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core/cortex-m0/curve25519: Integrate fast curve25519 implementation

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- Move generic implementation to curve25519-generic.o
- Always use optimized version on cortex-m0.

- Rename .s files to .S, remove unnecessary lines in assembly files.
- Rename crypto_scalarmult_curve25519 to x25519_scalar_mult to match
  the signature provided by the generic implementation.
- Replace some handcoded memcpy with function calls
- Remove unnecessary "volatile" specifications in the code.

BRANCH=none
BUG=b:62813194
TEST=To test old implementation only:
        - Increase CONFIG_RO_SIZE to 60kb
        - Increase console stack size to 2048
     make BOARD=hammer PROJECT=x25519 TEST_BUILD=y
     ./util/flash_ec --board=hammer --image=build/hammer/x25519.bin
     EC console: runtest, taskinfo
     => Used to takes ~4'17" to run (X25519 duration 256347 us).
        1496/2048 stack size usage in CONSOLE task
     => Now takes ~1'25" to run (X25519 duration 84520 us)
        732/2048 stack size usage in CONSOLE task
TEST=In test/x25519.c, uncomment #define TEST_X25519_1M_ITERATIONS
     make BOARD=hammer PROJECT=x25519 TEST_BUILD=y
     ./util/flash_ec --board=hammer --image=build/hammer/x25519.bin
     EC console: runtest, wait ~23 hours, test passes.
TEST=- Define CONFIG_CURVE25519_CORTEXM0 (next patch)
     makes newsizes
     build/hammer/RW/ec.RW.flat shrank by 1888 bytes: (52208 to 50320)

Change-Id: Icce38d3c32f431a85ac0f951cf34456b490dc665
Reviewed-on: https://chromium-review.googlesource.com/540962
Commit-Ready: Nicolas Boichat <drinkcat@chromium.org>
Tested-by: Nicolas Boichat <drinkcat@chromium.org>
Reviewed-by: Nicolas Boichat <drinkcat@chromium.org>
This commit is contained in:
Nicolas Boichat
2017-06-22 10:34:39 +08:00
committed by chrome-bot
parent 136a80e113
commit edc668ea6c
10 changed files with 858 additions and 1012 deletions
Download Patch File Download Diff File Expand all files Collapse all files

3
common/build.mk
View File

@@ -45,6 +45,9 @@ common-$(CONFIG_COMMON_RUNTIME)+=hooks.o main.o system.o
common-$(CONFIG_COMMON_TIMER)+=timer.o
common-$(CONFIG_CRC8)+= crc8.o
common-$(CONFIG_CURVE25519)+=curve25519.o
ifneq ($(CORE),cortex-m0)
common-$(CONFIG_CURVE25519)+=curve25519-generic.o
endif
common-$(CONFIG_DEVICE_EVENT)+=device_event.o
common-$(CONFIG_DEVICE_STATE)+=device_state.o
common-$(CONFIG_DPTF)+=dptf.o

821
common/curve25519-generic.c Normal file
View File

@@ -0,0 +1,821 @@
/* Copyright (c) 2015, Google Inc.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
* 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as
* public domain but this file has the ISC license just to keep licencing
* simple.
*
* The field functions are shared by Ed25519 and X25519 where possible. */
#include "curve25519.h"
#include "util.h"
/*
* fe means field element. Here the field is \Z/(2^255-19). An element t,
* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
* context.
*/
typedef int32_t fe[10];
static const int64_t kBottom25Bits = INT64_C(0x1ffffff);
static const int64_t kBottom26Bits = INT64_C(0x3ffffff);
static const int64_t kTop39Bits = INT64_C(0xfffffffffe000000);
static const int64_t kTop38Bits = INT64_C(0xfffffffffc000000);
static uint64_t load_3(const uint8_t *in) {
uint64_t result;
result = (uint64_t)in[0];
result |= ((uint64_t)in[1]) << 8;
result |= ((uint64_t)in[2]) << 16;
return result;
}
static uint64_t load_4(const uint8_t *in) {
uint64_t result;
result = (uint64_t)in[0];
result |= ((uint64_t)in[1]) << 8;
result |= ((uint64_t)in[2]) << 16;
result |= ((uint64_t)in[3]) << 24;
return result;
}
static void fe_frombytes(fe h, const uint8_t *s) {
/* Ignores top bit of h. */
int64_t h0 = load_4(s);
int64_t h1 = load_3(s + 4) << 6;
int64_t h2 = load_3(s + 7) << 5;
int64_t h3 = load_3(s + 10) << 3;
int64_t h4 = load_3(s + 13) << 2;
int64_t h5 = load_4(s + 16);
int64_t h6 = load_3(s + 20) << 7;
int64_t h7 = load_3(s + 23) << 5;
int64_t h8 = load_3(s + 26) << 4;
int64_t h9 = (load_3(s + 29) & 8388607) << 2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
/* Preconditions:
* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*
* Write p=2^255-19; q=floor(h/p).
* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
*
* Proof:
* Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
* Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
*
* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
* Then 0<y<1.
*
* Write r=h-pq.
* Have 0<=r<=p-1=2^255-20.
* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
*
* Write x=r+19(2^-255)r+y.
* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
*
* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
static void fe_tobytes(uint8_t *s, const fe h) {
int32_t h0 = h[0];
int32_t h1 = h[1];
int32_t h2 = h[2];
int32_t h3 = h[3];
int32_t h4 = h[4];
int32_t h5 = h[5];
int32_t h6 = h[6];
int32_t h7 = h[7];
int32_t h8 = h[8];
int32_t h9 = h[9];
int32_t q;
q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
q = (h0 + q) >> 26;
q = (h1 + q) >> 25;
q = (h2 + q) >> 26;
q = (h3 + q) >> 25;
q = (h4 + q) >> 26;
q = (h5 + q) >> 25;
q = (h6 + q) >> 26;
q = (h7 + q) >> 25;
q = (h8 + q) >> 26;
q = (h9 + q) >> 25;
/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
h0 += 19 * q;
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
h1 += h0 >> 26; h0 &= kBottom26Bits;
h2 += h1 >> 25; h1 &= kBottom25Bits;
h3 += h2 >> 26; h2 &= kBottom26Bits;
h4 += h3 >> 25; h3 &= kBottom25Bits;
h5 += h4 >> 26; h4 &= kBottom26Bits;
h6 += h5 >> 25; h5 &= kBottom25Bits;
h7 += h6 >> 26; h6 &= kBottom26Bits;
h8 += h7 >> 25; h7 &= kBottom25Bits;
h9 += h8 >> 26; h8 &= kBottom26Bits;
h9 &= kBottom25Bits;
/* h10 = carry9 */
/* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
* Have h0+...+2^230 h9 between 0 and 2^255-1;
* evidently 2^255 h10-2^255 q = 0.
* Goal: Output h0+...+2^230 h9. */
s[0] = h0 >> 0;
s[1] = h0 >> 8;
s[2] = h0 >> 16;
s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
s[4] = h1 >> 6;
s[5] = h1 >> 14;
s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
s[7] = h2 >> 5;
s[8] = h2 >> 13;
s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
s[10] = h3 >> 3;
s[11] = h3 >> 11;
s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
s[13] = h4 >> 2;
s[14] = h4 >> 10;
s[15] = h4 >> 18;
s[16] = h5 >> 0;
s[17] = h5 >> 8;
s[18] = h5 >> 16;
s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
s[20] = h6 >> 7;
s[21] = h6 >> 15;
s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
s[23] = h7 >> 5;
s[24] = h7 >> 13;
s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
s[26] = h8 >> 4;
s[27] = h8 >> 12;
s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
s[29] = h9 >> 2;
s[30] = h9 >> 10;
s[31] = h9 >> 18;
}
/* h = f */
static void fe_copy(fe h, const fe f) {
memmove(h, f, sizeof(int32_t) * 10);
}
/* h = 0 */
static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
/* h = 1 */
static void fe_1(fe h) {
memset(h, 0, sizeof(int32_t) * 10);
h[0] = 1;
}
/* h = f + g
* Can overlap h with f or g.
*
* Preconditions:
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
static void fe_add(fe h, const fe f, const fe g) {
unsigned i;
for (i = 0; i < 10; i++) {
h[i] = f[i] + g[i];
}
}
/* h = f - g
* Can overlap h with f or g.
*
* Preconditions:
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
static void fe_sub(fe h, const fe f, const fe g) {
unsigned i;
for (i = 0; i < 10; i++) {
h[i] = f[i] - g[i];
}
}
/* h = f * g
* Can overlap h with f or g.
*
* Preconditions:
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
* |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
*
* Postconditions:
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*
* Notes on implementation strategy:
*
* Using schoolbook multiplication.
* Karatsuba would save a little in some cost models.
*
* Most multiplications by 2 and 19 are 32-bit precomputations;
* cheaper than 64-bit postcomputations.
*
* There is one remaining multiplication by 19 in the carry chain;
* one *19 precomputation can be merged into this,
* but the resulting data flow is considerably less clean.
*
* There are 12 carries below.
* 10 of them are 2-way parallelizable and vectorizable.
* Can get away with 11 carries, but then data flow is much deeper.
*
* With tighter constraints on inputs can squeeze carries into int32. */
static void fe_mul(fe h, const fe f, const fe g) {
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
int32_t g3_19 = 19 * g3;
int32_t g4_19 = 19 * g4;
int32_t g5_19 = 19 * g5;
int32_t g6_19 = 19 * g6;
int32_t g7_19 = 19 * g7;
int32_t g8_19 = 19 * g8;
int32_t g9_19 = 19 * g9;
int32_t f1_2 = 2 * f1;
int32_t f3_2 = 2 * f3;
int32_t f5_2 = 2 * f5;
int32_t f7_2 = 2 * f7;
int32_t f9_2 = 2 * f9;
int64_t f0g0 = f0 * (int64_t) g0;
int64_t f0g1 = f0 * (int64_t) g1;
int64_t f0g2 = f0 * (int64_t) g2;
int64_t f0g3 = f0 * (int64_t) g3;
int64_t f0g4 = f0 * (int64_t) g4;
int64_t f0g5 = f0 * (int64_t) g5;
int64_t f0g6 = f0 * (int64_t) g6;
int64_t f0g7 = f0 * (int64_t) g7;
int64_t f0g8 = f0 * (int64_t) g8;
int64_t f0g9 = f0 * (int64_t) g9;
int64_t f1g0 = f1 * (int64_t) g0;
int64_t f1g1_2 = f1_2 * (int64_t) g1;
int64_t f1g2 = f1 * (int64_t) g2;
int64_t f1g3_2 = f1_2 * (int64_t) g3;
int64_t f1g4 = f1 * (int64_t) g4;
int64_t f1g5_2 = f1_2 * (int64_t) g5;
int64_t f1g6 = f1 * (int64_t) g6;
int64_t f1g7_2 = f1_2 * (int64_t) g7;
int64_t f1g8 = f1 * (int64_t) g8;
int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
int64_t f2g0 = f2 * (int64_t) g0;
int64_t f2g1 = f2 * (int64_t) g1;
int64_t f2g2 = f2 * (int64_t) g2;
int64_t f2g3 = f2 * (int64_t) g3;
int64_t f2g4 = f2 * (int64_t) g4;
int64_t f2g5 = f2 * (int64_t) g5;
int64_t f2g6 = f2 * (int64_t) g6;
int64_t f2g7 = f2 * (int64_t) g7;
int64_t f2g8_19 = f2 * (int64_t) g8_19;
int64_t f2g9_19 = f2 * (int64_t) g9_19;
int64_t f3g0 = f3 * (int64_t) g0;
int64_t f3g1_2 = f3_2 * (int64_t) g1;
int64_t f3g2 = f3 * (int64_t) g2;
int64_t f3g3_2 = f3_2 * (int64_t) g3;
int64_t f3g4 = f3 * (int64_t) g4;
int64_t f3g5_2 = f3_2 * (int64_t) g5;
int64_t f3g6 = f3 * (int64_t) g6;
int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
int64_t f3g8_19 = f3 * (int64_t) g8_19;
int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
int64_t f4g0 = f4 * (int64_t) g0;
int64_t f4g1 = f4 * (int64_t) g1;
int64_t f4g2 = f4 * (int64_t) g2;
int64_t f4g3 = f4 * (int64_t) g3;
int64_t f4g4 = f4 * (int64_t) g4;
int64_t f4g5 = f4 * (int64_t) g5;
int64_t f4g6_19 = f4 * (int64_t) g6_19;
int64_t f4g7_19 = f4 * (int64_t) g7_19;
int64_t f4g8_19 = f4 * (int64_t) g8_19;
int64_t f4g9_19 = f4 * (int64_t) g9_19;
int64_t f5g0 = f5 * (int64_t) g0;
int64_t f5g1_2 = f5_2 * (int64_t) g1;
int64_t f5g2 = f5 * (int64_t) g2;
int64_t f5g3_2 = f5_2 * (int64_t) g3;
int64_t f5g4 = f5 * (int64_t) g4;
int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
int64_t f5g6_19 = f5 * (int64_t) g6_19;
int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
int64_t f5g8_19 = f5 * (int64_t) g8_19;
int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
int64_t f6g0 = f6 * (int64_t) g0;
int64_t f6g1 = f6 * (int64_t) g1;
int64_t f6g2 = f6 * (int64_t) g2;
int64_t f6g3 = f6 * (int64_t) g3;
int64_t f6g4_19 = f6 * (int64_t) g4_19;
int64_t f6g5_19 = f6 * (int64_t) g5_19;
int64_t f6g6_19 = f6 * (int64_t) g6_19;
int64_t f6g7_19 = f6 * (int64_t) g7_19;
int64_t f6g8_19 = f6 * (int64_t) g8_19;
int64_t f6g9_19 = f6 * (int64_t) g9_19;
int64_t f7g0 = f7 * (int64_t) g0;
int64_t f7g1_2 = f7_2 * (int64_t) g1;
int64_t f7g2 = f7 * (int64_t) g2;
int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
int64_t f7g4_19 = f7 * (int64_t) g4_19;
int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
int64_t f7g6_19 = f7 * (int64_t) g6_19;
int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
int64_t f7g8_19 = f7 * (int64_t) g8_19;
int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
int64_t f8g0 = f8 * (int64_t) g0;
int64_t f8g1 = f8 * (int64_t) g1;
int64_t f8g2_19 = f8 * (int64_t) g2_19;
int64_t f8g3_19 = f8 * (int64_t) g3_19;
int64_t f8g4_19 = f8 * (int64_t) g4_19;
int64_t f8g5_19 = f8 * (int64_t) g5_19;
int64_t f8g6_19 = f8 * (int64_t) g6_19;
int64_t f8g7_19 = f8 * (int64_t) g7_19;
int64_t f8g8_19 = f8 * (int64_t) g8_19;
int64_t f8g9_19 = f8 * (int64_t) g9_19;
int64_t f9g0 = f9 * (int64_t) g0;
int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
int64_t f9g2_19 = f9 * (int64_t) g2_19;
int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
int64_t f9g4_19 = f9 * (int64_t) g4_19;
int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
int64_t f9g6_19 = f9 * (int64_t) g6_19;
int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
int64_t f9g8_19 = f9 * (int64_t) g8_19;
int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
/* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
* i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
* |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
* i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.41*2^60 */
/* |h6| <= 1.41*2^60 */
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.71*2^59 */
/* |h7| <= 1.71*2^59 */
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.72*2^34 */
/* |h8| <= 1.41*2^60 */
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.71*2^59 */
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
/* h = f * f
* Can overlap h with f.
*
* Preconditions:
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
*
* Postconditions:
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*
* See fe_mul.c for discussion of implementation strategy. */
static void fe_sq(fe h, const fe f) {
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t f0_2 = 2 * f0;
int32_t f1_2 = 2 * f1;
int32_t f2_2 = 2 * f2;
int32_t f3_2 = 2 * f3;
int32_t f4_2 = 2 * f4;
int32_t f5_2 = 2 * f5;
int32_t f6_2 = 2 * f6;
int32_t f7_2 = 2 * f7;
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
int64_t f0f0 = f0 * (int64_t) f0;
int64_t f0f1_2 = f0_2 * (int64_t) f1;
int64_t f0f2_2 = f0_2 * (int64_t) f2;
int64_t f0f3_2 = f0_2 * (int64_t) f3;
int64_t f0f4_2 = f0_2 * (int64_t) f4;
int64_t f0f5_2 = f0_2 * (int64_t) f5;
int64_t f0f6_2 = f0_2 * (int64_t) f6;
int64_t f0f7_2 = f0_2 * (int64_t) f7;
int64_t f0f8_2 = f0_2 * (int64_t) f8;
int64_t f0f9_2 = f0_2 * (int64_t) f9;
int64_t f1f1_2 = f1_2 * (int64_t) f1;
int64_t f1f2_2 = f1_2 * (int64_t) f2;
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
int64_t f1f4_2 = f1_2 * (int64_t) f4;
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
int64_t f1f6_2 = f1_2 * (int64_t) f6;
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
int64_t f1f8_2 = f1_2 * (int64_t) f8;
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
int64_t f2f2 = f2 * (int64_t) f2;
int64_t f2f3_2 = f2_2 * (int64_t) f3;
int64_t f2f4_2 = f2_2 * (int64_t) f4;
int64_t f2f5_2 = f2_2 * (int64_t) f5;
int64_t f2f6_2 = f2_2 * (int64_t) f6;
int64_t f2f7_2 = f2_2 * (int64_t) f7;
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
int64_t f2f9_38 = f2 * (int64_t) f9_38;
int64_t f3f3_2 = f3_2 * (int64_t) f3;
int64_t f3f4_2 = f3_2 * (int64_t) f4;
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
int64_t f3f6_2 = f3_2 * (int64_t) f6;
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
int64_t f4f4 = f4 * (int64_t) f4;
int64_t f4f5_2 = f4_2 * (int64_t) f5;
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
int64_t f4f7_38 = f4 * (int64_t) f7_38;
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
int64_t f4f9_38 = f4 * (int64_t) f9_38;
int64_t f5f5_38 = f5 * (int64_t) f5_38;
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
int64_t f6f6_19 = f6 * (int64_t) f6_19;
int64_t f6f7_38 = f6 * (int64_t) f7_38;
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
int64_t f6f9_38 = f6 * (int64_t) f9_38;
int64_t f7f7_38 = f7 * (int64_t) f7_38;
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
int64_t f8f8_19 = f8 * (int64_t) f8_19;
int64_t f8f9_38 = f8 * (int64_t) f9_38;
int64_t f9f9_38 = f9 * (int64_t) f9_38;
int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
static void fe_invert(fe out, const fe z) {
fe t0;
fe t1;
fe t2;
fe t3;
int i;
fe_sq(t0, z);
fe_sq(t1, t0);
for (i = 1; i < 2; ++i) {
fe_sq(t1, t1);
}
fe_mul(t1, z, t1);
fe_mul(t0, t0, t1);
fe_sq(t2, t0);
fe_mul(t1, t1, t2);
fe_sq(t2, t1);
for (i = 1; i < 5; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t2, t1);
for (i = 1; i < 10; ++i) {
fe_sq(t2, t2);
}
fe_mul(t2, t2, t1);
fe_sq(t3, t2);
for (i = 1; i < 20; ++i) {
fe_sq(t3, t3);
}
fe_mul(t2, t3, t2);
fe_sq(t2, t2);
for (i = 1; i < 10; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t2, t1);
for (i = 1; i < 50; ++i) {
fe_sq(t2, t2);
}
fe_mul(t2, t2, t1);
fe_sq(t3, t2);
for (i = 1; i < 100; ++i) {
fe_sq(t3, t3);
}
fe_mul(t2, t3, t2);
fe_sq(t2, t2);
for (i = 1; i < 50; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t1, t1);
for (i = 1; i < 5; ++i) {
fe_sq(t1, t1);
}
fe_mul(out, t1, t0);
}
/* Replace (f,g) with (g,f) if b == 1;
* replace (f,g) with (f,g) if b == 0.
*
* Preconditions: b in {0,1}. */
static void fe_cswap(fe f, fe g, unsigned int b) {
unsigned i;
b = 0-b;
for (i = 0; i < 10; i++) {
int32_t x = f[i] ^ g[i];
x &= b;
f[i] ^= x;
g[i] ^= x;
}
}
/* h = f * 121666
* Can overlap h with f.
*
* Preconditions:
* |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*
* Postconditions:
* |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
static void fe_mul121666(fe h, fe f) {
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int64_t h0 = f0 * (int64_t) 121666;
int64_t h1 = f1 * (int64_t) 121666;
int64_t h2 = f2 * (int64_t) 121666;
int64_t h3 = f3 * (int64_t) 121666;
int64_t h4 = f4 * (int64_t) 121666;
int64_t h5 = f5 * (int64_t) 121666;
int64_t h6 = f6 * (int64_t) 121666;
int64_t h7 = f7 * (int64_t) 121666;
int64_t h8 = f8 * (int64_t) 121666;
int64_t h9 = f9 * (int64_t) 121666;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
void x25519_scalar_mult(uint8_t out[32],
const uint8_t scalar[32],
const uint8_t point[32]) {
fe x1, x2, z2, x3, z3, tmp0, tmp1;
unsigned swap;
int pos;
uint8_t e[32];
memcpy(e, scalar, 32);
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
fe_frombytes(x1, point);
fe_1(x2);
fe_0(z2);
fe_copy(x3, x1);
fe_1(z3);
swap = 0;
for (pos = 254; pos >= 0; --pos) {
unsigned b = 1 & (e[pos / 8] >> (pos & 7));
swap ^= b;
fe_cswap(x2, x3, swap);
fe_cswap(z2, z3, swap);
swap = b;
fe_sub(tmp0, x3, z3);
fe_sub(tmp1, x2, z2);
fe_add(x2, x2, z2);
fe_add(z2, x3, z3);
fe_mul(z3, tmp0, x2);
fe_mul(z2, z2, tmp1);
fe_sq(tmp0, tmp1);
fe_sq(tmp1, x2);
fe_add(x3, z3, z2);
fe_sub(z2, z3, z2);
fe_mul(x2, tmp1, tmp0);
fe_sub(tmp1, tmp1, tmp0);
fe_sq(z2, z2);
fe_mul121666(z3, tmp1);
fe_sq(x3, x3);
fe_add(tmp0, tmp0, z3);
fe_mul(z3, x1, z2);
fe_mul(z2, tmp1, tmp0);
}
fe_cswap(x2, x3, swap);
fe_cswap(z2, z3, swap);
fe_invert(z2, z2);
fe_mul(x2, x2, z2);
fe_tobytes(out, x2);
}

805
common/curve25519.c
View File

@@ -19,815 +19,12 @@
*
* The field functions are shared by Ed25519 and X25519 where possible. */
#include "common.h"
#include "curve25519.h"
#include "trng.h"
#include "util.h"
#define CRYPTO_memcmp safe_memcmp
/*
* fe means field element. Here the field is \Z/(2^255-19). An element t,
* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
* context.
*/
typedef int32_t fe[10];
static const int64_t kBottom25Bits = INT64_C(0x1ffffff);
static const int64_t kBottom26Bits = INT64_C(0x3ffffff);
static const int64_t kTop39Bits = INT64_C(0xfffffffffe000000);
static const int64_t kTop38Bits = INT64_C(0xfffffffffc000000);
static uint64_t load_3(const uint8_t *in) {
uint64_t result;
result = (uint64_t)in[0];
result |= ((uint64_t)in[1]) << 8;
result |= ((uint64_t)in[2]) << 16;
return result;
}
static uint64_t load_4(const uint8_t *in) {
uint64_t result;
result = (uint64_t)in[0];
result |= ((uint64_t)in[1]) << 8;
result |= ((uint64_t)in[2]) << 16;
result |= ((uint64_t)in[3]) << 24;
return result;
}
static void fe_frombytes(fe h, const uint8_t *s) {
/* Ignores top bit of h. */
int64_t h0 = load_4(s);
int64_t h1 = load_3(s + 4) << 6;
int64_t h2 = load_3(s + 7) << 5;
int64_t h3 = load_3(s + 10) << 3;
int64_t h4 = load_3(s + 13) << 2;
int64_t h5 = load_4(s + 16);
int64_t h6 = load_3(s + 20) << 7;
int64_t h7 = load_3(s + 23) << 5;
int64_t h8 = load_3(s + 26) << 4;
int64_t h9 = (load_3(s + 29) & 8388607) << 2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
/* Preconditions:
* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*
* Write p=2^255-19; q=floor(h/p).
* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
*
* Proof:
* Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
* Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
*
* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
* Then 0<y<1.
*
* Write r=h-pq.
* Have 0<=r<=p-1=2^255-20.
* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
*
* Write x=r+19(2^-255)r+y.
* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
*
* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */
static void fe_tobytes(uint8_t *s, const fe h) {
int32_t h0 = h[0];
int32_t h1 = h[1];
int32_t h2 = h[2];
int32_t h3 = h[3];
int32_t h4 = h[4];
int32_t h5 = h[5];
int32_t h6 = h[6];
int32_t h7 = h[7];
int32_t h8 = h[8];
int32_t h9 = h[9];
int32_t q;
q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
q = (h0 + q) >> 26;
q = (h1 + q) >> 25;
q = (h2 + q) >> 26;
q = (h3 + q) >> 25;
q = (h4 + q) >> 26;
q = (h5 + q) >> 25;
q = (h6 + q) >> 26;
q = (h7 + q) >> 25;
q = (h8 + q) >> 26;
q = (h9 + q) >> 25;
/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
h0 += 19 * q;
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
h1 += h0 >> 26; h0 &= kBottom26Bits;
h2 += h1 >> 25; h1 &= kBottom25Bits;
h3 += h2 >> 26; h2 &= kBottom26Bits;
h4 += h3 >> 25; h3 &= kBottom25Bits;
h5 += h4 >> 26; h4 &= kBottom26Bits;
h6 += h5 >> 25; h5 &= kBottom25Bits;
h7 += h6 >> 26; h6 &= kBottom26Bits;
h8 += h7 >> 25; h7 &= kBottom25Bits;
h9 += h8 >> 26; h8 &= kBottom26Bits;
h9 &= kBottom25Bits;
/* h10 = carry9 */
/* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
* Have h0+...+2^230 h9 between 0 and 2^255-1;
* evidently 2^255 h10-2^255 q = 0.
* Goal: Output h0+...+2^230 h9. */
s[0] = h0 >> 0;
s[1] = h0 >> 8;
s[2] = h0 >> 16;
s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2);
s[4] = h1 >> 6;
s[5] = h1 >> 14;
s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3);
s[7] = h2 >> 5;
s[8] = h2 >> 13;
s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5);
s[10] = h3 >> 3;
s[11] = h3 >> 11;
s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6);
s[13] = h4 >> 2;
s[14] = h4 >> 10;
s[15] = h4 >> 18;
s[16] = h5 >> 0;
s[17] = h5 >> 8;
s[18] = h5 >> 16;
s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1);
s[20] = h6 >> 7;
s[21] = h6 >> 15;
s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3);
s[23] = h7 >> 5;
s[24] = h7 >> 13;
s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4);
s[26] = h8 >> 4;
s[27] = h8 >> 12;
s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6);
s[29] = h9 >> 2;
s[30] = h9 >> 10;
s[31] = h9 >> 18;
}
/* h = f */
static void fe_copy(fe h, const fe f) {
memmove(h, f, sizeof(int32_t) * 10);
}
/* h = 0 */
static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }
/* h = 1 */
static void fe_1(fe h) {
memset(h, 0, sizeof(int32_t) * 10);
h[0] = 1;
}
/* h = f + g
* Can overlap h with f or g.
*
* Preconditions:
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
static void fe_add(fe h, const fe f, const fe g) {
unsigned i;
for (i = 0; i < 10; i++) {
h[i] = f[i] + g[i];
}
}
/* h = f - g
* Can overlap h with f or g.
*
* Preconditions:
* |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
* |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*
* Postconditions:
* |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */
static void fe_sub(fe h, const fe f, const fe g) {
unsigned i;
for (i = 0; i < 10; i++) {
h[i] = f[i] - g[i];
}
}
/* h = f * g
* Can overlap h with f or g.
*
* Preconditions:
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
* |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
*
* Postconditions:
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*
* Notes on implementation strategy:
*
* Using schoolbook multiplication.
* Karatsuba would save a little in some cost models.
*
* Most multiplications by 2 and 19 are 32-bit precomputations;
* cheaper than 64-bit postcomputations.
*
* There is one remaining multiplication by 19 in the carry chain;
* one *19 precomputation can be merged into this,
* but the resulting data flow is considerably less clean.
*
* There are 12 carries below.
* 10 of them are 2-way parallelizable and vectorizable.
* Can get away with 11 carries, but then data flow is much deeper.
*
* With tighter constraints on inputs can squeeze carries into int32. */
static void fe_mul(fe h, const fe f, const fe g) {
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
int32_t g3_19 = 19 * g3;
int32_t g4_19 = 19 * g4;
int32_t g5_19 = 19 * g5;
int32_t g6_19 = 19 * g6;
int32_t g7_19 = 19 * g7;
int32_t g8_19 = 19 * g8;
int32_t g9_19 = 19 * g9;
int32_t f1_2 = 2 * f1;
int32_t f3_2 = 2 * f3;
int32_t f5_2 = 2 * f5;
int32_t f7_2 = 2 * f7;
int32_t f9_2 = 2 * f9;
int64_t f0g0 = f0 * (int64_t) g0;
int64_t f0g1 = f0 * (int64_t) g1;
int64_t f0g2 = f0 * (int64_t) g2;
int64_t f0g3 = f0 * (int64_t) g3;
int64_t f0g4 = f0 * (int64_t) g4;
int64_t f0g5 = f0 * (int64_t) g5;
int64_t f0g6 = f0 * (int64_t) g6;
int64_t f0g7 = f0 * (int64_t) g7;
int64_t f0g8 = f0 * (int64_t) g8;
int64_t f0g9 = f0 * (int64_t) g9;
int64_t f1g0 = f1 * (int64_t) g0;
int64_t f1g1_2 = f1_2 * (int64_t) g1;
int64_t f1g2 = f1 * (int64_t) g2;
int64_t f1g3_2 = f1_2 * (int64_t) g3;
int64_t f1g4 = f1 * (int64_t) g4;
int64_t f1g5_2 = f1_2 * (int64_t) g5;
int64_t f1g6 = f1 * (int64_t) g6;
int64_t f1g7_2 = f1_2 * (int64_t) g7;
int64_t f1g8 = f1 * (int64_t) g8;
int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
int64_t f2g0 = f2 * (int64_t) g0;
int64_t f2g1 = f2 * (int64_t) g1;
int64_t f2g2 = f2 * (int64_t) g2;
int64_t f2g3 = f2 * (int64_t) g3;
int64_t f2g4 = f2 * (int64_t) g4;
int64_t f2g5 = f2 * (int64_t) g5;
int64_t f2g6 = f2 * (int64_t) g6;
int64_t f2g7 = f2 * (int64_t) g7;
int64_t f2g8_19 = f2 * (int64_t) g8_19;
int64_t f2g9_19 = f2 * (int64_t) g9_19;
int64_t f3g0 = f3 * (int64_t) g0;
int64_t f3g1_2 = f3_2 * (int64_t) g1;
int64_t f3g2 = f3 * (int64_t) g2;
int64_t f3g3_2 = f3_2 * (int64_t) g3;
int64_t f3g4 = f3 * (int64_t) g4;
int64_t f3g5_2 = f3_2 * (int64_t) g5;
int64_t f3g6 = f3 * (int64_t) g6;
int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
int64_t f3g8_19 = f3 * (int64_t) g8_19;
int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
int64_t f4g0 = f4 * (int64_t) g0;
int64_t f4g1 = f4 * (int64_t) g1;
int64_t f4g2 = f4 * (int64_t) g2;
int64_t f4g3 = f4 * (int64_t) g3;
int64_t f4g4 = f4 * (int64_t) g4;
int64_t f4g5 = f4 * (int64_t) g5;
int64_t f4g6_19 = f4 * (int64_t) g6_19;
int64_t f4g7_19 = f4 * (int64_t) g7_19;
int64_t f4g8_19 = f4 * (int64_t) g8_19;
int64_t f4g9_19 = f4 * (int64_t) g9_19;
int64_t f5g0 = f5 * (int64_t) g0;
int64_t f5g1_2 = f5_2 * (int64_t) g1;
int64_t f5g2 = f5 * (int64_t) g2;
int64_t f5g3_2 = f5_2 * (int64_t) g3;
int64_t f5g4 = f5 * (int64_t) g4;
int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
int64_t f5g6_19 = f5 * (int64_t) g6_19;
int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
int64_t f5g8_19 = f5 * (int64_t) g8_19;
int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
int64_t f6g0 = f6 * (int64_t) g0;
int64_t f6g1 = f6 * (int64_t) g1;
int64_t f6g2 = f6 * (int64_t) g2;
int64_t f6g3 = f6 * (int64_t) g3;
int64_t f6g4_19 = f6 * (int64_t) g4_19;
int64_t f6g5_19 = f6 * (int64_t) g5_19;
int64_t f6g6_19 = f6 * (int64_t) g6_19;
int64_t f6g7_19 = f6 * (int64_t) g7_19;
int64_t f6g8_19 = f6 * (int64_t) g8_19;
int64_t f6g9_19 = f6 * (int64_t) g9_19;
int64_t f7g0 = f7 * (int64_t) g0;
int64_t f7g1_2 = f7_2 * (int64_t) g1;
int64_t f7g2 = f7 * (int64_t) g2;
int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
int64_t f7g4_19 = f7 * (int64_t) g4_19;
int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
int64_t f7g6_19 = f7 * (int64_t) g6_19;
int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
int64_t f7g8_19 = f7 * (int64_t) g8_19;
int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
int64_t f8g0 = f8 * (int64_t) g0;
int64_t f8g1 = f8 * (int64_t) g1;
int64_t f8g2_19 = f8 * (int64_t) g2_19;
int64_t f8g3_19 = f8 * (int64_t) g3_19;
int64_t f8g4_19 = f8 * (int64_t) g4_19;
int64_t f8g5_19 = f8 * (int64_t) g5_19;
int64_t f8g6_19 = f8 * (int64_t) g6_19;
int64_t f8g7_19 = f8 * (int64_t) g7_19;
int64_t f8g8_19 = f8 * (int64_t) g8_19;
int64_t f8g9_19 = f8 * (int64_t) g9_19;
int64_t f9g0 = f9 * (int64_t) g0;
int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
int64_t f9g2_19 = f9 * (int64_t) g2_19;
int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
int64_t f9g4_19 = f9 * (int64_t) g4_19;
int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
int64_t f9g6_19 = f9 * (int64_t) g6_19;
int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
int64_t f9g8_19 = f9 * (int64_t) g8_19;
int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
/* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
* i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
* |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
* i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.41*2^60 */
/* |h6| <= 1.41*2^60 */
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.71*2^59 */
/* |h7| <= 1.71*2^59 */
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.72*2^34 */
/* |h8| <= 1.41*2^60 */
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.71*2^59 */
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
/* h = f * f
* Can overlap h with f.
*
* Preconditions:
* |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
*
* Postconditions:
* |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*
* See fe_mul.c for discussion of implementation strategy. */
static void fe_sq(fe h, const fe f) {
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t f0_2 = 2 * f0;
int32_t f1_2 = 2 * f1;
int32_t f2_2 = 2 * f2;
int32_t f3_2 = 2 * f3;
int32_t f4_2 = 2 * f4;
int32_t f5_2 = 2 * f5;
int32_t f6_2 = 2 * f6;
int32_t f7_2 = 2 * f7;
int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
int64_t f0f0 = f0 * (int64_t) f0;
int64_t f0f1_2 = f0_2 * (int64_t) f1;
int64_t f0f2_2 = f0_2 * (int64_t) f2;
int64_t f0f3_2 = f0_2 * (int64_t) f3;
int64_t f0f4_2 = f0_2 * (int64_t) f4;
int64_t f0f5_2 = f0_2 * (int64_t) f5;
int64_t f0f6_2 = f0_2 * (int64_t) f6;
int64_t f0f7_2 = f0_2 * (int64_t) f7;
int64_t f0f8_2 = f0_2 * (int64_t) f8;
int64_t f0f9_2 = f0_2 * (int64_t) f9;
int64_t f1f1_2 = f1_2 * (int64_t) f1;
int64_t f1f2_2 = f1_2 * (int64_t) f2;
int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
int64_t f1f4_2 = f1_2 * (int64_t) f4;
int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
int64_t f1f6_2 = f1_2 * (int64_t) f6;
int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
int64_t f1f8_2 = f1_2 * (int64_t) f8;
int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
int64_t f2f2 = f2 * (int64_t) f2;
int64_t f2f3_2 = f2_2 * (int64_t) f3;
int64_t f2f4_2 = f2_2 * (int64_t) f4;
int64_t f2f5_2 = f2_2 * (int64_t) f5;
int64_t f2f6_2 = f2_2 * (int64_t) f6;
int64_t f2f7_2 = f2_2 * (int64_t) f7;
int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
int64_t f2f9_38 = f2 * (int64_t) f9_38;
int64_t f3f3_2 = f3_2 * (int64_t) f3;
int64_t f3f4_2 = f3_2 * (int64_t) f4;
int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
int64_t f3f6_2 = f3_2 * (int64_t) f6;
int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
int64_t f4f4 = f4 * (int64_t) f4;
int64_t f4f5_2 = f4_2 * (int64_t) f5;
int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
int64_t f4f7_38 = f4 * (int64_t) f7_38;
int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
int64_t f4f9_38 = f4 * (int64_t) f9_38;
int64_t f5f5_38 = f5 * (int64_t) f5_38;
int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
int64_t f6f6_19 = f6 * (int64_t) f6_19;
int64_t f6f7_38 = f6 * (int64_t) f7_38;
int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
int64_t f6f9_38 = f6 * (int64_t) f9_38;
int64_t f7f7_38 = f7 * (int64_t) f7_38;
int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
int64_t f8f8_19 = f8 * (int64_t) f8_19;
int64_t f8f9_38 = f8 * (int64_t) f9_38;
int64_t f9f9_38 = f9 * (int64_t) f9_38;
int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
static void fe_invert(fe out, const fe z) {
fe t0;
fe t1;
fe t2;
fe t3;
int i;
fe_sq(t0, z);
fe_sq(t1, t0);
for (i = 1; i < 2; ++i) {
fe_sq(t1, t1);
}
fe_mul(t1, z, t1);
fe_mul(t0, t0, t1);
fe_sq(t2, t0);
fe_mul(t1, t1, t2);
fe_sq(t2, t1);
for (i = 1; i < 5; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t2, t1);
for (i = 1; i < 10; ++i) {
fe_sq(t2, t2);
}
fe_mul(t2, t2, t1);
fe_sq(t3, t2);
for (i = 1; i < 20; ++i) {
fe_sq(t3, t3);
}
fe_mul(t2, t3, t2);
fe_sq(t2, t2);
for (i = 1; i < 10; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t2, t1);
for (i = 1; i < 50; ++i) {
fe_sq(t2, t2);
}
fe_mul(t2, t2, t1);
fe_sq(t3, t2);
for (i = 1; i < 100; ++i) {
fe_sq(t3, t3);
}
fe_mul(t2, t3, t2);
fe_sq(t2, t2);
for (i = 1; i < 50; ++i) {
fe_sq(t2, t2);
}
fe_mul(t1, t2, t1);
fe_sq(t1, t1);
for (i = 1; i < 5; ++i) {
fe_sq(t1, t1);
}
fe_mul(out, t1, t0);
}
/* Replace (f,g) with (g,f) if b == 1;
* replace (f,g) with (f,g) if b == 0.
*
* Preconditions: b in {0,1}. */
static void fe_cswap(fe f, fe g, unsigned int b) {
unsigned i;
b = 0-b;
for (i = 0; i < 10; i++) {
int32_t x = f[i] ^ g[i];
x &= b;
f[i] ^= x;
g[i] ^= x;
}
}
/* h = f * 121666
* Can overlap h with f.
*
* Preconditions:
* |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*
* Postconditions:
* |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */
static void fe_mul121666(fe h, fe f) {
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int64_t h0 = f0 * (int64_t) 121666;
int64_t h1 = f1 * (int64_t) 121666;
int64_t h2 = f2 * (int64_t) 121666;
int64_t h3 = f3 * (int64_t) 121666;
int64_t h4 = f4 * (int64_t) 121666;
int64_t h5 = f5 * (int64_t) 121666;
int64_t h6 = f6 * (int64_t) 121666;
int64_t h7 = f7 * (int64_t) 121666;
int64_t h8 = f8 * (int64_t) 121666;
int64_t h9 = f9 * (int64_t) 121666;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
static void x25519_scalar_mult_generic(uint8_t out[32],
const uint8_t scalar[32],
const uint8_t point[32]) {
fe x1, x2, z2, x3, z3, tmp0, tmp1;
unsigned swap;
int pos;
uint8_t e[32];
memcpy(e, scalar, 32);
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
fe_frombytes(x1, point);
fe_1(x2);
fe_0(z2);
fe_copy(x3, x1);
fe_1(z3);
swap = 0;
for (pos = 254; pos >= 0; --pos) {
unsigned b = 1 & (e[pos / 8] >> (pos & 7));
swap ^= b;
fe_cswap(x2, x3, swap);
fe_cswap(z2, z3, swap);
swap = b;
fe_sub(tmp0, x3, z3);
fe_sub(tmp1, x2, z2);
fe_add(x2, x2, z2);
fe_add(z2, x3, z3);
fe_mul(z3, tmp0, x2);
fe_mul(z2, z2, tmp1);
fe_sq(tmp0, tmp1);
fe_sq(tmp1, x2);
fe_add(x3, z3, z2);
fe_sub(z2, z3, z2);
fe_mul(x2, tmp1, tmp0);
fe_sub(tmp1, tmp1, tmp0);
fe_sq(z2, z2);
fe_mul121666(z3, tmp1);
fe_sq(x3, x3);
fe_add(tmp0, tmp0, z3);
fe_mul(z3, x1, z2);
fe_mul(z2, tmp1, tmp0);
}
fe_cswap(x2, x3, swap);
fe_cswap(z2, z3, swap);
fe_invert(z2, z2);
fe_mul(x2, x2, z2);
fe_tobytes(out, x2);
}
static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
const uint8_t point[32]) {
x25519_scalar_mult_generic(out, scalar, point);
}
#ifdef CONFIG_RNG
void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) {
rand_bytes(out_private_key, 32);

9
core/cortex-m0/build.mk
View File

@@ -21,4 +21,13 @@ endif
core-y=cpu.o init.o thumb_case.o div.o lmul.o ldivmod.o uldivmod.o
core-$(CONFIG_COMMON_PANIC_OUTPUT)+=panic.o
core-$(CONFIG_COMMON_RUNTIME)+=switch.o task.o
dirs-y += core/$(CORE)/curve25519
core-$(CONFIG_CURVE25519)+=curve25519/mpy121666.o
core-$(CONFIG_CURVE25519)+=curve25519/reduce25519.o
core-$(CONFIG_CURVE25519)+=curve25519/mul.o
core-$(CONFIG_CURVE25519)+=curve25519/scalarmult.o
core-$(CONFIG_CURVE25519)+=curve25519/sqr.o
core-$(CONFIG_WATCHDOG)+=watchdog.o

20
core/cortex-m0/curve25519/cortex_m0_mpy121666.s → core/cortex-m0/curve25519/mpy121666.S
View File

@@ -11,21 +11,7 @@
// Not yet tested on target hardware.
.cpu cortex-m0
.fpu softvfp
.eabi_attribute 20, 1
.eabi_attribute 21, 1
.eabi_attribute 23, 3
.eabi_attribute 24, 1
.eabi_attribute 25, 1
.eabi_attribute 26, 1
.eabi_attribute 30, 2
.eabi_attribute 34, 0
.eabi_attribute 18, 4
.code 16
.file "cortex_m0_reduce25519.s"
.text
.align 2
@@ -36,7 +22,7 @@
fe25519_mpyWith121666_asm:
push {r4,r5,r6,r7,r14}
ldr r7,__label_for_immediate_56130
ldr r7,=56130
ldr r2,[r1,#28]
lsl r5,r2,#16
lsr r6,r2,#16
@@ -191,9 +177,5 @@ fe25519_mpyWith121666_asm:
str r6,[r0,#28]
pop {r4,r5,r6,r7,r15}
.align 2
__label_for_immediate_56130:
.word 56130
.size fe25519_mpyWith121666_asm, .-fe25519_mpyWith121666_asm

0
core/cortex-m0/curve25519/mul.s → core/cortex-m0/curve25519/mul.S
View File

13
core/cortex-m0/curve25519/cortex_m0_reduce25519.s → core/cortex-m0/curve25519/reduce25519.S
View File

@@ -8,21 +8,8 @@
// Generated and tested with C++ functions in the test subdirectory and on the target.
//
.cpu cortex-m0
.fpu softvfp
.eabi_attribute 20, 1
.eabi_attribute 21, 1
.eabi_attribute 23, 3
.eabi_attribute 24, 1
.eabi_attribute 25, 1
.eabi_attribute 26, 1
.eabi_attribute 30, 2
.eabi_attribute 34, 0
.eabi_attribute 18, 4
.code 16
.file "cortex_m0_reduce25519.s"
.text
.align 2

59
core/cortex-m0/curve25519/scalarmult.c
View File

@@ -57,12 +57,14 @@
Creative Commons CC0 1.0 Universal public domain dedication
============================================================================*/
#include <inttypes.h>
#include "curve25519.h"
#include "util.h"
// comment out this line if implementing conditional swaps by data moves
//#define DH_SWAP_BY_POINTERS
// Define the symbol to 0 in order to only use ladder steps
#define DH_REPLACE_LAST_THREE_LADDERSTEPS_WITH_DOUBLINGS 0
//#define DH_REPLACE_LAST_THREE_LADDERSTEPS_WITH_DOUBLINGS 1
typedef uint8_t uint8;
@@ -142,26 +144,17 @@ fe25519_cpy(
const fe25519* source
)
{
uint32 ctr;
for (ctr = 0; ctr < 8; ctr++)
{
dest->as_uint32[ctr] = source->as_uint32[ctr];
}
memcpy(dest, source, 32);
}
static void
fe25519_unpack(
volatile fe25519* out,
fe25519* out,
const unsigned char in[32]
)
{
uint8 ctr;
memcpy(out, in, 32);
for (ctr = 0; ctr < 32; ctr++)
{
out->as_uint8[ctr] = in[ctr];
}
out->as_uint8[31] &= 0x7f; // make sure that the last bit is cleared.
}
@@ -257,7 +250,7 @@ fe25519_square(
static void
fe25519_reduceCompletely(
volatile fe25519* inout
fe25519* inout
)
{
uint32 numberOfTimesToSubstractPrime;
@@ -307,17 +300,12 @@ fe25519_reduceCompletely(
static void
fe25519_pack(
unsigned char out[32],
volatile fe25519* in
fe25519* in
)
{
uint8 ctr;
fe25519_reduceCompletely(in);
for (ctr = 0; ctr < 32; ctr++)
{
out[ctr] = in->as_uint8[ctr];
}
memcpy(out, in, 32);
}
// Note, that r and x are allowed to overlap!
@@ -511,7 +499,7 @@ typedef struct _ST_curve25519ladderstepWorkingState
fe25519 xq;
fe25519 zq;
volatile UN_256bitValue s;
UN_256bitValue s;
int nextScalarBitToProcess;
uint8 previousProcessedBit;
@@ -649,11 +637,11 @@ curve25519_doublePointP (ST_curve25519ladderstepWorkingState* pState)
#endif // #ifdef DH_REPLACE_LAST_THREE_LADDERSTEPS_WITH_DOUBLINGS
int
crypto_scalarmult_curve25519(
unsigned char* r,
const unsigned char* s,
const unsigned char* p
void
x25519_scalar_mult(
uint8_t r[32],
const uint8_t s[32],
const uint8_t p[32]
)
{
ST_curve25519ladderstepWorkingState state;
@@ -741,21 +729,4 @@ crypto_scalarmult_curve25519(
fe25519_pack (r, &state.xp);
#endif
return 0;
}
int
crypto_scalarmult_curve25519_base(
unsigned char* q,
const unsigned char* n
)
{
static const uint8 base[32] =
{
9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};
return crypto_scalarmult_curve25519(q, n, base);
}

132
core/cortex-m0/curve25519/sqr.s → core/cortex-m0/curve25519/sqr.S
View File

@@ -17,17 +17,9 @@ square256_asm:
push {r1,r4,r5,r6,r7,r14}
.syntax unified
mov r3,r8
.syntax divided
.syntax unified
mov r4,r9
.syntax divided
.syntax unified
mov r5,r10
.syntax divided
.syntax unified
mov r6,r11
.syntax divided
.syntax unified
mov r7,r12
.syntax divided
push {r3,r4,r5,r6,r7}
@@ -41,8 +33,6 @@ square256_asm:
// clobbers all registers except for r14
.syntax unified
mov r0,r4
.syntax divided
.syntax unified
mov r1,r5
.syntax divided
sub r0,r6
@@ -54,11 +44,7 @@ square256_asm:
sbc r1,r2
.syntax unified
mov r8,r0
.syntax divided
.syntax unified
mov r9,r1
.syntax divided
.syntax unified
mov r10,r6
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -144,17 +130,9 @@ square256_asm:
// Leaves r6 zero.
.syntax unified
mov r6,r10
.syntax divided
.syntax unified
mov r10,r0
.syntax divided
.syntax unified
mov r11,r1
.syntax divided
.syntax unified
mov r12,r2
.syntax divided
.syntax unified
mov r1,r3
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -247,17 +225,9 @@ square256_asm:
adc r5,r6
.syntax unified
mov r12,r2
.syntax divided
.syntax unified
mov r2,r8
.syntax divided
.syntax unified
mov r8,r3
.syntax divided
.syntax unified
mov r3,r9
.syntax divided
.syntax unified
mov r9,r4
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -343,19 +313,13 @@ square256_asm:
// Returns r4 as zero.
.syntax unified
mov r2,r12
.syntax divided
.syntax unified
mov r3,r8
.syntax divided
.syntax unified
mov r4,r9
.syntax divided
sub r2,r6
sbc r3,r7
.syntax unified
mov r6,r4
.syntax divided
.syntax unified
mov r7,r5
.syntax divided
sbc r4,r0
@@ -401,8 +365,6 @@ square256_asm:
// clobbers all registers except for r14
.syntax unified
mov r0,r4
.syntax divided
.syntax unified
mov r1,r5
.syntax divided
sub r0,r6
@@ -414,11 +376,7 @@ square256_asm:
sbc r1,r2
.syntax unified
mov r8,r0
.syntax divided
.syntax unified
mov r9,r1
.syntax divided
.syntax unified
mov r10,r6
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -504,17 +462,9 @@ square256_asm:
// Leaves r6 zero.
.syntax unified
mov r6,r10
.syntax divided
.syntax unified
mov r10,r0
.syntax divided
.syntax unified
mov r11,r1
.syntax divided
.syntax unified
mov r12,r2
.syntax divided
.syntax unified
mov r1,r3
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -607,17 +557,9 @@ square256_asm:
adc r5,r6
.syntax unified
mov r12,r2
.syntax divided
.syntax unified
mov r2,r8
.syntax divided
.syntax unified
mov r8,r3
.syntax divided
.syntax unified
mov r3,r9
.syntax divided
.syntax unified
mov r9,r4
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -703,19 +645,13 @@ square256_asm:
// Returns r4 as zero.
.syntax unified
mov r2,r12
.syntax divided
.syntax unified
mov r3,r8
.syntax divided
.syntax unified
mov r4,r9
.syntax divided
sub r2,r6
sbc r3,r7
.syntax unified
mov r6,r4
.syntax divided
.syntax unified
mov r7,r5
.syntax divided
sbc r4,r0
@@ -749,14 +685,8 @@ square256_asm:
// Result in r0 ... r7
.syntax unified
mov r8,r4
.syntax divided
.syntax unified
mov r9,r5
.syntax divided
.syntax unified
mov r10,r6
.syntax divided
.syntax unified
mov r11,r7
.syntax divided
pop {r4,r5,r6,r7}
@@ -766,17 +696,9 @@ square256_asm:
adc r3,r7
.syntax unified
mov r4,r8
.syntax divided
.syntax unified
mov r5,r9
.syntax divided
.syntax unified
mov r6,r10
.syntax divided
.syntax unified
mov r7,r11
.syntax divided
.syntax unified
mov r8,r0
.syntax divided
mov r0,#0
@@ -809,8 +731,6 @@ square256_asm:
// clobbers all registers except for r14
.syntax unified
mov r0,r4
.syntax divided
.syntax unified
mov r1,r5
.syntax divided
sub r0,r6
@@ -822,11 +742,7 @@ square256_asm:
sbc r1,r2
.syntax unified
mov r8,r0
.syntax divided
.syntax unified
mov r9,r1
.syntax divided
.syntax unified
mov r10,r6
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -912,17 +828,9 @@ square256_asm:
// Leaves r6 zero.
.syntax unified
mov r6,r10
.syntax divided
.syntax unified
mov r10,r0
.syntax divided
.syntax unified
mov r11,r1
.syntax divided
.syntax unified
mov r12,r2
.syntax divided
.syntax unified
mov r1,r3
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -1015,17 +923,9 @@ square256_asm:
adc r5,r6
.syntax unified
mov r12,r2
.syntax divided
.syntax unified
mov r2,r8
.syntax divided
.syntax unified
mov r8,r3
.syntax divided
.syntax unified
mov r3,r9
.syntax divided
.syntax unified
mov r9,r4
.syntax divided
// START: sqr 64 Refined Karatsuba
@@ -1111,19 +1011,13 @@ square256_asm:
// Returns r4 as zero.
.syntax unified
mov r2,r12
.syntax divided
.syntax unified
mov r3,r8
.syntax divided
.syntax unified
mov r4,r9
.syntax divided
sub r2,r6
sbc r3,r7
.syntax unified
mov r6,r4
.syntax divided
.syntax unified
mov r7,r5
.syntax divided
sbc r4,r0
@@ -1165,14 +1059,8 @@ square256_asm:
mvn r7,r7
.syntax unified
mov r8,r4
.syntax divided
.syntax unified
mov r9,r5
.syntax divided
.syntax unified
mov r10,r6
.syntax divided
.syntax unified
mov r11,r7
.syntax divided
mov r4,#143
@@ -1190,29 +1078,21 @@ square256_asm:
stm r4!,{r0,r1,r2,r3}
.syntax unified
mov r4,r12
.syntax divided
.syntax unified
mov r0,r8
.syntax divided
adc r0,r4
.syntax unified
mov r8,r0
.syntax divided
.syntax unified
mov r1,r9
.syntax divided
adc r1,r5
.syntax unified
mov r9,r1
.syntax divided
.syntax unified
mov r2,r10
.syntax divided
adc r2,r6
.syntax unified
mov r10,r2
.syntax divided
.syntax unified
mov r3,r11
.syntax divided
adc r3,r7
@@ -1223,8 +1103,6 @@ square256_asm:
adc r0,r0
.syntax unified
mov r12,r0
.syntax divided
.syntax unified
mov r0,r14
.syntax divided
ldm r0,{r0,r1,r2,r3,r4,r5,r6,r7}
@@ -1237,8 +1115,6 @@ square256_asm:
stm r4!,{r0,r1,r2,r3}
.syntax unified
mov r14,r4
.syntax divided
.syntax unified
mov r0,r13
.syntax divided
ldm r0!,{r4,r5,r6,r7}
@@ -1278,17 +1154,9 @@ square256_asm:
pop {r3,r4,r5,r6,r7}
.syntax unified
mov r8,r3
.syntax divided
.syntax unified
mov r9,r4
.syntax divided
.syntax unified
mov r10,r5
.syntax divided
.syntax unified
mov r11,r6
.syntax divided
.syntax unified
mov r12,r7
.syntax divided
pop {r0,r4,r5,r6,r7,r15}

8
include/curve25519.h
View File

@@ -59,4 +59,12 @@ int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
void X25519_public_from_private(uint8_t out_public_value[32],
const uint8_t private_key[32]);
/*
* Low-level x25519 function, defined by either the generic or cortex-m0
* implementation. Must not be called directly.
*/
void x25519_scalar_mult(uint8_t out[32],
const uint8_t scalar[32],
const uint8_t point[32]);
#endif /* __CROS_EC_CURVE25519_H */