| // Copyright (c) 2013 The Chromium Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| /* |
| * curve25519-donna: Curve25519 elliptic curve, public key function |
| * |
| * http://code.google.com/p/curve25519-donna/ |
| * |
| * Adam Langley <agl@imperialviolet.org> |
| * |
| * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to> |
| * |
| * More information about curve25519 can be found here |
| * http://cr.yp.to/ecdh.html |
| * |
| * djb's sample implementation of curve25519 is written in a special assembly |
| * language called qhasm and uses the floating point registers. |
| * |
| * This is, almost, a clean room reimplementation from the curve25519 paper. It |
| * uses many of the tricks described therein. Only the crecip function is taken |
| * from the sample implementation. |
| */ |
| |
| #include <string.h> |
| #include <stdint.h> |
| |
| typedef uint8_t u8; |
| typedef int32_t s32; |
| typedef int64_t limb; |
| |
| /* Field element representation: |
| * |
| * Field elements are written as an array of signed, 64-bit limbs, least |
| * significant first. The value of the field element is: |
| * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ... |
| * |
| * i.e. the limbs are 26, 25, 26, 25, ... bits wide. |
| */ |
| |
| /* Sum two numbers: output += in */ |
| static void fsum(limb *output, const limb *in) { |
| unsigned i; |
| for (i = 0; i < 10; i += 2) { |
| output[0+i] = (output[0+i] + in[0+i]); |
| output[1+i] = (output[1+i] + in[1+i]); |
| } |
| } |
| |
| /* Find the difference of two numbers: output = in - output |
| * (note the order of the arguments!) |
| */ |
| static void fdifference(limb *output, const limb *in) { |
| unsigned i; |
| for (i = 0; i < 10; ++i) { |
| output[i] = (in[i] - output[i]); |
| } |
| } |
| |
| /* Multiply a number my a scalar: output = in * scalar */ |
| static void fscalar_product(limb *output, const limb *in, const limb scalar) { |
| unsigned i; |
| for (i = 0; i < 10; ++i) { |
| output[i] = in[i] * scalar; |
| } |
| } |
| |
| /* Multiply two numbers: output = in2 * in |
| * |
| * output must be distinct to both inputs. The inputs are reduced coefficient |
| * form, the output is not. |
| */ |
| static void fproduct(limb *output, const limb *in2, const limb *in) { |
| output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]); |
| output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) + |
| ((limb) ((s32) in2[1])) * ((s32) in[0]); |
| output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) + |
| ((limb) ((s32) in2[0])) * ((s32) in[2]) + |
| ((limb) ((s32) in2[2])) * ((s32) in[0]); |
| output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) + |
| ((limb) ((s32) in2[2])) * ((s32) in[1]) + |
| ((limb) ((s32) in2[0])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[3])) * ((s32) in[0]); |
| output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) + |
| 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[3])) * ((s32) in[1])) + |
| ((limb) ((s32) in2[0])) * ((s32) in[4]) + |
| ((limb) ((s32) in2[4])) * ((s32) in[0]); |
| output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[3])) * ((s32) in[2]) + |
| ((limb) ((s32) in2[1])) * ((s32) in[4]) + |
| ((limb) ((s32) in2[4])) * ((s32) in[1]) + |
| ((limb) ((s32) in2[0])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[5])) * ((s32) in[0]); |
| output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[1])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[5])) * ((s32) in[1])) + |
| ((limb) ((s32) in2[2])) * ((s32) in[4]) + |
| ((limb) ((s32) in2[4])) * ((s32) in[2]) + |
| ((limb) ((s32) in2[0])) * ((s32) in[6]) + |
| ((limb) ((s32) in2[6])) * ((s32) in[0]); |
| output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) + |
| ((limb) ((s32) in2[4])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[2])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[5])) * ((s32) in[2]) + |
| ((limb) ((s32) in2[1])) * ((s32) in[6]) + |
| ((limb) ((s32) in2[6])) * ((s32) in[1]) + |
| ((limb) ((s32) in2[0])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[7])) * ((s32) in[0]); |
| output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) + |
| 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[5])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[1])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[7])) * ((s32) in[1])) + |
| ((limb) ((s32) in2[2])) * ((s32) in[6]) + |
| ((limb) ((s32) in2[6])) * ((s32) in[2]) + |
| ((limb) ((s32) in2[0])) * ((s32) in[8]) + |
| ((limb) ((s32) in2[8])) * ((s32) in[0]); |
| output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[5])) * ((s32) in[4]) + |
| ((limb) ((s32) in2[3])) * ((s32) in[6]) + |
| ((limb) ((s32) in2[6])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[2])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[7])) * ((s32) in[2]) + |
| ((limb) ((s32) in2[1])) * ((s32) in[8]) + |
| ((limb) ((s32) in2[8])) * ((s32) in[1]) + |
| ((limb) ((s32) in2[0])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[0]); |
| output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[3])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[7])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[1])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[1])) + |
| ((limb) ((s32) in2[4])) * ((s32) in[6]) + |
| ((limb) ((s32) in2[6])) * ((s32) in[4]) + |
| ((limb) ((s32) in2[2])) * ((s32) in[8]) + |
| ((limb) ((s32) in2[8])) * ((s32) in[2]); |
| output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) + |
| ((limb) ((s32) in2[6])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[4])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[7])) * ((s32) in[4]) + |
| ((limb) ((s32) in2[3])) * ((s32) in[8]) + |
| ((limb) ((s32) in2[8])) * ((s32) in[3]) + |
| ((limb) ((s32) in2[2])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[2]); |
| output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) + |
| 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[7])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[3])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[3])) + |
| ((limb) ((s32) in2[4])) * ((s32) in[8]) + |
| ((limb) ((s32) in2[8])) * ((s32) in[4]); |
| output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[7])) * ((s32) in[6]) + |
| ((limb) ((s32) in2[5])) * ((s32) in[8]) + |
| ((limb) ((s32) in2[8])) * ((s32) in[5]) + |
| ((limb) ((s32) in2[4])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[4]); |
| output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[5])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[5])) + |
| ((limb) ((s32) in2[6])) * ((s32) in[8]) + |
| ((limb) ((s32) in2[8])) * ((s32) in[6]); |
| output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) + |
| ((limb) ((s32) in2[8])) * ((s32) in[7]) + |
| ((limb) ((s32) in2[6])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[6]); |
| output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) + |
| 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[7])); |
| output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) + |
| ((limb) ((s32) in2[9])) * ((s32) in[8]); |
| output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]); |
| } |
| |
| /* Reduce a long form to a short form by taking the input mod 2^255 - 19. */ |
| static void freduce_degree(limb *output) { |
| /* Each of these shifts and adds ends up multiplying the value by 19. */ |
| output[8] += output[18] << 4; |
| output[8] += output[18] << 1; |
| output[8] += output[18]; |
| output[7] += output[17] << 4; |
| output[7] += output[17] << 1; |
| output[7] += output[17]; |
| output[6] += output[16] << 4; |
| output[6] += output[16] << 1; |
| output[6] += output[16]; |
| output[5] += output[15] << 4; |
| output[5] += output[15] << 1; |
| output[5] += output[15]; |
| output[4] += output[14] << 4; |
| output[4] += output[14] << 1; |
| output[4] += output[14]; |
| output[3] += output[13] << 4; |
| output[3] += output[13] << 1; |
| output[3] += output[13]; |
| output[2] += output[12] << 4; |
| output[2] += output[12] << 1; |
| output[2] += output[12]; |
| output[1] += output[11] << 4; |
| output[1] += output[11] << 1; |
| output[1] += output[11]; |
| output[0] += output[10] << 4; |
| output[0] += output[10] << 1; |
| output[0] += output[10]; |
| } |
| |
| /* Reduce all coefficients of the short form input so that |x| < 2^26. |
| * |
| * On entry: |output[i]| < 2^62 |
| */ |
| static void freduce_coefficients(limb *output) { |
| unsigned i; |
| do { |
| output[10] = 0; |
| |
| for (i = 0; i < 10; i += 2) { |
| limb over = output[i] / 0x4000000l; |
| output[i+1] += over; |
| output[i] -= over * 0x4000000l; |
| |
| over = output[i+1] / 0x2000000; |
| output[i+2] += over; |
| output[i+1] -= over * 0x2000000; |
| } |
| output[0] += 19 * output[10]; |
| } while (output[10]); |
| } |
| |
| /* A helpful wrapper around fproduct: output = in * in2. |
| * |
| * output must be distinct to both inputs. The output is reduced degree and |
| * reduced coefficient. |
| */ |
| static void |
| fmul(limb *output, const limb *in, const limb *in2) { |
| limb t[19]; |
| fproduct(t, in, in2); |
| freduce_degree(t); |
| freduce_coefficients(t); |
| memcpy(output, t, sizeof(limb) * 10); |
| } |
| |
| static void fsquare_inner(limb *output, const limb *in) { |
| output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]); |
| output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]); |
| output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) + |
| ((limb) ((s32) in[0])) * ((s32) in[2])); |
| output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) + |
| ((limb) ((s32) in[0])) * ((s32) in[3])); |
| output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) + |
| 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) + |
| 2 * ((limb) ((s32) in[0])) * ((s32) in[4]); |
| output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) + |
| ((limb) ((s32) in[1])) * ((s32) in[4]) + |
| ((limb) ((s32) in[0])) * ((s32) in[5])); |
| output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) + |
| ((limb) ((s32) in[2])) * ((s32) in[4]) + |
| ((limb) ((s32) in[0])) * ((s32) in[6]) + |
| 2 * ((limb) ((s32) in[1])) * ((s32) in[5])); |
| output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) + |
| ((limb) ((s32) in[2])) * ((s32) in[5]) + |
| ((limb) ((s32) in[1])) * ((s32) in[6]) + |
| ((limb) ((s32) in[0])) * ((s32) in[7])); |
| output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) + |
| 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) + |
| ((limb) ((s32) in[0])) * ((s32) in[8]) + |
| 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) + |
| ((limb) ((s32) in[3])) * ((s32) in[5]))); |
| output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) + |
| ((limb) ((s32) in[3])) * ((s32) in[6]) + |
| ((limb) ((s32) in[2])) * ((s32) in[7]) + |
| ((limb) ((s32) in[1])) * ((s32) in[8]) + |
| ((limb) ((s32) in[0])) * ((s32) in[9])); |
| output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) + |
| ((limb) ((s32) in[4])) * ((s32) in[6]) + |
| ((limb) ((s32) in[2])) * ((s32) in[8]) + |
| 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) + |
| ((limb) ((s32) in[1])) * ((s32) in[9]))); |
| output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) + |
| ((limb) ((s32) in[4])) * ((s32) in[7]) + |
| ((limb) ((s32) in[3])) * ((s32) in[8]) + |
| ((limb) ((s32) in[2])) * ((s32) in[9])); |
| output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) + |
| 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) + |
| 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) + |
| ((limb) ((s32) in[3])) * ((s32) in[9]))); |
| output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) + |
| ((limb) ((s32) in[5])) * ((s32) in[8]) + |
| ((limb) ((s32) in[4])) * ((s32) in[9])); |
| output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) + |
| ((limb) ((s32) in[6])) * ((s32) in[8]) + |
| 2 * ((limb) ((s32) in[5])) * ((s32) in[9])); |
| output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) + |
| ((limb) ((s32) in[6])) * ((s32) in[9])); |
| output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) + |
| 4 * ((limb) ((s32) in[7])) * ((s32) in[9]); |
| output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]); |
| output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]); |
| } |
| |
| static void |
| fsquare(limb *output, const limb *in) { |
| limb t[19]; |
| fsquare_inner(t, in); |
| freduce_degree(t); |
| freduce_coefficients(t); |
| memcpy(output, t, sizeof(limb) * 10); |
| } |
| |
| /* Take a little-endian, 32-byte number and expand it into polynomial form */ |
| static void |
| fexpand(limb *output, const u8 *input) { |
| #define F(n,start,shift,mask) \ |
| output[n] = ((((limb) input[start + 0]) | \ |
| ((limb) input[start + 1]) << 8 | \ |
| ((limb) input[start + 2]) << 16 | \ |
| ((limb) input[start + 3]) << 24) >> shift) & mask; |
| F(0, 0, 0, 0x3ffffff); |
| F(1, 3, 2, 0x1ffffff); |
| F(2, 6, 3, 0x3ffffff); |
| F(3, 9, 5, 0x1ffffff); |
| F(4, 12, 6, 0x3ffffff); |
| F(5, 16, 0, 0x1ffffff); |
| F(6, 19, 1, 0x3ffffff); |
| F(7, 22, 3, 0x1ffffff); |
| F(8, 25, 4, 0x3ffffff); |
| F(9, 28, 6, 0x1ffffff); |
| #undef F |
| } |
| |
| /* Take a fully reduced polynomial form number and contract it into a |
| * little-endian, 32-byte array |
| */ |
| static void |
| fcontract(u8 *output, limb *input) { |
| int i; |
| |
| do { |
| for (i = 0; i < 9; ++i) { |
| if ((i & 1) == 1) { |
| while (input[i] < 0) { |
| input[i] += 0x2000000; |
| input[i + 1]--; |
| } |
| } else { |
| while (input[i] < 0) { |
| input[i] += 0x4000000; |
| input[i + 1]--; |
| } |
| } |
| } |
| while (input[9] < 0) { |
| input[9] += 0x2000000; |
| input[0] -= 19; |
| } |
| } while (input[0] < 0); |
| |
| input[1] <<= 2; |
| input[2] <<= 3; |
| input[3] <<= 5; |
| input[4] <<= 6; |
| input[6] <<= 1; |
| input[7] <<= 3; |
| input[8] <<= 4; |
| input[9] <<= 6; |
| #define F(i, s) \ |
| output[s+0] |= input[i] & 0xff; \ |
| output[s+1] = (input[i] >> 8) & 0xff; \ |
| output[s+2] = (input[i] >> 16) & 0xff; \ |
| output[s+3] = (input[i] >> 24) & 0xff; |
| output[0] = 0; |
| output[16] = 0; |
| F(0,0); |
| F(1,3); |
| F(2,6); |
| F(3,9); |
| F(4,12); |
| F(5,16); |
| F(6,19); |
| F(7,22); |
| F(8,25); |
| F(9,28); |
| #undef F |
| } |
| |
| /* Input: Q, Q', Q-Q' |
| * Output: 2Q, Q+Q' |
| * |
| * x2 z3: long form |
| * x3 z3: long form |
| * x z: short form, destroyed |
| * xprime zprime: short form, destroyed |
| * qmqp: short form, preserved |
| */ |
| static void fmonty(limb *x2, limb *z2, /* output 2Q */ |
| limb *x3, limb *z3, /* output Q + Q' */ |
| limb *x, limb *z, /* input Q */ |
| limb *xprime, limb *zprime, /* input Q' */ |
| const limb *qmqp /* input Q - Q' */) { |
| limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], |
| zzprime[19], zzzprime[19], xxxprime[19]; |
| |
| memcpy(origx, x, 10 * sizeof(limb)); |
| fsum(x, z); |
| fdifference(z, origx); // does x - z |
| |
| memcpy(origxprime, xprime, sizeof(limb) * 10); |
| fsum(xprime, zprime); |
| fdifference(zprime, origxprime); |
| fproduct(xxprime, xprime, z); |
| fproduct(zzprime, x, zprime); |
| freduce_degree(xxprime); |
| freduce_coefficients(xxprime); |
| freduce_degree(zzprime); |
| freduce_coefficients(zzprime); |
| memcpy(origxprime, xxprime, sizeof(limb) * 10); |
| fsum(xxprime, zzprime); |
| fdifference(zzprime, origxprime); |
| fsquare(xxxprime, xxprime); |
| fsquare(zzzprime, zzprime); |
| fproduct(zzprime, zzzprime, qmqp); |
| freduce_degree(zzprime); |
| freduce_coefficients(zzprime); |
| memcpy(x3, xxxprime, sizeof(limb) * 10); |
| memcpy(z3, zzprime, sizeof(limb) * 10); |
| |
| fsquare(xx, x); |
| fsquare(zz, z); |
| fproduct(x2, xx, zz); |
| freduce_degree(x2); |
| freduce_coefficients(x2); |
| fdifference(zz, xx); // does zz = xx - zz |
| memset(zzz + 10, 0, sizeof(limb) * 9); |
| fscalar_product(zzz, zz, 121665); |
| freduce_degree(zzz); |
| freduce_coefficients(zzz); |
| fsum(zzz, xx); |
| fproduct(z2, zz, zzz); |
| freduce_degree(z2); |
| freduce_coefficients(z2); |
| } |
| |
| /* Calculates nQ where Q is the x-coordinate of a point on the curve |
| * |
| * resultx/resultz: the x coordinate of the resulting curve point (short form) |
| * n: a little endian, 32-byte number |
| * q: a point of the curve (short form) |
| */ |
| static void |
| cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) { |
| limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0}; |
| limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; |
| limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1}; |
| limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; |
| |
| unsigned i, j; |
| |
| memcpy(nqpqx, q, sizeof(limb) * 10); |
| |
| for (i = 0; i < 32; ++i) { |
| u8 byte = n[31 - i]; |
| for (j = 0; j < 8; ++j) { |
| if (byte & 0x80) { |
| fmonty(nqpqx2, nqpqz2, |
| nqx2, nqz2, |
| nqpqx, nqpqz, |
| nqx, nqz, |
| q); |
| } else { |
| fmonty(nqx2, nqz2, |
| nqpqx2, nqpqz2, |
| nqx, nqz, |
| nqpqx, nqpqz, |
| q); |
| } |
| |
| t = nqx; |
| nqx = nqx2; |
| nqx2 = t; |
| t = nqz; |
| nqz = nqz2; |
| nqz2 = t; |
| t = nqpqx; |
| nqpqx = nqpqx2; |
| nqpqx2 = t; |
| t = nqpqz; |
| nqpqz = nqpqz2; |
| nqpqz2 = t; |
| |
| byte <<= 1; |
| } |
| } |
| |
| memcpy(resultx, nqx, sizeof(limb) * 10); |
| memcpy(resultz, nqz, sizeof(limb) * 10); |
| } |
| |
| // ----------------------------------------------------------------------------- |
| // Shamelessly copied from djb's code |
| // ----------------------------------------------------------------------------- |
| static void |
| crecip(limb *out, const limb *z) { |
| limb z2[10]; |
| limb z9[10]; |
| limb z11[10]; |
| limb z2_5_0[10]; |
| limb z2_10_0[10]; |
| limb z2_20_0[10]; |
| limb z2_50_0[10]; |
| limb z2_100_0[10]; |
| limb t0[10]; |
| limb t1[10]; |
| int i; |
| |
| /* 2 */ fsquare(z2,z); |
| /* 4 */ fsquare(t1,z2); |
| /* 8 */ fsquare(t0,t1); |
| /* 9 */ fmul(z9,t0,z); |
| /* 11 */ fmul(z11,z9,z2); |
| /* 22 */ fsquare(t0,z11); |
| /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9); |
| |
| /* 2^6 - 2^1 */ fsquare(t0,z2_5_0); |
| /* 2^7 - 2^2 */ fsquare(t1,t0); |
| /* 2^8 - 2^3 */ fsquare(t0,t1); |
| /* 2^9 - 2^4 */ fsquare(t1,t0); |
| /* 2^10 - 2^5 */ fsquare(t0,t1); |
| /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0); |
| |
| /* 2^11 - 2^1 */ fsquare(t0,z2_10_0); |
| /* 2^12 - 2^2 */ fsquare(t1,t0); |
| /* 2^20 - 2^10 */ |
| for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
| /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0); |
| |
| /* 2^21 - 2^1 */ fsquare(t0,z2_20_0); |
| /* 2^22 - 2^2 */ fsquare(t1,t0); |
| /* 2^40 - 2^20 */ |
| for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
| /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0); |
| |
| /* 2^41 - 2^1 */ fsquare(t1,t0); |
| /* 2^42 - 2^2 */ fsquare(t0,t1); |
| /* 2^50 - 2^10 */ |
| for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } |
| /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0); |
| |
| /* 2^51 - 2^1 */ fsquare(t0,z2_50_0); |
| /* 2^52 - 2^2 */ fsquare(t1,t0); |
| /* 2^100 - 2^50 */ |
| for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
| /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0); |
| |
| /* 2^101 - 2^1 */ fsquare(t1,z2_100_0); |
| /* 2^102 - 2^2 */ fsquare(t0,t1); |
| /* 2^200 - 2^100 */ |
| for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } |
| /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0); |
| |
| /* 2^201 - 2^1 */ fsquare(t0,t1); |
| /* 2^202 - 2^2 */ fsquare(t1,t0); |
| /* 2^250 - 2^50 */ |
| for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
| /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0); |
| |
| /* 2^251 - 2^1 */ fsquare(t1,t0); |
| /* 2^252 - 2^2 */ fsquare(t0,t1); |
| /* 2^253 - 2^3 */ fsquare(t1,t0); |
| /* 2^254 - 2^4 */ fsquare(t0,t1); |
| /* 2^255 - 2^5 */ fsquare(t1,t0); |
| /* 2^255 - 21 */ fmul(out,t1,z11); |
| } |
| |
| int |
| curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) { |
| limb bp[10], x[10], z[10], zmone[10]; |
| uint8_t e[32]; |
| int i; |
| |
| for (i = 0; i < 32; ++i) e[i] = secret[i]; |
| e[0] &= 248; |
| e[31] &= 127; |
| e[31] |= 64; |
| |
| fexpand(bp, basepoint); |
| cmult(x, z, e, bp); |
| crecip(zmone, z); |
| fmul(z, x, zmone); |
| fcontract(mypublic, z); |
| return 0; |
| } |
