FPGA_WORD)(SI[2*w+1] << (FPGA_WORD_WIDTH / 2));
+		cw1 |= (FPGA_WORD_EXTENDED)cw_carry;
+
+			// accumulate once again
+		fpga_lowlevel_add47(cw0, cw1, &cw1);
+
+			// store current word...
+		C[w] = (FPGA_WORD)cw1;
+
+			// ...and carry
+		cw_carry = (FPGA_WORD_REDUCED) (cw1 >> FPGA_WORD_WIDTH);
+	}
+}
+
+
+//------------------------------------------------------------------------------
+//
+// Custom modular inversion.
+//
+// This uses Fermat's little theorem to calculate A1 = A ^ -1.
+//
+// The corresponding addition chain which Bernstein calls "straightforward
+// sequence of 254 squarings and 11 multiplications" in his original paper was
+// taken from here:
+// https://briansmith.org/ecc-inversion-addition-chains-01
+//
+//------------------------------------------------------------------------------
+void fpga_modular_inv_abstract(const FPGA_BUFFER *A, FPGA_BUFFER *A1, const FPGA_BUFFER *N)
+{
+	int cyc_count;	// counter
+
+		// temporary variables
+	FPGA_BUFFER R1, R2;
+	FPGA_BUFFER T_1;
+	FPGA_BUFFER T_10;
+	FPGA_BUFFER T_1001;
+	FPGA_BUFFER T_1011;
+	FPGA_BUFFER T_X5;
+	FPGA_BUFFER T_X10;
+	FPGA_BUFFER T_X20;
+	FPGA_BUFFER T_X40;
+	FPGA_BUFFER T_X50;
+	FPGA_BUFFER T_X100;
+
+		// let's go
+	fpga_multiword_copy(A, &T_1);
+	//
+	fpga_modular_mul(&T_1, &T_1, &T_10, &CURVE25519_2P);
+	//
+	fpga_modular_mul(&T_10, &T_10, &R1, &CURVE25519_2P);
+	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);
+	fpga_modular_mul(&R2, &T_1, &T_1001, &CURVE25519_2P);
+	//
+	fpga_modular_mul(&T_1001, &T_10, &T_1011, &CURVE25519_2P);
+	//
+	fpga_modular_mul(&T_1011, &T_1011, &R1, &CURVE25519_2P);
+	fpga_modular_mul(&R1, &T_1001, &T_X5, &CURVE25519_2P);
+	//
+	fpga_multiword_copy(&T_X5, &R1);
+	for (cyc_count=0; cyc_count<5; cyc_count++)
+	{	if (!(cyc_count % 2))	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);
+		else					fpga_modular_mul(&R2, &R2, &R1, &CURVE25519_2P);
+	}
+	fpga_modular_mul(&R2, &T_X5, &T_X10, &CURVE25519_2P);
+	//
+	fpga_multiword_copy(&T_X10, &R1);
+	for (cyc_count=0; cyc_count<10; cyc_count++)
+	{	if (!(cyc_count % 2))	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);
+		else					fpga_modular_mul(&R2, &R2, &R1, &CURVE25519_2P);
+	}
+	fpga_modular_mul(&R1, &T_X10, &T_X20, &CURVE25519_2P);
+	//
+	fpga_multiword_copy(&T_X20, &R1);
+	for (cyc_count=0; cyc_count<20; cyc_count++)
+	{	if (!(cyc_count % 2))	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);
+		else					fpga_modular_mul(&R2, &R2, &R1, &CURVE25519_2P);
+	}
+	fpga_modular_mul(&R1, &T_X20, &T_X40, &CURVE25519_2P);
+	//
+	fpga_multiword_copy(&T_X40, &R1);
+	for (cyc_count=0; cyc_count<10; cyc_count++)
+	{	if (!(cyc_count % 2))	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);
+		else					fpga_modular_mul(&R2, &R2, &R1, &CURVE25519_2P);
+	}
+	fpga_modular_mul(&R1, &T_X10, &T_X50, &CURVE25519_2P);
+	//
+	fpga_multiword_copy(&T_X50, &R1);
+	for (cyc_count=0; cyc_count<50; cyc_count++)
+	{	if (!(cyc_count % 2))	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);
+		else					fpga_modular_mul(&R2, &R2, &R1, &CURVE25519_2P);
+	}
+	fpga_modular_mul(&R1, &T_X50, &T_X100, &CURVE25519_2P);
+	//
+	fpga_multiword_copy(&T_X100, &R1);
+	for (cyc_count=0; cyc_count<100; cyc_count++)
+	{	if (!(cyc_count % 2))	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);
+		else					fpga_modular_mul(&R2, &R2, &R1, &CURVE25519_2P);
+	}
+	//
+	fpga_modular_mul(&R1, &T_X100, &R2, &CURVE25519_2P);
+	//
+	for (cyc_count=0; cyc_count<50; cyc_count++)
+	{	if ((cyc_count % 2))	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);	// inverse order here!
+		else					fpga_modular_mul(&R2, &R2, &R1, &CURVE25519_2P);
+	}
+	//
+	fpga_modular_mul(&R2, &T_X50, &R1, &CURVE25519_2P);
+	//
+	for (cyc_count=0; cyc_count<5; cyc_count++)
+	{	if (!(cyc_count % 2))	fpga_modular_mul(&R1, &R1, &R2, &CURVE25519_2P);
+		else					fpga_modular_mul(&R2, &R2, &R1, &CURVE25519_2P);
+	}
+	//
+	fpga_modular_mul(&R2, &T_1011, A1, &CURVE25519_2P);
+}
+
+
+//------------------------------------------------------------------------------
+// End-of-File
+//------------------------------------------------------------------------------
diff --git a/curve25519/curve25519_fpga_modular.h b/curve25519/curve25519_fpga_modular.h
new file mode 100644
index 0000000..c5f2cb0
--- /dev/null
+++ b/curve25519/curve25519_fpga_modular.h
@@ -0,0 +1,78 @@
+//------------------------------------------------------------------------------
+//
+// curve25519_fpga_modular.h
+// ------------------------------------------
+// Modular arithmetic routines for Curve25519
+//
+// 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.
+//
+//------------------------------------------------------------------------------
+
+
+//------------------------------------------------------------------------------
+// Curve25519 Parameters
+//------------------------------------------------------------------------------
+
+/* modulus (2^255 - 19) */
+#define CURVE25519_1P_INIT		{0x7FFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, \
+								 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFED}
+
+/* double modulus (2^256 - 38) */
+#define CURVE25519_2P_INIT		{0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, \
+								 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFDA}
+
+//------------------------------------------------------------------------------
+// Globals
+//------------------------------------------------------------------------------
+extern FPGA_BUFFER CURVE25519_1P;
+extern FPGA_BUFFER CURVE25519_2P;
+
+
+//------------------------------------------------------------------------------
+// Prototypes
+//------------------------------------------------------------------------------
+void	fpga_modular_init					();
+
+void	fpga_modular_add					(const FPGA_BUFFER *A, const FPGA_BUFFER *B, FPGA_BUFFER *S, const FPGA_BUFFER *N);
+void	fpga_modular_sub					(const FPGA_BUFFER *A, const FPGA_BUFFER *B, FPGA_BUFFER *D, const FPGA_BUFFER *N);
+
+void	fpga_modular_mul					(const FPGA_BUFFER *A, const FPGA_BUFFER *B, FPGA_BUFFER *P, const FPGA_BUFFER *N);
+
+void	fpga_modular_inv_abstract			(const FPGA_BUFFER *A, FPGA_BUFFER *A1, const FPGA_BUFFER *N);
+
+void	fpga_modular_mul_helper_multiply	(const FPGA_BUFFER *A, const FPGA_BUFFER *B, FPGA_WORD_EXTENDED *SI);
+void	fpga_modular_mul_helper_accumulate	(const FPGA_WORD_EXTENDED *SI, FPGA_WORD *C);
+void	fpga_modular_mul_helper_reduce		(const FPGA_WORD *C, FPGA_BUFFER *P, const FPGA_BUFFER *N);
+
+
+//------------------------------------------------------------------------------
+// End-of-File
+//------------------------------------------------------------------------------