| /* Copyright lowRISC Contributors. |
| * Copyright 2016 The Chromium OS Authors. All rights reserved. |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE.dcrypto file. |
| * |
| * Derived from code in |
| * https://chromium.googlesource.com/chromiumos/platform/ec/+/refs/heads/cr50_stab/chip/g/dcrypto/dcrypto_bn.c |
| */ |
| |
| |
| .text |
| .globl modexp_var |
| |
| /** |
| * Precomputation of a constant m0' for Montgomery modular arithmetic |
| * |
| * Word-wise Montgomery modular arithmetic requires a quantity m0' to be |
| * precomputed once per modulus M. m0' is the negative of the |
| * modular multiplicative inverse of the lowest limb m0 of the modulus M, in |
| * the field GF(2^w), where w is the number of bits per limb. w is set to 256 |
| * in this subroutine. |
| * |
| * Returns: m0' = -m0^(-1) mod 2^256 |
| * with m0 being the lowest limb of the modulus M |
| * |
| * This subroutine implements the Dusse-Kaliski method for computing the |
| * multiplicative modular inverse when the modulus is of the form 2^k. |
| * [Dus] DOI https://doi.org/10.1007/3-540-46877-3_21 section 3.2 |
| * (Algorithm "Modular Inverse" on p. 235) |
| * |
| * Flags: When leaving this subroutine, flags of FG0 depend on a |
| * the final subtraction and can be used if needed. |
| * FG0.M, FG0.L, FG0.Z depend directly on the value of the result m0'. |
| * FG0.C is always set. |
| * FG1 is not modified in this subroutine. |
| * |
| * @param[in] x16: dptr_m, pointer to modulus M in dmem |
| * @param[in] x17: dptr_m0inv, pointer to dmem location to store m0inv |
| * @param[in] w31: all-zero. |
| * |
| * clobbered registers: x8, w0, w1, w28, w29 |
| * clobbered flag groups: FG0 |
| */ |
| compute_m0inv: |
| |
| /* load lowest limb of modulus to w28 */ |
| li x8, 28 |
| bn.lid x8, 0(x16) |
| |
| /* w0 keeps track of loop iterations in one-hot encoding, i.e. |
| w0 = 2^i in the loop body below and initialized here with w0 = 1 |
| It is used for both the comparison in step 4 of [Dus] and the |
| addition in step 6 of [Dus] */ |
| bn.xor w0, w0, w0 |
| bn.addi w0, w0, 1 |
| |
| /* according to [Dus] the result variable y is initialized with 1 */ |
| /* w29 = y_0 = 1 */ |
| bn.mov w29, w0 |
| |
| /* iterate over all 256 bits of m0. |
| i refers to the loop cycle 0..255 in the loop body below. */ |
| loopi 256, 13 |
| |
| /* y_i <= m*y_{i-1] */ |
| bn.mulqacc.z w28.0, w29.0, 0 |
| bn.mulqacc w28.1, w29.0, 64 |
| bn.mulqacc.so w1.L, w28.0, w29.1, 64 |
| bn.mulqacc w28.2, w29.0, 0 |
| bn.mulqacc w28.1, w29.1, 0 |
| bn.mulqacc w28.0, w29.2, 0 |
| bn.mulqacc w28.3, w29.0, 64 |
| bn.mulqacc w28.2, w29.1, 64 |
| bn.mulqacc w28.1, w29.2, 64 |
| bn.mulqacc.so w1.U, w28.0, w29.3, 64 |
| |
| /* This checks if w1 = y_i = m0*y_(i-1) < 2^(i-1) mod 2^i |
| Due to the mathematical properties it can be shown that y_i at this point, |
| is either 1 or (10..0..01)_(i). Therefore, just probing the i_th bit is |
| the same as the full compare. */ |
| bn.and w1, w1, w0 |
| |
| /* Compute |
| y_i=w29 <= w1=m0*y_(i-1) < 2^(i-1) mod 2^i y_i ? : y_{i-1}+2^i : y_{i-1} |
| there cannot be overlaps => or'ing is as good as adding */ |
| bn.or w29, w29, w1 |
| |
| /* double w0 (w0 <= w0 << 1) i.e. w0=2^i */ |
| bn.add w0, w0, w0 |
| |
| /* finally, compute m0' (negative of inverse) |
| w29 = m0' = -(m0^-1) mod 2^256 = -y_255 = 0 - y_255 = w31 - w29 */ |
| bn.sub w29, w31, w29 |
| |
| /* Store Montgomery constant in dmem */ |
| li x8, 29 |
| bn.sid x8, 0(x17) |
| |
| ret |
| |
| |
| /** |
| * Variable time multi-limb bigint compare |
| * |
| * Compares two bigints (a, b) located in regfile (a) and dmem (b). |
| * |
| * Flags: When leaving this subroutine, flags of FG1 depend on the comparison |
| * result of the highest unequal limba, or, if all limbs are equal on |
| * those of the lowest limbs. |
| * |
| * @param[in] x10: constant 3, used as pointer to w3 |
| * @param[in] x11: constant 2, used as pointer to w2 |
| * @param[in] x8: rptr_a, pointer to lowest limb of a in regfile |
| * @param[in] x9: rptr_a_h, pointer to highest limb of a in regfile |
| * @param[in] x17: dptr_b_h, pointer to highest limb of b in dmem |
| * @param[out] x3, bit 0: (b > a), equals FG1.C |
| * @param[out] x3, bit 3: (a == b), equals FG1.Z |
| * |
| * clobbered registers: x3, x5, x7, x9, x17, x19, w2, w3 |
| * clobbered flag groups: FG1 |
| */ |
| cmp_dmem_reg_buf: |
| |
| addi x19, x17, 0 |
| addi x7, x9, 0 |
| |
| cmp_loop: |
| |
| /* load limbs from dmem and regfile: w2 <= a[i]; w3 <= b[i] */ |
| bn.lid x10, 0(x19) |
| bn.movr x11, x7 |
| |
| /* compare limbs and store comparison result in x3 */ |
| bn.cmp w2, w3, FG1 |
| csrrs x3, 0x7c1, x0 |
| |
| /* leave loop if lowest limb was reached */ |
| beq x8, x7, cmp_end |
| |
| /* reduce limb pointers */ |
| addi x19, x19, -32 |
| addi x7, x7, -1 |
| |
| /* if limbs were equal (FG1.Z == 1), compare next lower limb */ |
| andi x5, x3, 8 |
| bne x5, x0, cmp_loop |
| |
| cmp_end: |
| nop |
| ret |
| |
| |
| /** |
| * Compute square of Montgomery modulus |
| * |
| * Returns RR = R^2 mod M |
| * with M being the Modulus of length 256..4096 bit |
| * R = 2^(256*N), N is the number of limbs per bigint |
| * |
| * The squared Montgomery modulus (RR) is needed to transform bigints to and |
| * from the Montgomery domain. |
| * |
| * RR is computed in this subroutine by iteratively doubling and reduction. |
| * |
| * Flags: The states of both FG0 and FG1 depend on intermediate values and are |
| * not usable after return. |
| * |
| * @param[in] x16: dptr_n, pointer to first limb of modulus in dmem |
| * @param[in] x18: dptr_rr: dmem pointer to first limb of output buffer for RR |
| * @param[in] x30: N, number of limbs |
| * @param[in] x31: N-1, number of limbs minus 1 |
| * @param[in] w31: all-zero |
| * @param[out] dmem[x18+N*32:x18]: computed RR |
| * |
| * clobbered registers: x3, x4, x5, x8, x9, x10, x11, x16, x18, x22, x24 |
| * w0, w2, w3, w4, w5 to w20 depending on N |
| * clobbered flag groups: FG0, FG1 |
| */ |
| compute_rr: |
| /* save pointer to modulus x22 <= dptr_m = x16 */ |
| addi x22, x16, 0 |
| |
| /* x17 = dptr_m + (N-1)*32 points to highest limb of modulus in dmem */ |
| slli x17, x31, 5 |
| add x17, x22, x17 |
| |
| li x8, 5 |
| |
| /* x9 = rptr_buf_h <= rptr_buf + N-1 */ |
| add x9, x31, x8 |
| |
| /* compute full length of current bigint size in bits |
| N*w = x24 <= N*256 = N*2^8 = x30 << 8 */ |
| slli x24, x30, 8 |
| |
| /* reg pointers to current limb of buffer and modulus |
| /* x10 = rptr_limb_mod = &w3 */ |
| li x10, 3 |
| /* x11 = rptr_limb_buf = &w2 */ |
| li x11, 2 |
| |
| |
| /* clear flags */ |
| bn.add w31, w31, w31 |
| /* init buffer with R - m |
| buf = w[5+N-1:5] <= R - m = unsigned(0 - m) */ |
| |
| loop x30, 3 |
| bn.lid x10, 0(x16++) |
| bn.subb w3, w31, w3 |
| bn.movr x8++, x10 |
| |
| /* Compute R^2 mod M = R*2^(N*w) mod M. |
| R^2 mod M can be computed by performing N*w duplications of R, |
| interleaved with conditional subtractions of modulus. Modulus is |
| subtracted if dobiling result is greater than modulus, i.e. either |
| there was a final carry at the end of the doubling procedure or the lower |
| N*w bits of the result are greater than the modulus. */ |
| loop x24, 27 |
| |
| /* Duplicate the intermediate bigint result. This can overflow such that |
| bit 2^(N*w) (represented by the carry flag after final loop cycle) |
| is set. */ |
| li x8, 5 |
| bn.add w31, w31, w31, FG1 |
| loop x30, 3 |
| bn.movr x11, x8 |
| bn.addc w2, w2, w2, FG1 |
| bn.movr x8++, x11 |
| |
| /* In case of final carry in doubling procedure substract modulus */ |
| /* Jump to 'rr_sub' if FG1.C == 1 */ |
| csrrs x3, 0x7c1, x0 |
| andi x3, x3, 1 |
| bne x3, x0, rr_sub |
| |
| /* In case there was no final carry in the addition, we have to check |
| wether the N*w sized bigint w/o carry is greater than the modulus. */ |
| bn.lid x10, 0(x17) |
| bn.movr x11, x9 |
| bn.cmp w2, w3, FG1 |
| csrrs x3, 0x7c1, x0 |
| |
| /* If the highest limbs of buf and mod are equal we have to run a |
| multi-limb comparison. This is very unlikely to happen. If this |
| verification is not used with keys where this situation occurs, the |
| following 3 lines and (if not needed elsewhere) the compare routine |
| can be removed. */ |
| andi x5, x3, 8 |
| beq x5, x0, rr_cmp |
| jal x1, cmp_dmem_reg_buf |
| |
| /* if m > r: jump to end_loop (without subtraction) */ |
| rr_cmp: |
| andi x5, x3, 1 |
| bne x5, x0, rr_end_loop |
| |
| /* subtract modulus from current buffer |
| buf = w[5+N-1:5] <= buf - m */ |
| rr_sub: |
| li x8, 5 |
| addi x16, x22, 0 |
| bn.add w31, w31, w31, FG1 |
| loop x30, 4 |
| bn.lid x10, 0(x16++) |
| bn.movr x11, x8 |
| bn.subb w3, w2, w3, FG1 |
| bn.movr x8++, x10 |
| |
| rr_end_loop: |
| nop |
| |
| /* store computed RR in dmem |
| [dmem[dptr_RR+N*32-1]:dmem[dptr_RR]] <= buf = w[5+N-1:5] */ |
| li x8, 5 |
| loop x30, 2 |
| bn.sid x8, 0(x18++) |
| addi x8, x8, 1 |
| |
| ret |
| |
| |
| /** |
| * Unrolled 512=256x256 bit multiplication. |
| * |
| * Returns c = a x b. |
| * |
| * Flags: No flags are set in this subroutine |
| * |
| * @param[in] w30: a, first operand |
| * @param[in] w25: b, second operand |
| * @param[out] [w26, w27]: c, result |
| * |
| * clobbered registers: w26, w27 |
| * clobbered flag groups: none |
| */ |
| mul256_w30xw25: |
| bn.mulqacc.z w30.0, w25.0, 0 |
| bn.mulqacc w30.1, w25.0, 64 |
| bn.mulqacc.so w27.L, w30.0, w25.1, 64 |
| bn.mulqacc w30.2, w25.0, 0 |
| bn.mulqacc w30.1, w25.1, 0 |
| bn.mulqacc w30.0, w25.2, 0 |
| bn.mulqacc w30.3, w25.0, 64 |
| bn.mulqacc w30.2, w25.1, 64 |
| bn.mulqacc w30.1, w25.2, 64 |
| bn.mulqacc.so w27.U, w30.0, w25.3, 64 |
| bn.mulqacc w30.3, w25.1, 0 |
| bn.mulqacc w30.2, w25.2, 0 |
| bn.mulqacc w30.1, w25.3, 0 |
| bn.mulqacc w30.3, w25.2, 64 |
| bn.mulqacc.so w26.L, w30.2, w25.3, 64 |
| bn.mulqacc.so w26.U, w30.3, w25.3, 0 |
| |
| ret |
| |
| |
| /** |
| * Unrolled 512=256x256 bit multiplication. |
| * |
| * Returns c = a x b. |
| * |
| * Flags: No flags are set in this subroutine |
| * |
| * @param[in] w30: a, first operand |
| * @param[in] w2: b, second operand |
| * @param[out] [w26, w27]: c, result |
| * |
| * clobbered registers: w26, w27 |
| * clobbered flag groups: none |
| */ |
| mul256_w30xw2: |
| bn.mulqacc.z w30.0, w2.0, 0 |
| bn.mulqacc w30.1, w2.0, 64 |
| bn.mulqacc.so w27.L, w30.0, w2.1, 64 |
| bn.mulqacc w30.2, w2.0, 0 |
| bn.mulqacc w30.1, w2.1, 0 |
| bn.mulqacc w30.0, w2.2, 0 |
| bn.mulqacc w30.3, w2.0, 64 |
| bn.mulqacc w30.2, w2.1, 64 |
| bn.mulqacc w30.1, w2.2, 64 |
| bn.mulqacc.so w27.U, w30.0, w2.3, 64 |
| bn.mulqacc w30.3, w2.1, 0 |
| bn.mulqacc w30.2, w2.2, 0 |
| bn.mulqacc w30.1, w2.3, 0 |
| bn.mulqacc w30.3, w2.2, 64 |
| bn.mulqacc.so w26.L, w30.2, w2.3, 64 |
| bn.mulqacc.so w26.U, w30.3, w2.3, 0 |
| |
| ret |
| |
| |
| /** |
| * Main loop body for variable-time Montgomery Modular Multiplication |
| * |
| * Returns: C <= (C + A*b_i + M*m0'*(C[0] + A[0]*b_i))/(2^WLEN) mod R |
| * |
| * This implements the main loop body for the Montgomery Modular Multiplication |
| * as well as the conditional subtraction. See e.g. Handbook of Applied |
| * Cryptography (HAC) 14.36 (steps 2.1 and 2.2) and step 3. |
| * This subroutine has to be called for every iteration of the loop in step 2 |
| * of HAC 14.36, i.e. once per limb of operand B (x in HAC notation). The limb |
| * is supplied via w2. In the comments below, the index i refers to the |
| * i_th call to this subroutine within one full Montgomery Multiplication run. |
| * Step 3 of HAC 14.36 is replaced by the approach to perform the conditional |
| * subtraction when the intermediate result is larger than R instead of m. See |
| * e.g. https://eprint.iacr.org/2017/1057 section 2.4.2 for a justification. |
| * This does not omit the conditional subtraction. |
| * Variable names of HAC are mapped as follows to the ones used in the |
| * this library: x=B, y=A, A=C, b=2^WLEN, m=M, R=R, m' = m0', n=N. |
| * |
| * Flags: The states of both FG0 and FG1 depend on intermediate values and are |
| * not usable after return. |
| * |
| * @param[in] x16: dmem pointer to first limb of modulus M |
| * @param[in] x19: dmem pointer to first limb operand A |
| * @param[in] x31: N-1, number of limbs minus one |
| * @param[in] w2: current limb of operand B, b_i |
| * @param[in] w3: Montgomery constant m0' |
| * @param[in] w31: all-zero |
| * @param[in] [w[4+N-1]:w4] intermediate result A |
| * @param[out] [w[4+N-1]:w4] intermediate result A |
| * |
| * clobbered registers: x8, x10, x12, x13, x16, x19 |
| * w24, w25, w26, w27, w28, w29, w30, w4 to w[4+N-1] |
| * clobbered Flag Groups: FG0, FG1 |
| */ |
| mont_loop: |
| /* save pointer to modulus */ |
| addi x22, x16, 0 |
| |
| /* pointers to temp. wregs */ |
| li x12, 30 |
| li x13, 24 |
| |
| /* buffer read pointer */ |
| li x8, 4 |
| |
| /* buffer write pointer */ |
| li x10, 4 |
| |
| /* load 1st limb of input y (operand a): w30 = y[0] */ |
| bn.lid x12, 0(x19++) |
| |
| /* This is x_i*y_0 in step 2.1 of HAC 14.36 */ |
| /* [w26, w27] = w30*w2 = y[0]*x_i */ |
| jal x1, mul256_w30xw2 |
| |
| /* w24 = w4 = A[0] */ |
| bn.movr x13, x8++ |
| |
| /* add A[0]: [w29, w30] = [w26, w27] + w24 = y[0]*x_i + A[0] */ |
| bn.add w30, w27, w24 |
| |
| /* this serves as c_xy in the first cycle of the loop below */ |
| bn.addc w29, w26, w31 |
| |
| /* w25 = w3 = m0' */ |
| bn.mov w25, w3 |
| |
| /* multiply by m0', this concludes Step 2.1 of HAC 14.36 */ |
| /* [_, u_i] = [w26, w27] = w30*w25 = (y[0]*x_i + A[0])*m0'*/ |
| jal x1, mul256_w30xw25 |
| |
| |
| /* With the computation of u_i, the compuations for a cycle 0 for the loop |
| below are already partly done. The following instructions (until the |
| start of the loop) implement the remaining steps, such that cylce 0 can be |
| omitted in the loop */ |
| |
| /* [_, u_i] = [w28, w25] = [w26, w27] */ |
| bn.mov w25, w27 |
| bn.mov w28, w26 |
| |
| /* w24 = w30 = y[0]*x_i + A[0] mod b */ |
| bn.mov w24, w30 |
| |
| /* load first limb of modulus: w30 = m[0] */ |
| bn.lid x12, 0(x16++) |
| |
| /* [w26, w27] = w30*w25 = m[0]*u_i*/ |
| jal x1, mul256_w30xw25 |
| |
| /* [w28, w27] = [w26, w27] + w24 = m[0]*u_i + (y[0]*x_i + A[0] mod b) */ |
| bn.add w27, w27, w24 |
| /* this serves as c_m in the first cycle of the loop below */ |
| bn.addc w28, w26, w31 |
| |
| |
| /* This loop implements step 2.2 of HAC 14.36 with a word-by-word approach. |
| The loop body is subdivided into two steps. Each step performs one |
| multiplication and subsequently adds two WLEN sized words to the |
| 2WLEN-sized result, such that there are no overflows at the end of each |
| step- |
| Two carry words are required between the cycles. Those are c_xy and c_m. |
| Assume that the variable j runs from 1 to N-1 in the explanations below. |
| A cycle 0 is omitted, since the results from the computations above are |
| re-used */ |
| loop x31, 14 |
| /* Step 1: First multiplication takes a limb of each of the operands and |
| computes the product. The carry word from the previous cycle c_xy and |
| the j_th limb of the buffer A, A[j] arre added to the multiplication |
| result. |
| |
| /* load limb of y (operand a) and mult. with x_i: [w26, w27] <= y[j]*x_i */ |
| bn.lid x12, 0(x19++) |
| jal x1, mul256_w30xw2 |
| /* add limb of buffer: [w26, w27] <= [w26,w27] + w24 = y[j]*x_i + A[j] */ |
| bn.movr x13, x8++ |
| bn.add w27, w27, w24 |
| bn.addc w26, w26, w31 |
| /* add carry word from previous cycle: |
| [c_xy, a_tmp] = [w29, w24] <= [w26,w27] + w29 = y[j]*x_i + A[j] + c_xy*/ |
| bn.add w24, w27, w29 |
| bn.addc w29, w26, w31 |
| |
| |
| /* Step 2: Second multiplication computes the product of a limb m[j] of |
| the modulus with u_i. The 2nd carry word from the previous loop cycle |
| c_m and the lower word a_tmp of the result of Step 1 are added. */ |
| |
| /* load limb m[j] of modulus and multiply with u_i: |
| [w26, w27] = w30*w25 = m[j+1]*u_i */ |
| bn.lid x12, 0(x16++) |
| jal x1, mul256_w30xw25 |
| /* add result from first step |
| [w26, w27] <= [w26,w27] + w24 = m[j+1]*u_i + a_tmp */ |
| bn.add w27, w27, w24 |
| bn.addc w26, w26, w31 |
| /* [c_m, A[j]] = [w28, w24] = m[j+1]*u_i + a_tmp + c_m */ |
| bn.add w24, w27, w28, FG1 |
| /* store at w[4+j] = A[j-1] |
| This includes the reduction by 2^WLEN = 2^b in step 2.2 of HAC 14.36 */ |
| bn.movr x10++, x13 |
| bn.addc w28, w26, w31, FG1 |
| |
| |
| /* Most significant limb of A is sum of the carry words of last loop cycle |
| A[N-1] = w24 <= w29 + w28 = c_xy + c_m */ |
| bn.addc w24, w29, w28, FG1 |
| bn.movr x10++, x13 |
| |
| /* No subtracion if carry bit of addition of carry words not set. */ |
| csrrs x2, 0x7c1, x0 |
| andi x2, x2, 1 |
| beq x2, x0, mont_loop_no_sub |
| |
| /* limb-wise subtraction */ |
| li x12, 30 |
| li x13, 24 |
| addi x16, x22, 0 |
| li x8, 4 |
| loop x30, 4 |
| bn.lid x13, 0(x16++) |
| bn.movr x12, x8 |
| bn.subb w24, w30, w24 |
| bn.movr x8++, x13 |
| |
| |
| mont_loop_no_sub: |
| |
| /* restore pointers */ |
| li x8, 4 |
| li x10, 4 |
| |
| ret |
| |
| |
| /** |
| * Variable-time Montgomery Modular Multiplication |
| * |
| * Returns: C = montmul(A,B) = A*B*R^(-1) mod M |
| * |
| * This implements the limb-by-limb interleadved Montgomory Modular |
| * Multiplication Algorithm. This is only a wrapper around the main loop body. |
| * For algorithmic implementation details see the mont_loop subroutine. |
| * |
| * Flags: The states of both FG0 and FG1 depend on intermediate values and are |
| * not usable after return. |
| * |
| * @param[in] x16: dptr_M, dmem pointer to first limb of modulus M |
| * @param[in] x17: dptr_m0d, dmem pointer to Montgomery Constant m0' |
| * @param[in] x19: dptr_a, dmem pointer to first limb of operand A |
| * @param[in] x20: dptr_b, dmem pointer to first limb of operand B |
| * @param[in] w31: all-zero |
| * @param[in] x30: N, number of limbs |
| * @param[in] x31: N-1, number of limbs minus one |
| * @param[in] x9: pointer to temp reg, must be set to 3 |
| * @param[in] x10: pointer to temp reg, must be set to 4 |
| * @param[in] x11: pointer to temp reg, must be set to 2 |
| * @param[out] [w[4+N-1]:w4]: result C |
| * |
| * clobbered registers: x5, x6, x7, x8, x10, x12, x13, x17, x19, x20, x21 |
| * w2, w3, w24 to w30, w4 to w[4+N-1] |
| * clobbered Flag Groups: FG0, FG1 |
| */ |
| montmul: |
| /* load Montgomery constant: w3 = dmem[x17] = dmem[dptr_m0d] = m0' */ |
| bn.lid x9, 0(x17) |
| |
| /* init regfile bigint buffer with zeros */ |
| bn.mov w2, w31 |
| loop x30, 1 |
| bn.movr x10++, x11 |
| |
| /* iterate over limbs of operand B */ |
| loop x30, 8 |
| |
| /* load limb of operand b */ |
| bn.lid x11, 0(x20++) |
| |
| /* save some regs */ |
| addi x6, x16, 0 |
| addi x7, x19, 0 |
| |
| /* Main loop body of Montgomory Multiplication algorithm */ |
| jal x1, mont_loop |
| |
| /* restore regs */ |
| addi x16, x6, 0 |
| addi x19, x7, 0 |
| |
| /* restore pointers */ |
| li x8, 4 |
| li x10, 4 |
| |
| ret |
| |
| |
| /** |
| * Variable time modular exponentiation with exponent of the form e=2^e'+1 |
| * |
| * Returns: C = modexp(A,2^e'+1) = A^(2^e'+1) mod M |
| * |
| * This implements the square and multiply algorithm for exponents of the |
| * form e=2^e'+1. Thus, the routine can be used for exponentiation with Fermat |
| * primes (by setting e'=16 for e=F4=65537 and e'=1 for e=F0=3). |
| * |
| * The squared Montgomery modulus RR and the Montgomery constant m0' have to |
| * be precomputed and provided at the appropriate locations in dmem. |
| * |
| * Flags: The states of both FG0 and FG1 depend on intermediate values and are |
| * not usable after return. |
| * |
| * The base bignum A is expected in the input buffer, the result C is written |
| * to the output buffer. Note, that the content of the input buffer is |
| * modified during execution. |
| * |
| * @param[in] dmem[0] e': number for exponent derivation (e = 2^e+1) |
| * @param[in] dmem[4] N: Number of limbs per bignum |
| * @param[in] dmem[8] dptr_m0inv: pointer to m0' in dmem |
| * @param[in] dmem[12] dptr_rr: pointer to RR in dmem |
| * @param[in] dmem[16] dptr_m: pointer to first limb of modulus M in dmem |
| * @param[in] dmem[20] dptr_sig: pointer to signature in dmem |
| * @param[in] dmem[28] dptr_out: pointer to recovered message |
| * |
| * clobbered registers: x2, x5 to x13, x16 to x21, x29, x30, x31 |
| w2, w3, w24 to w31, w4 to w[4+N-1] |
| * clobbered Flag Groups: FG0, FG1 |
| */ |
| modexp_var: |
| /* prepare all-zero reg */ |
| bn.xor w31, w31, w31 |
| |
| /* load number of limbs (x30 <= N; x31 = N-1 <= N1) */ |
| lw x30, 4(x0) |
| addi x31, x30, -1 |
| |
| /* load pointer to modulus (x16 <= dptr_m) */ |
| lw x16, 16(x0) |
| |
| /* load pointer to m0' (x17 <= dptr_m0inv)*/ |
| lw x17, 8(x0) |
| |
| /* load pointer to RR (x18 <= dptr_rr) */ |
| lw x18, 12(x0) |
| |
| /* load exponent (x29 <= e') */ |
| lw x29, 0(x0) |
| |
| /* Compute Montgomery constants and reload clobbered pointers */ |
| jal x1, compute_m0inv |
| jal x1, compute_rr |
| lw x16, 16(x0) |
| lw x17, 8(x0) |
| lw x18, 12(x0) |
| |
| /* prepare pointers to temp regs */ |
| li x8, 4 |
| li x9, 3 |
| li x10, 4 |
| li x11, 2 |
| |
| /* convert signature to Montgomery domain |
| out_buf = *x28 = *dmem[28] |
| <= montmul(*x19, *x20) = montmul(*dptr_sig, *dptr_rr) = sig*R mod M */ |
| lw x19, 20(x0) |
| lw x20, 12(x0) |
| lw x21, 28(x0) |
| jal x1, montmul |
| /* store result in dmem starting at dmem[dptr_out] */ |
| loop x30, 2 |
| bn.sid x8, 0(x21++) |
| addi x8, x8, 1 |
| |
| /* 16 consecutive Montgomery squares on the outbut buffer, i.e. after loop: |
| out_buf <= out_buf^65536*R mod M */ |
| loop x29, 8 |
| /* out_buf = *x28 = *dmem[28] |
| <= montmul(*x28, *x20) = montmul(*dptr_out, *dptr_out) |
| = out_buf^2*R mod M */ |
| lw x19, 28(x0) |
| lw x20, 28(x0) |
| lw x21, 28(x0) |
| jal x1, montmul |
| /* Store result in dmem starting at dmem[dptr_out] */ |
| loop x30, 2 |
| bn.sid x8, 0(x21++) |
| addi x8, x8, 1 |
| nop |
| |
| /* final multiplication and conversion of result from Montgomery domain |
| out_buf = *x28 = *dmem[28] |
| <= montmul(*x28, *x20) = montmul(*dptr_sig, *dptr_out) |
| = out_buf*sig/R mod M = sig^65537 mod M */ |
| lw x19, 20(x0) |
| lw x20, 28(x0) |
| lw x21, 28(x0) |
| jal x1, montmul |
| |
| /* Final conditional subtraction of modulus if mod >= out_buf. This could |
| be done in variable time, but for the sake of reduced code we use a loop |
| with N cycles. */ |
| bn.add w31, w31, w31 |
| li x17, 16 |
| loop x30, 4 |
| bn.movr x11, x8++ |
| bn.lid x9, 0(x16++) |
| bn.subb w2, w2, w3 |
| bn.movr x17++, x11 |
| csrrs x2, 0x7c0, x0 |
| /* TODO: currently we subtract the modulus if out_buf == M. This should |
| never happen in an RSA context. We could catch this and raise an |
| alert. */ |
| andi x2, x2, 1 |
| li x8, 4 |
| bne x2, x0, no_sub |
| li x8, 16 |
| no_sub: |
| |
| /* store result in dmem starting at dmem[dptr_out] */ |
| lw x21, 28(x0) |
| loop x30, 2 |
| bn.sid x8, 0(x21++) |
| addi x8, x8, 1 |
| |
| ret |
