| /* Copyright lowRISC contributors. */ |
| /* Licensed under the Apache License, Version 2.0, see LICENSE for details. */ |
| /* SPDX-License-Identifier: Apache-2.0 */ |
| /* |
| * This library contains: |
| * - P-384 specific routines for point addition in projective space |
| * - P-384 domain parameters |
| */ |
| |
| .section .text |
| |
| /** |
| * 384-bit modular multiplication based on Barrett reduction algorithm |
| * optimized for the special modulus of the NIST P-384 curve. |
| * |
| * Returns c = a x b % p. |
| * |
| * Expects: two operands, modulus p and pre-calculated parameter u for barrett |
| * reduction (usually greek mu in literature). u is expected without the |
| * leading 1 at bit 384. u has to be pre-calculated as u = floor(2^768/p). |
| * |
| * This implementation mostly follows the description in the |
| * "Handbook of Applied Cryptography" in Algorithm 14.42. |
| * Differences: |
| * - This implementation incorporates a multiplication before the reduction. |
| * Therefore it expects two operands (a, b) instead of a wider integer x. |
| * - The computation of q2 ignores the MSbs of q1 and u to allow using |
| * a 384x384 bit multiplication. This is compensated later by |
| * individual (conditional) additions. |
| * - The truncations in step 2 of HAC 14.42 in the form of (... mod b^(k+1) ) |
| * are not implemented here and the full register width is used. This |
| * allows to omit computation of r1 (since r1=x) and step 3 of HAC 14.42 |
| * |
| * Flags: Flags have no meaning beyond the scope of this subroutine. |
| * |
| * @param[in] [w11, w10]: a, first operand, max. length 384 bit, a < m. |
| * @param[in] [w17, w16]: b, second operand, max. length 384 bit, b < m. |
| * @param[in] [w13, w12]: p, modulus of P384 i.e.: |
| m = 2^384 - 2^128 - 2^96 + 2^32 - 1. |
| * @param[in] [w15, w14]: u, pre-computed Barrett constant (without u[384]/MSb |
| * of u which is always 1 for the allowed range but |
| * has to be set to 0 here). |
| * @param[in] w31: all-zero. |
| * @param[out] [w17, w16]: c, result, max. length 384 bit. |
| * |
| * Clobbered registers: w10, w11, w16, w17, w18, w19, w20, w21, w22, w23, w24 |
| * Clobbered flag groups: FG0 |
| */ |
| .globl barrett384_p384 |
| barrett384_p384: |
| /* Compute the integer product of the operands x = a * b |
| x = [w18, w22, w21] = a * b = [w11, w10] * [w17, w16] |
| => max. length x: 768 bit */ |
| bn.mulqacc.z w10.0, w16.0, 0 |
| bn.mulqacc w10.0, w16.1, 64 |
| bn.mulqacc.so w21.L, w10.1, w16.0, 64 |
| bn.mulqacc w10.0, w16.2, 0 |
| bn.mulqacc w10.1, w16.1, 0 |
| bn.mulqacc w10.2, w16.0, 0 |
| bn.mulqacc w10.0, w16.3, 64 |
| bn.mulqacc w10.1, w16.2, 64 |
| bn.mulqacc w10.2, w16.1, 64 |
| bn.mulqacc.so w21.U, w10.3, w16.0, 64 |
| bn.mulqacc w10.0, w17.0, 0 |
| bn.mulqacc w10.1, w16.3, 0 |
| bn.mulqacc w10.2, w16.2, 0 |
| bn.mulqacc w10.3, w16.1, 0 |
| bn.mulqacc w11.0, w16.0, 0 |
| bn.mulqacc w10.0, w17.1, 64 |
| bn.mulqacc w10.1, w17.0, 64 |
| bn.mulqacc w10.2, w16.3, 64 |
| bn.mulqacc w10.3, w16.2, 64 |
| bn.mulqacc w11.0, w16.1, 64 |
| bn.mulqacc.so w22.L, w11.1, w16.0, 64 |
| bn.mulqacc w10.1, w17.1, 0 |
| bn.mulqacc w10.2, w17.0, 0 |
| bn.mulqacc w10.3, w16.3, 0 |
| bn.mulqacc w11.0, w16.2, 0 |
| bn.mulqacc w11.1, w16.1, 0 |
| bn.mulqacc w10.2, w17.1, 64 |
| bn.mulqacc w10.3, w17.0, 64 |
| bn.mulqacc w11.0, w16.3, 64 |
| bn.mulqacc.so w22.U, w11.1, w16.2, 64 |
| bn.mulqacc w10.3, w17.1, 0 |
| bn.mulqacc w11.0, w17.0, 0 |
| bn.mulqacc w11.1, w16.3, 0 |
| bn.mulqacc w11.0, w17.1, 64 |
| bn.mulqacc.so w18.L, w11.1, w17.0, 64 |
| bn.mulqacc.so w18.U, w11.1, w17.1, 0 |
| |
| /* Store correction factor to compensate for later neglected MSb of x. |
| x is 768 bit wide and therefore the 383 bit right shifted version q1 |
| (below) contains 385 bit. Bit 384 of q1 is neglected to allow using a |
| 384x384 multiplier. For the MSb of x being set we temporary store u |
| (or zero) here to be used in a later constant time correction of a |
| multiplication with u. Note that this requires the MSb flag being carried |
| over from the multiplication routine. */ |
| bn.sel w23, w14, w31, M |
| bn.sel w24, w15, w31, M |
| |
| /* Compute q1 = x >> 383 |
| q1 = [w11, w10] = [w18, w22, w21] >> 383 = [w18, w21] >> 127 |
| => max length q1: 385 bits */ |
| bn.rshi w11, w31, w18 >> 127 |
| bn.rshi w10, w18, w22 >> 127 |
| |
| /* Compute q2 = q1*u |
| Instead of full q2 (which would be up to 770 bits) we ignore the MSb of u |
| and the MSb of q1 and correct this later. This allows using a 384x384 |
| multiplier. We use the property that u for the modulus of P384 is zero in |
| the bits 383 downto 129 and use a 384x192 multiplication routine. |
| => max. length q2': 513 bit |
| q2' = q1[383:0]*u[128:0] = [w18, w17, w16] = [w11, w10] * [w15, w14] */ |
| |
| /* 576 = 384*192 bit multiplication kernel */ |
| bn.mulqacc.z w10.0, w14.0, 0 |
| bn.mulqacc w10.0, w14.1, 64 |
| bn.mulqacc.so w16.L, w10.1, w14.0, 64 |
| bn.mulqacc w10.0, w14.2, 0 |
| bn.mulqacc w10.1, w14.1, 0 |
| bn.mulqacc w10.2, w14.0, 0 |
| bn.mulqacc w10.1, w14.2, 64 |
| bn.mulqacc w10.2, w14.1, 64 |
| bn.mulqacc.so w16.U, w10.3, w14.0, 64 |
| bn.mulqacc w10.2, w14.2, 0 |
| bn.mulqacc w10.3, w14.1, 0 |
| bn.mulqacc w11.0, w14.0, 0 |
| bn.mulqacc w10.3, w14.2, 64 |
| bn.mulqacc w11.0, w14.1, 64 |
| bn.mulqacc.so w17.L, w11.1, w14.0, 64 |
| bn.mulqacc w11.0, w14.2, 0 |
| bn.mulqacc w11.1, w14.1, 0 |
| bn.mulqacc.so w17.U, w11.1, w14.2, 64 |
| |
| /* w14.3 is always zero here due to structure of Barrett constant */ |
| bn.mulqacc.wo w18, w11.1, w14.3, 64 |
| |
| /* q3 = q2 >> 385 |
| In this step, the compensation for the neglected MSbs of q1 and u is |
| carried out along the way. To add them in the q2 domain, they would have |
| to be left shifted by 384 bit first. To directly add them we first shift |
| q2' by 384 bit to the right, perform the additions, and shift the result |
| another bit to the right. The additions cannot overflow due to leading |
| zeros after shift. |
| q2'' = q2' >> 384 = [w20, w19] = [w18, w17, w16] >> 384 |
| = [w18, w17] >> 128 */ |
| bn.rshi w20, w31, w18 >> 128 |
| bn.rshi w19, w18, w17 >> 128 |
| /* Add q1. This is unconditional since MSb of u is always 1. |
| This cannot overflow due to leading zeros. |
| q2''' = q2'' + q1 = [w20, w19] = [w20, w19] + [w10, w11] */ |
| bn.add w19, w19, w10 |
| bn.addc w20, w20, w11 |
| /* Conditionally add u (without leading 1) in case of MSb of x being set. |
| This is the "real" q2 but shifted by 384 bits to the right. This cannot |
| overflow due to leading zeros. |
| q2'''' = x[767]?q2'''+u[383:0]:q2''' |
| = [w20, w19] + [w24, w23] = q2 >> 384 */ |
| bn.add w19, w19, w23 |
| bn.addc w20, w20, w24 |
| /* finally this gives q3 by shifting the remaining bit to the right |
| q3 = q2 >> 385 = q2'''' >> 1 = [w11, w10] = [w20, w19] >> 1 */ |
| bn.rshi w11, w31, w20 >> 1 |
| bn.rshi w10, w20, w19 >> 1 |
| |
| /* r2 = q3*m[511:0] = [w17, w16] = ([w11, w10] * [w13, w12])[511:0] |
| A 384x384 bit multiplication kernel is used here, hence both q3 and p |
| must not be wider than 384 bit. This is always the case for p. For q3 it |
| is the case if a<p and b<p. |
| The 256 highest bits of the multiplication result are not needed, |
| so we do not compute them. */ |
| bn.mulqacc.z w10.0, w12.0, 0 |
| bn.mulqacc w10.0, w12.1, 64 |
| bn.mulqacc.so w16.L, w10.1, w12.0, 64 |
| bn.mulqacc w10.0, w12.2, 0 |
| bn.mulqacc w10.1, w12.1, 0 |
| bn.mulqacc w10.2, w12.0, 0 |
| bn.mulqacc w10.0, w12.3, 64 |
| bn.mulqacc w10.1, w12.2, 64 |
| bn.mulqacc w10.2, w12.1, 64 |
| bn.mulqacc.so w16.U, w10.3, w12.0, 64 |
| bn.mulqacc w10.0, w13.0, 0 |
| bn.mulqacc w10.1, w12.3, 0 |
| bn.mulqacc w10.2, w12.2, 0 |
| bn.mulqacc w10.3, w12.1, 0 |
| bn.mulqacc w11.0, w12.0, 0 |
| bn.mulqacc w10.0, w13.1, 64 |
| bn.mulqacc w10.1, w13.0, 64 |
| bn.mulqacc w10.2, w12.3, 64 |
| bn.mulqacc w10.3, w12.2, 64 |
| bn.mulqacc w11.0, w12.1, 64 |
| bn.mulqacc.so w17.L, w11.1, w12.0, 64 |
| bn.mulqacc w10.1, w13.1, 0 |
| bn.mulqacc w10.2, w13.0, 0 |
| bn.mulqacc w10.3, w12.3, 0 |
| bn.mulqacc w11.0, w12.2, 0 |
| bn.mulqacc w11.1, w12.1, 0 |
| bn.mulqacc w10.2, w13.1, 64 |
| bn.mulqacc w10.3, w13.0, 64 |
| bn.mulqacc w11.0, w12.3, 64 |
| bn.mulqacc.so w17.U, w11.1, w12.2, 64 |
| |
| /* Compute r = x-r2 = x-q3*p |
| since 0 <= r < 3*p, we only need to consider the lower limbs of x and r2 |
| r[511:0] = [w22, w21] - [w17, w16] */ |
| bn.sub w21, w21, w16 |
| bn.subb w22, w22, w17 |
| |
| /* Barrett algorithm requires subtraction of the modulus at most two times if |
| result is too large. However in the special case of P-384 we need to |
| subtract only once */ |
| bn.sub w16, w21, w12 |
| bn.subb w17, w22, w13 |
| bn.sel w16, w21, w16, C |
| bn.sel w17, w22, w17, C |
| |
| /* return result: c =[w17, w16] = a * b % p. */ |
| ret |
| |
| |
| /** |
| * P-384 point addition in projective space |
| * |
| * returns R = (x_r, y_r, z_r) <= P+Q = (x_p, y_p, z_p) + (x_q, y_q, z_q) |
| * with R, P and Q being valid P-384 curve points |
| * in projective coordinates |
| * |
| * This routine adds two valid P-384 curve points in projective space. |
| * Point addition is performed based on the complete formulas of Bosma and |
| * Lenstra for Weierstrass curves as first published in [1] and |
| * optimized in [2]. |
| * The implemented version follows Algorithm 4 of [2] which is an optimized |
| * variant for Weierstrass curves with domain parameter 'a' set to a=-3. |
| * Numbering of the steps below and naming of symbols follows the |
| * terminology of Algorithm 4 of [2]. |
| * The routine is limited to P-384 curve points due to: |
| * - fixed a=-3 domain parameter |
| * - usage of a P-384 optimized Barrett multiplication kernel |
| * This routine runs in constant time. |
| * |
| * [1] https://doi.org/10.1006/jnth.1995.1088 |
| * [2] https://doi.org/10.1007/978-3-662-49890-3_16 |
| * |
| * @param[in] x22: set to 10, pointer to in reg for Barrett routine |
| * @param[in] x23: set to 11, pointer to in reg for Barrett routine |
| * @param[in] x24: set to 16, pointer to in/out reg for Barrett routine |
| * @param[in] x25: set to 17, pointer to in/out reg for Barrett routine |
| * @param[in] x26: dptr_p_p, dmem pointer to point P in dmem (projective) |
| * @param[in] x27: dptr_q_p, dmem pointer to point Q in dmem (projective) |
| * @param[in] x28: dptr_b, dmem pointer to domain parameter b of P-384 in dmem |
| * @param[in] [w13, w12]: p, modulus of underlying field of P-384 |
| * @param[in] [w15, w14]: u[383:0] lower 384 bit of Barrett constant u for |
| * modulus p |
| * @param[in] w31: all-zero. |
| * @param[out] [w26, w25]: x_r, x-coordinate of resulting point R |
| * @param[out] [w28, w27]: y_r, y-coordinate of resulting point R |
| * @param[out] [w30, w29]: z_r, z-coordinate of resulting point R |
| * |
| * Flags: Flags have no meaning beyond the scope of this subroutine. |
| * |
| * clobbered registers: w0 to w30 |
| * clobbered flag groups: FG0 |
| */ |
| .globl proj_add_p384 |
| proj_add_p384: |
| /* mapping of parameters to symbols of [2] (Algorithm 4): |
| X1 = x_p; Y1 = y_p; Z1 = z_p; X2 = x_q; Y2 = y_q; Z2 = z_q |
| X3 = x_r; Y3 = y_r; Z3 = z_r */ |
| |
| /* 1: [w1, w0] = t0 <= X1*X2 = dmem[x26+0]*dmem[x27+0] */ |
| bn.lid x22, 0(x26) |
| bn.lid x23, 32(x26) |
| bn.lid x24, 0(x27) |
| bn.lid x25, 32(x27) |
| jal x1, barrett384_p384 |
| bn.mov w0, w16 |
| bn.mov w1, w17 |
| |
| /* 2: [w3, w2] = t1 <= Y1*Y2 = dmem[x26+64]*dmem[x27+64] */ |
| bn.lid x22, 64(x26) |
| bn.lid x23, 96(x26) |
| bn.lid x24, 64(x27) |
| bn.lid x25, 96(x27) |
| jal x1, barrett384_p384 |
| bn.mov w2, w16 |
| bn.mov w3, w17 |
| |
| /* 3: [w5, w4] = t2 <= Z1*Z2 = dmem[x26+128]*dmem[x27+128] */ |
| bn.lid x22, 128(x26) |
| bn.lid x23, 160(x26) |
| bn.lid x24, 128(x27) |
| bn.lid x25, 160(x27) |
| jal x1, barrett384_p384 |
| bn.mov w4, w16 |
| bn.mov w5, w17 |
| |
| /* 4: [w7, w6] = t3 <= X1+Y1 = dmem[x26+0]+dmem[x26+64] */ |
| bn.lid x22, 0(x26) |
| bn.lid x23, 32(x26) |
| bn.lid x24, 64(x26) |
| bn.lid x25, 96(x26) |
| bn.add w16, w10, w16 |
| bn.addc w17, w11, w17 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w6, w16 |
| bn.mov w7, w17 |
| |
| /* 5: [w9, w8] = t4 <= X2+Y2 = dmem[x27+0]+dmem[x27+64] */ |
| bn.lid x22, 0(x27) |
| bn.lid x23, 32(x27) |
| bn.lid x24, 64(x27) |
| bn.lid x25, 96(x27) |
| bn.add w16, w10, w16 |
| bn.addc w17, w11, w17 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w8, w16 |
| bn.mov w9, w17 |
| |
| /* 6: [w7, w6] = t3 <= t3*t4 = [w7, w6]*[w9, w8] */ |
| bn.mov w10, w6 |
| bn.mov w11, w7 |
| bn.mov w16, w8 |
| bn.mov w17, w9 |
| jal x1, barrett384_p384 |
| bn.mov w6, w16 |
| bn.mov w7, w17 |
| |
| /* 7: [w9, w8] = t4 <= t0+t1 = [w1, w0]+[w3, w2] */ |
| bn.add w16, w0, w2 |
| bn.addc w17, w1, w3 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w8, w16 |
| bn.mov w9, w17 |
| |
| /* 8: [w7, w6] = t3 <= t3-t4 = [w7, w6]-[w9, w8] */ |
| bn.sub w16, w6, w8 |
| bn.subb w17, w7, w9 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w6, w16 |
| bn.mov w7, w17 |
| |
| /* 9: [w9, w8] = t4 <= Y1+Z1 = dmem[x26+64]+dmem[x26+128] */ |
| bn.lid x22, 64(x26) |
| bn.lid x23, 96(x26) |
| bn.lid x24, 128(x26) |
| bn.lid x25, 160(x26) |
| bn.add w16, w10, w16 |
| bn.addc w17, w11, w17 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w8, w16 |
| bn.mov w9, w17 |
| |
| /* 10: [w26, w25] = X3 <= Y2+Z2 = dmem[x27+64]+dmem[x27+128] */ |
| bn.lid x22, 64(x27) |
| bn.lid x23, 96(x27) |
| bn.lid x24, 128(x27) |
| bn.lid x25, 160(x27) |
| bn.add w16, w10, w16 |
| bn.addc w17, w11, w17 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 11: [w9, w8] = t4 <= t4*X3 = [w9, w8]*[w26, w25] */ |
| bn.mov w10, w8 |
| bn.mov w11, w9 |
| bn.mov w16, w25 |
| bn.mov w17, w26 |
| jal x1, barrett384_p384 |
| bn.mov w8, w16 |
| bn.mov w9, w17 |
| |
| /* 12: [w26, w25] = X3 <= t1+t2 = [w3, w2]+[w5, w4] */ |
| bn.add w16, w2, w4 |
| bn.addc w17, w3, w5 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 13: [w9, w8] = t4 <= t4-X3 = [w9, w8]-[w26, w25] */ |
| bn.sub w16, w8, w25 |
| bn.subb w17, w9, w26 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w8, w16 |
| bn.mov w9, w17 |
| |
| /* 14: [w26, w25] = X3 <= X1+Z1 = dmem[x26+0]+dmem[x26+128] */ |
| bn.lid x22, 0(x26) |
| bn.lid x23, 32(x26) |
| bn.lid x24, 128(x26) |
| bn.lid x25, 160(x26) |
| bn.add w16, w10, w16 |
| bn.addc w17, w11, w17 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 15: [w28, w27] = Y3 <= X2+Z2 = dmem[x27+0]+dmem[x27+128] */ |
| bn.lid x22, 0(x27) |
| bn.lid x23, 32(x27) |
| bn.lid x24, 128(x27) |
| bn.lid x25, 160(x27) |
| bn.add w16, w10, w16 |
| bn.addc w17, w11, w17 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 16: [w26, w25] = X3 <= X3*Y3 = [w26, w25]*[w28, w27] */ |
| bn.mov w10, w25 |
| bn.mov w11, w26 |
| bn.mov w16, w27 |
| bn.mov w17, w28 |
| jal x1, barrett384_p384 |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 17: [w28, w27] = Y3 <= t0+t2 = [w1, w0]+[w5, w4] */ |
| bn.add w16, w0, w4 |
| bn.addc w17, w1, w5 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 18: [w28, w27] = Y3 <= X3-Y3 = [w26, w25]-[w28, w27] */ |
| bn.sub w16, w25, w27 |
| bn.subb w17, w26, w28 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 19: [w30, w29] = Z3 <= b*t2 = dmem[x28+0]*[w5, w4] */ |
| bn.lid x22, 0(x28) |
| bn.lid x23, 32(x28) |
| bn.mov w16, w4 |
| bn.mov w17, w5 |
| jal x1, barrett384_p384 |
| bn.mov w29, w16 |
| bn.mov w30, w17 |
| |
| /* 20: [w26, w25] = X3 <= Y3-Z3 = [w28, w27]-[w30, w29] */ |
| bn.sub w16, w27, w29 |
| bn.subb w17, w28, w30 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 21: [w30, w29] = Z3 <= X3+X3 = [w26, w25]+[w26, w25] */ |
| bn.add w16, w25, w25 |
| bn.addc w17, w26, w26 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w29, w16 |
| bn.mov w30, w17 |
| |
| /* 22: [w26, w25] = X3 <= X3+Z3 = [w26, w25]+[w30, w29] */ |
| bn.add w16, w25, w29 |
| bn.addc w17, w26, w30 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 23: [w30, w29] = Z3 <= t1-X3 = [w3, w2]-[w26, w25] */ |
| bn.sub w16, w2, w25 |
| bn.subb w17, w3, w26 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w29, w16 |
| bn.mov w30, w17 |
| |
| /* 24: [w26, w25] = X3 <= t1+X3 = [w3, w2]+[w26, w25] */ |
| bn.add w16, w2, w25 |
| bn.addc w17, w3, w26 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 25: [w28, w27] = Y3 <= b*Y3 = dmem[x28+0]*[w28, w27] */ |
| bn.lid x22, 0(x28) |
| bn.lid x23, 32(x28) |
| bn.mov w16, w27 |
| bn.mov w17, w28 |
| jal x1, barrett384_p384 |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 26: [w3, w2] = t1 <= t2+t2 = [w5, w4]+[w5, w4] */ |
| bn.add w16, w4, w4 |
| bn.addc w17, w5, w5 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w2, w16 |
| bn.mov w3, w17 |
| |
| /* 27: [w5, w4] = t2 <= t1+t2 = [w3, w2]+[w5, w4] */ |
| bn.add w16, w2, w4 |
| bn.addc w17, w3, w5 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w4, w16 |
| bn.mov w5, w17 |
| |
| /* 28: [w28, w27] = Y3 <= Y3-t2 = [w28, w27]-[w5, w4] */ |
| bn.sub w16, w27, w4 |
| bn.subb w17, w28, w5 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 29: [w28, w27] = Y3 <= Y3-t0 = [w28, w27]-[w1, w0] */ |
| bn.sub w16, w27, w0 |
| bn.subb w17, w28, w1 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 30: [w3, w2] = t1 <= Y3+Y3 = [w28, w27]+[w28, w27] */ |
| bn.add w16, w27, w27 |
| bn.addc w17, w28, w28 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w2, w16 |
| bn.mov w3, w17 |
| |
| /* 31: [w28, w27] = Y3 <= t1+Y3 = [w3, w2]+[w28, w27] */ |
| bn.add w16, w2, w27 |
| bn.addc w17, w3, w28 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 32: [w3, w2] = t1 <= t0+t0 = [w1, w0]+[w1, w0] */ |
| bn.add w16, w0, w0 |
| bn.addc w17, w1, w1 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w2, w16 |
| bn.mov w3, w17 |
| |
| /* 33: [w1, w0] = t0 <= t1+t0 = [w3, w2]+[w1, w0] */ |
| bn.add w16, w2, w0 |
| bn.addc w17, w3, w1 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w0, w16 |
| bn.mov w1, w17 |
| |
| /* 34: [w1, w0] = t0 <= t0-t2 = [w1, w0]-[w5, w4] */ |
| bn.sub w16, w0, w4 |
| bn.subb w17, w1, w5 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w0, w16 |
| bn.mov w1, w17 |
| |
| /* 35: [w3, w2] = t1 <= t4*Y3 = [w9, w8]*[w28, w27] */ |
| bn.mov w10, w8 |
| bn.mov w11, w9 |
| bn.mov w16, w27 |
| bn.mov w17, w28 |
| jal x1, barrett384_p384 |
| bn.mov w2, w16 |
| bn.mov w3, w17 |
| |
| /* 36: [w5, w4] = t2 <= t0*Y3 = [w1, w0]*[w28, w27] */ |
| bn.mov w10, w0 |
| bn.mov w11, w1 |
| bn.mov w16, w27 |
| bn.mov w17, w28 |
| jal x1, barrett384_p384 |
| bn.mov w4, w16 |
| bn.mov w5, w17 |
| |
| /* 37: [w28, w27] = Y3 <= X3*Z3 = [w26, w25]*[w30, w29] */ |
| bn.mov w10, w25 |
| bn.mov w11, w26 |
| bn.mov w16, w29 |
| bn.mov w17, w30 |
| jal x1, barrett384_p384 |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 38: [w28, w27] = Y3 <= Y3+t2 = [w28, w27]+[w5, w4] */ |
| bn.add w16, w27, w4 |
| bn.addc w17, w28, w5 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w27, w16 |
| bn.mov w28, w17 |
| |
| /* 39: [w26, w25] = X3 <= t3*X3 = [w7, w6]*[w26, w25] */ |
| bn.mov w10, w6 |
| bn.mov w11, w7 |
| bn.mov w16, w25 |
| bn.mov w17, w26 |
| jal x1, barrett384_p384 |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 40: [w26, w25] = X3 <= X3-t1 = [w26, w25]-[w3, w2] */ |
| bn.sub w16, w25, w2 |
| bn.subb w17, w26, w3 |
| bn.add w10, w16, w12 |
| bn.addc w11, w17, w13 |
| bn.sel w16, w10, w16, C |
| bn.sel w17, w11, w17, C |
| bn.mov w25, w16 |
| bn.mov w26, w17 |
| |
| /* 41: [w30, w29] = Z3 <= t4*Z3 = [w9, w8]*[w30, w29] */ |
| bn.mov w10, w8 |
| bn.mov w11, w9 |
| bn.mov w16, w29 |
| bn.mov w17, w30 |
| jal x1, barrett384_p384 |
| bn.mov w29, w16 |
| bn.mov w30, w17 |
| |
| /* 42: [w3, w2] = t1 <= t3*t0 = [w7, w6]*[w1, w0] */ |
| bn.mov w10, w6 |
| bn.mov w11, w7 |
| bn.mov w16, w0 |
| bn.mov w17, w1 |
| jal x1, barrett384_p384 |
| bn.mov w2, w16 |
| bn.mov w3, w17 |
| |
| /* 43: [w30, w29] = Z3 <= Z3+t1 = [w30, w29]+[w3, w2] */ |
| bn.add w16, w29, w2 |
| bn.addc w17, w30, w3 |
| bn.sub w10, w16, w12 |
| bn.subb w11, w17, w13 |
| bn.sel w16, w16, w10, C |
| bn.sel w17, w17, w11, C |
| bn.mov w29, w16 |
| bn.mov w30, w17 |
| |
| ret |
| |
| |
| .section .data |
| |
| /* P-384 domain parameter b */ |
| .globl p384_b |
| p384_b: |
| .word 0xd3ec2aef |
| .word 0x2a85c8ed |
| .word 0x8a2ed19d |
| .word 0xc656398d |
| .word 0x5013875a |
| .word 0x0314088f |
| .word 0xfe814112 |
| .word 0x181d9c6e |
| .word 0xe3f82d19 |
| .word 0x988e056b |
| .word 0xe23ee7e4 |
| .word 0xb3312fa7 |
| .zero 16 |
| |
| /* P-384 domain parameter p (modulus) */ |
| .globl p384_p |
| p384_p: |
| .word 0xffffffff |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0xffffffff |
| .word 0xfffffffe |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .zero 16 |
| |
| /* barrett constant u for modulus p */ |
| .globl p384_u_p |
| p384_u_p: |
| .word 0x00000001 |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0x00000000 |
| .word 0x00000001 |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .zero 16 |
| |
| /* P-384 domain parameter n (order of base point) */ |
| .globl p384_n |
| p384_n: |
| .word 0xccc52973 |
| .word 0xecec196a |
| .word 0x48b0a77a |
| .word 0x581a0db2 |
| .word 0xf4372ddf |
| .word 0xc7634d81 |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .word 0xffffffff |
| .zero 16 |
| |
| /* barrett constant u for n */ |
| .globl p384_u_n |
| p384_u_n: |
| .word 0x333ad68d |
| .word 0x1313e695 |
| .word 0xb74f5885 |
| .word 0xa7e5f24d |
| .word 0x0bc8d220 |
| .word 0x389cb27e |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .word 0x00000000 |
| .zero 16 |
| |
| /* P-384 basepoint G affine x-coordinate */ |
| .globl p384_gx |
| p384_gx: |
| .word 0x72760ab7 |
| .word 0x3a545e38 |
| .word 0xbf55296c |
| .word 0x5502f25d |
| .word 0x82542a38 |
| .word 0x59f741e0 |
| .word 0x8ba79b98 |
| .word 0x6e1d3b62 |
| .word 0xf320ad74 |
| .word 0x8eb1c71e |
| .word 0xbe8b0537 |
| .word 0xaa87ca22 |
| .zero 16 |
| |
| /* P-384 basepoint G affine y-coordinate */ |
| .globl p384_gy |
| p384_gy: |
| .word 0x90ea0e5f |
| .word 0x7a431d7c |
| .word 0x1d7e819d |
| .word 0x0a60b1ce |
| .word 0xb5f0b8c0 |
| .word 0xe9da3113 |
| .word 0x289a147c |
| .word 0xf8f41dbd |
| .word 0x9292dc29 |
| .word 0x5d9e98bf |
| .word 0x96262c6f |
| .word 0x3617de4a |
| .zero 16 |
