diff options
author | Xu Yizhou <xuyizhou1@huawei.com> | 2023-08-23 17:30:09 +0800 |
---|---|---|
committer | Tomas Mraz <tomas@openssl.org> | 2023-08-24 14:57:35 +0200 |
commit | 6399d7856c75abde9ed23782d10960013de03810 (patch) | |
tree | d45527466a10cd60f73d5da80752ba9086665bf4 /crypto | |
parent | ce7a9e23fb1ea249e08c3dfa9c9f701a701f2719 (diff) | |
download | openssl-6399d7856c75abde9ed23782d10960013de03810.tar.gz |
Optimize SM2 on aarch64
Signed-off-by: Xu Yizhou <xuyizhou1@huawei.com>
Reviewed-by: Dmitry Belyavskiy <beldmit@gmail.com>
Reviewed-by: Tomas Mraz <tomas@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/20754)
Diffstat (limited to 'crypto')
-rw-r--r-- | crypto/ec/asm/ecp_sm2p256-armv8.pl | 820 | ||||
-rw-r--r-- | crypto/ec/build.info | 12 | ||||
-rw-r--r-- | crypto/ec/ec_curve.c | 11 | ||||
-rw-r--r-- | crypto/ec/ec_local.h | 5 | ||||
-rw-r--r-- | crypto/ec/ecp_sm2p256.c | 800 | ||||
-rw-r--r-- | crypto/ec/ecp_sm2p256_table.c | 16387 |
6 files changed, 18032 insertions, 3 deletions
diff --git a/crypto/ec/asm/ecp_sm2p256-armv8.pl b/crypto/ec/asm/ecp_sm2p256-armv8.pl new file mode 100644 index 0000000000..da4c16c309 --- /dev/null +++ b/crypto/ec/asm/ecp_sm2p256-armv8.pl @@ -0,0 +1,820 @@ +#! /usr/bin/env perl +# Copyright 2023 The OpenSSL Project Authors. All Rights Reserved. +# +# Licensed under the OpenSSL license (the "License"). You may not use +# this file except in compliance with the License. You can obtain a copy +# in the file LICENSE in the source distribution or at +# https://www.openssl.org/source/license.html + +$flavour = shift; +while (($output=shift) && ($output!~/\w[\w\-]*\.\w+$/)) {} + +$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; +( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or +( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or +die "can't locate arm-xlate.pl"; + +open OUT,"| \"$^X\" $xlate $flavour $output"; +*STDOUT=*OUT; + +my ($s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7)=map("x$_",(7..14)); +my ($a8,$a10,$a12,$a14,$a9,$a11,$a13,$a15)=map("x$_",(7..14)); +my ($t0,$t1,$t2,$t3)=map("x$_",(3..6)); +my ($t4,$t5,$t6,$t7,$t8)=map("x$_",(15..19)); + +sub bn_mod_add() { + my $mod = shift; +$code.=<<___; + # Load inputs + ldp $s0,$s1,[x1] + ldp $s2,$s3,[x1,#16] + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + + # Addition + adds $s0,$s0,$s4 + adcs $s1,$s1,$s5 + adcs $s2,$s2,$s6 + adcs $s3,$s3,$s7 + adc $t4,xzr,xzr + + # Load polynomial + adr x2,$mod + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + + # Backup Addition + mov $t0,$s0 + mov $t1,$s1 + mov $t2,$s2 + mov $t3,$s3 + + # Sub polynomial + subs $t0,$t0,$s4 + sbcs $t1,$t1,$s5 + sbcs $t2,$t2,$s6 + sbcs $t3,$t3,$s7 + sbcs $t4,$t4,xzr + + # Select based on carry + csel $s0,$s0,$t0,cc + csel $s1,$s1,$t1,cc + csel $s2,$s2,$t2,cc + csel $s3,$s3,$t3,cc + + # Store results + stp $s0,$s1,[x0] + stp $s2,$s3,[x0,#16] +___ +} + +sub bn_mod_sub() { + my $mod = shift; +$code.=<<___; + # Load inputs + ldp $s0,$s1,[x1] + ldp $s2,$s3,[x1,#16] + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + + # Subtraction + subs $s0,$s0,$s4 + sbcs $s1,$s1,$s5 + sbcs $s2,$s2,$s6 + sbcs $s3,$s3,$s7 + sbc $t4,xzr,xzr + + # Load polynomial + adr x2,$mod + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + + # Backup subtraction + mov $t0,$s0 + mov $t1,$s1 + mov $t2,$s2 + mov $t3,$s3 + + # Add polynomial + adds $t0,$t0,$s4 + adcs $t1,$t1,$s5 + adcs $t2,$t2,$s6 + adcs $t3,$t3,$s7 + tst $t4,$t4 + + # Select based on carry + csel $s0,$s0,$t0,eq + csel $s1,$s1,$t1,eq + csel $s2,$s2,$t2,eq + csel $s3,$s3,$t3,eq + + # Store results + stp $s0,$s1,[x0] + stp $s2,$s3,[x0,#16] +___ +} + +sub bn_mod_div_by_2() { + my $mod = shift; +$code.=<<___; + # Load inputs + ldp $s0,$s1,[x1] + ldp $s2,$s3,[x1,#16] + + # Save the least significant bit + mov $t0,$s0 + + # Right shift 1 + extr $s0,$s1,$s0,#1 + extr $s1,$s2,$s1,#1 + extr $s2,$s3,$s2,#1 + lsr $s3,$s3,#1 + + # Load mod + adr x2,$mod + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + + # Parity check + tst $t0,#1 + csel $s4,xzr,$s4,eq + csel $s5,xzr,$s5,eq + csel $s6,xzr,$s6,eq + csel $s7,xzr,$s7,eq + + # Add + adds $s0,$s0,$s4 + adcs $s1,$s1,$s5 + adcs $s2,$s2,$s6 + adc $s3,$s3,$s7 + + # Store results + stp $s0,$s1,[x0] + stp $s2,$s3,[x0,#16] +___ +} + +{ +$code.=<<___; +#include "arm_arch.h" +.arch armv8-a +.text + +.align 5 +// The polynomial p +.Lpoly: +.quad 0xffffffffffffffff,0xffffffff00000000,0xffffffffffffffff,0xfffffffeffffffff +// The order of polynomial n +.Lord: +.quad 0x53bbf40939d54123,0x7203df6b21c6052b,0xffffffffffffffff,0xfffffffeffffffff +// (p + 1) / 2 +.Lpoly_div_2: +.quad 0x8000000000000000,0xffffffff80000000,0xffffffffffffffff,0x7fffffff7fffffff +// (n + 1) / 2 +.Lord_div_2: +.quad 0xa9ddfa049ceaa092,0xb901efb590e30295,0xffffffffffffffff,0x7fffffff7fffffff + +// void bn_rshift1(BN_ULONG *a); +.globl bn_rshift1 +.type bn_rshift1,%function +.align 5 +bn_rshift1: + AARCH64_VALID_CALL_TARGET + # Load inputs + ldp $s0,$s1,[x0] + ldp $s2,$s3,[x0,#16] + + # Right shift + extr $s0,$s1,$s0,#1 + extr $s1,$s2,$s1,#1 + extr $s2,$s3,$s2,#1 + lsr $s3,$s3,#1 + + # Store results + stp $s0,$s1,[x0] + stp $s2,$s3,[x0,#16] + + ret +.size bn_rshift1,.-bn_rshift1 + +// void bn_sub(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b); +.globl bn_sub +.type bn_sub,%function +.align 5 +bn_sub: + AARCH64_VALID_CALL_TARGET + # Load inputs + ldp $s0,$s1,[x1] + ldp $s2,$s3,[x1,#16] + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + + # Subtraction + subs $s0,$s0,$s4 + sbcs $s1,$s1,$s5 + sbcs $s2,$s2,$s6 + sbc $s3,$s3,$s7 + + # Store results + stp $s0,$s1,[x0] + stp $s2,$s3,[x0,#16] + + ret +.size bn_sub,.-bn_sub + +// void ecp_sm2p256_div_by_2(BN_ULONG *r,const BN_ULONG *a); +.globl ecp_sm2p256_div_by_2 +.type ecp_sm2p256_div_by_2,%function +.align 5 +ecp_sm2p256_div_by_2: + AARCH64_VALID_CALL_TARGET +___ + &bn_mod_div_by_2(".Lpoly_div_2"); +$code.=<<___; + ret +.size ecp_sm2p256_div_by_2,.-ecp_sm2p256_div_by_2 + +// void ecp_sm2p256_div_by_2_mod_ord(BN_ULONG *r,const BN_ULONG *a); +.globl ecp_sm2p256_div_by_2_mod_ord +.type ecp_sm2p256_div_by_2_mod_ord,%function +.align 5 +ecp_sm2p256_div_by_2_mod_ord: + AARCH64_VALID_CALL_TARGET +___ + &bn_mod_div_by_2(".Lord_div_2"); +$code.=<<___; + ret +.size ecp_sm2p256_div_by_2_mod_ord,.-ecp_sm2p256_div_by_2_mod_ord + +// void ecp_sm2p256_mul_by_3(BN_ULONG *r,const BN_ULONG *a); +.globl ecp_sm2p256_mul_by_3 +.type ecp_sm2p256_mul_by_3,%function +.align 5 +ecp_sm2p256_mul_by_3: + AARCH64_VALID_CALL_TARGET + # Load inputs + ldp $s0,$s1,[x1] + ldp $s2,$s3,[x1,#16] + + # 2*a + adds $s0,$s0,$s0 + adcs $s1,$s1,$s1 + adcs $s2,$s2,$s2 + adcs $s3,$s3,$s3 + adcs $t4,xzr,xzr + + mov $t0,$s0 + mov $t1,$s1 + mov $t2,$s2 + mov $t3,$s3 + + # Sub polynomial + adr x2,.Lpoly + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + subs $s0,$s0,$s4 + sbcs $s1,$s1,$s5 + sbcs $s2,$s2,$s6 + sbcs $s3,$s3,$s7 + sbcs $t4,$t4,xzr + + csel $s0,$s0,$t0,cs + csel $s1,$s1,$t1,cs + csel $s2,$s2,$t2,cs + csel $s3,$s3,$t3,cs + eor $t4,$t4,$t4 + + # 3*a + ldp $s4,$s5,[x1] + ldp $s6,$s7,[x1,#16] + adds $s0,$s0,$s4 + adcs $s1,$s1,$s5 + adcs $s2,$s2,$s6 + adcs $s3,$s3,$s7 + adcs $t4,xzr,xzr + + mov $t0,$s0 + mov $t1,$s1 + mov $t2,$s2 + mov $t3,$s3 + + # Sub polynomial + adr x2,.Lpoly + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + subs $s0,$s0,$s4 + sbcs $s1,$s1,$s5 + sbcs $s2,$s2,$s6 + sbcs $s3,$s3,$s7 + sbcs $t4,$t4,xzr + + csel $s0,$s0,$t0,cs + csel $s1,$s1,$t1,cs + csel $s2,$s2,$t2,cs + csel $s3,$s3,$t3,cs + + # Store results + stp $s0,$s1,[x0] + stp $s2,$s3,[x0,#16] + + ret +.size ecp_sm2p256_mul_by_3,.-ecp_sm2p256_mul_by_3 + +// void ecp_sm2p256_add(BN_ULONG *r,const BN_ULONG *a,const BN_ULONG *b); +.globl ecp_sm2p256_add +.type ecp_sm2p256_add,%function +.align 5 +ecp_sm2p256_add: + AARCH64_VALID_CALL_TARGET +___ + &bn_mod_add(".Lpoly"); +$code.=<<___; + ret +.size ecp_sm2p256_add,.-ecp_sm2p256_add + +// void ecp_sm2p256_sub(BN_ULONG *r,const BN_ULONG *a,const BN_ULONG *b); +.globl ecp_sm2p256_sub +.type ecp_sm2p256_sub,%function +.align 5 +ecp_sm2p256_sub: + AARCH64_VALID_CALL_TARGET +___ + &bn_mod_sub(".Lpoly"); +$code.=<<___; + ret +.size ecp_sm2p256_sub,.-ecp_sm2p256_sub + +// void ecp_sm2p256_sub_mod_ord(BN_ULONG *r,const BN_ULONG *a,const BN_ULONG *b); +.globl ecp_sm2p256_sub_mod_ord +.type ecp_sm2p256_sub_mod_ord,%function +.align 5 +ecp_sm2p256_sub_mod_ord: + AARCH64_VALID_CALL_TARGET +___ + &bn_mod_sub(".Lord"); +$code.=<<___; + ret +.size ecp_sm2p256_sub_mod_ord,.-ecp_sm2p256_sub_mod_ord + +.macro RDC + # a = | s7 | ... | s0 |, where si are 64-bit quantities + # = |a15|a14| ... |a1|a0|, where ai are 32-bit quantities + # | s7 | s6 | s5 | s4 | + # | a15 | a14 | a13 | a12 | a11 | a10 | a9 | a8 | + # | s3 | s2 | s1 | s0 | + # | a7 | a6 | a5 | a4 | a3 | a2 | a1 | a0 | + # ================================================= + # | a8 | a11 | a10 | a9 | a8 | 0 | s4 | (+) + # | a9 | a15 | s6 | a11 | 0 | a10 | a9 | (+) + # | a10 | 0 | a14 | a13 | a12 | 0 | s5 | (+) + # | a11 | 0 | s7 | a13 | 0 | a12 | a11 | (+) + # | a12 | 0 | s7 | a13 | 0 | s6 | (+) + # | a12 | 0 | 0 | a15 | a14 | 0 | a14 | a13 | (+) + # | a13 | 0 | 0 | 0 | a15 | 0 | a14 | a13 | (+) + # | a13 | 0 | 0 | 0 | 0 | 0 | s7 | (+) + # | a14 | 0 | 0 | 0 | 0 | 0 | s7 | (+) + # | a14 | 0 | 0 | 0 | 0 | 0 | 0 | a15 | (+) + # | a15 | 0 | 0 | 0 | 0 | 0 | 0 | a15 | (+) + # | a15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | (+) + # | s7 | 0 | 0 | 0 | 0 | 0 | 0 | (+) + # | 0 | 0 | 0 | 0 | 0 | a8 | 0 | 0 | (-) + # | 0 | 0 | 0 | 0 | 0 | a9 | 0 | 0 | (-) + # | 0 | 0 | 0 | 0 | 0 | a13 | 0 | 0 | (-) + # | 0 | 0 | 0 | 0 | 0 | a14 | 0 | 0 | (-) + # | U[7]| U[6]| U[5]| U[4]| U[3]| U[2]| U[1]| U[0]| + # | V[3] | V[2] | V[1] | V[0] | + + # 1. 64-bit addition + # t2=s6+s7+s7 + adds $t2,$s6,$s7 + adcs $t1,xzr,xzr + adds $t2,$t2,$s7 + adcs $t1,$t1,xzr + # t3=s4+s5+t2 + adds $t3,$s4,$t2 + adcs $t4,$t1,xzr + adds $t3,$t3,$s5 + adcs $t4,$t4,xzr + # sum + adds $s0,$s0,$t3 + adcs $s1,$s1,$t4 + adcs $s2,$s2,$t2 + adcs $s3,$s3,$s7 + adcs $t0,xzr,xzr + adds $s3,$s3,$t1 + adcs $t0,$t0,xzr + + stp $s0,$s1,[sp,#32] + stp $s2,$s3,[sp,#48] + + # 2. 64-bit to 32-bit spread + mov $t1,#0xffffffff + mov $s0,$s4 + mov $s1,$s5 + mov $s2,$s6 + mov $s3,$s7 + and $s0,$s0,$t1 // a8 + and $s1,$s1,$t1 // a10 + and $s2,$s2,$t1 // a12 + and $s3,$s3,$t1 // a14 + lsr $s4,$s4,#32 // a9 + lsr $s5,$s5,#32 // a11 + lsr $s6,$s6,#32 // a13 + lsr $s7,$s7,#32 // a15 + + # 3. 32-bit addition + add $t1,$a14,$a12 // t1 <- a12 + a14 + add $t2,$a15,$a13 // t2 <- a13 + a15 + add $t3,$a8,$a9 // t3 <- a8 + a9 + add $t4,$a14,$a10 // t4 <- a10 + a14 + add $a15,$a15,$a11 // a15 <- a11 + a15 + add $a12,$t2,$t1 // a12 <- a12 + a13 + a14 + a15 + add $a10,$a10,$a12 // a10 <- a10 + a12 + a13 + a14 + a15 + add $a10,$a10,$a12 // a10 <- a10 + 2*(a12 + a13 + a14 + a15) + add $a10,$a10,$t3 // a10 <- a8 + a9 + a10 + 2*(a12 + a13 + a14 + a15) + add $a10,$a10,$a11 // a10 <- a8 + a9 + a10 + a11 + 2*(a12 + a13 + a14 + a15) + add $a12,$a12,$a13 // a12 <- a12 + 2*a13 + a14 + a15 + add $a12,$a12,$a11 // a12 <- a11 + a12 + 2*a13 + a14 + a15 + add $a12,$a12,$a8 // a12 <- a8 + a11 + a12 + 2*a13 + a14 + a15 + add $t3,$t3,$a14 // t3 <- a8 + a9 + a14 + add $t3,$t3,$a13 // t3 <- a8 + a9 + a13 + a14 + add $a9,$a9,$t2 // a9 <- a9 + a13 + a15 + add $a11,$a11,$a9 // a11 <- a9 + a11 + a13 + a15 + add $a11,$a11,$t2 // a11 <- a9 + a11 + 2*(a13 + a15) + add $t1,$t1,$t4 // t1 <- a10 + a12 + 2*a14 + + # U[0] s5 a9 + a11 + 2*(a13 + a15) + # U[1] t1 a10 + a12 + 2*a14 + # U[2] -t3 a8 + a9 + a13 + a14 + # U[3] s2 a8 + a11 + a12 + 2*a13 + a14 + a15 + # U[4] s4 a9 + a13 + a15 + # U[5] t4 a10 + a14 + # U[6] s7 a11 + a15 + # U[7] s1 a8 + a9 + a10 + a11 + 2*(a12 + a13 + a14 + a15) + + # 4. 32-bit to 64-bit + lsl $s0,$t1,#32 + extr $t1,$s2,$t1,#32 + extr $s2,$t4,$s2,#32 + extr $t4,$s1,$t4,#32 + lsr $s1,$s1,#32 + + # 5. 64-bit addition + adds $s5,$s5,$s0 + adcs $t1,$t1,xzr + adcs $s4,$s4,$s2 + adcs $s7,$s7,$t4 + adcs $t0,$t0,$s1 + + # V[0] s5 + # V[1] t1 + # V[2] s4 + # V[3] s7 + # carry t0 + # sub t3 + + # 5. Process s0-s3 + ldp $s0,$s1,[sp,#32] + ldp $s2,$s3,[sp,#48] + # add with V0-V3 + adds $s0,$s0,$s5 + adcs $s1,$s1,$t1 + adcs $s2,$s2,$s4 + adcs $s3,$s3,$s7 + adcs $t0,$t0,xzr + # sub with t3 + subs $s1,$s1,$t3 + sbcs $s2,$s2,xzr + sbcs $s3,$s3,xzr + sbcs $t0,$t0,xzr + + # 6. MOD + # First Mod + lsl $t1,$t0,#32 + subs $t2,$t1,$t0 + + adds $s0,$s0,$t0 + adcs $s1,$s1,$t2 + adcs $s2,$s2,xzr + adcs $s3,$s3,$t1 + + # Last Mod + # return y - p if y > p else y + mov $s4,$s0 + mov $s5,$s1 + mov $s6,$s2 + mov $s7,$s3 + + adr $t0,.Lpoly + ldp $t1,$t2,[$t0] + ldp $t3,$t4,[$t0,#16] + + adcs $t5,xzr,xzr + + subs $s0,$s0,$t1 + sbcs $s1,$s1,$t2 + sbcs $s2,$s2,$t3 + sbcs $s3,$s3,$t4 + sbcs $t5,$t5,xzr + + csel $s0,$s0,$s4,cs + csel $s1,$s1,$s5,cs + csel $s2,$s2,$s6,cs + csel $s3,$s3,$s7,cs + +.endm + +// void ecp_sm2p256_mul(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b); +.globl ecp_sm2p256_mul +.type ecp_sm2p256_mul,%function +.align 5 +ecp_sm2p256_mul: + AARCH64_SIGN_LINK_REGISTER + # Store scalar registers + stp x29,x30,[sp,#-80]! + add x29,sp,#0 + stp x16,x17,[sp,#16] + stp x18,x19,[sp,#64] + + # Load inputs + ldp $s0,$s1,[x1] + ldp $s2,$s3,[x1,#16] + ldp $s4,$s5,[x2] + ldp $s6,$s7,[x2,#16] + +### multiplication ### + # ======================== + # s3 s2 s1 s0 + # * s7 s6 s5 s4 + # ------------------------ + # + s0 s0 s0 s0 + # * * * * + # s7 s6 s5 s4 + # s1 s1 s1 s1 + # * * * * + # s7 s6 s5 s4 + # s2 s2 s2 s2 + # * * * * + # s7 s6 s5 s4 + # s3 s3 s3 s3 + # * * * * + # s7 s6 s5 s4 + # ------------------------ + # s7 s6 s5 s4 s3 s2 s1 s0 + # ======================== + +### s0*s4 ### + mul $t5,$s0,$s4 + umulh $t2,$s0,$s4 + +### s1*s4 + s0*s5 ### + mul $t0,$s1,$s4 + umulh $t1,$s1,$s4 + adds $t2,$t2,$t0 + adcs $t3,$t1,xzr + + mul $t0,$s0,$s5 + umulh $t1,$s0,$s5 + adds $t2,$t2,$t0 + adcs $t3,$t3,$t1 + adcs $t4,xzr,xzr + +### s2*s4 + s1*s5 + s0*s6 ### + mul $t0,$s2,$s4 + umulh $t1,$s2,$s4 + adds $t3,$t3,$t0 + adcs $t4,$t4,$t1 + + mul $t0,$s1,$s5 + umulh $t1,$s1,$s5 + adds $t3,$t3,$t0 + adcs $t4,$t4,$t1 + adcs $t6,xzr,xzr + + mul $t0,$s0,$s6 + umulh $t1,$s0,$s6 + adds $t3,$t3,$t0 + adcs $t4,$t4,$t1 + adcs $t6,$t6,xzr + +### s3*s4 + s2*s5 + s1*s6 + s0*s7 ### + mul $t0,$s3,$s4 + umulh $t1,$s3,$s4 + adds $t4,$t4,$t0 + adcs $t6,$t6,$t1 + adcs $t7,xzr,xzr + + mul $t0,$s2,$s5 + umulh $t1,$s2,$s5 + adds $t4,$t4,$t0 + adcs $t6,$t6,$t1 + adcs $t7,$t7,xzr + + mul $t0,$s1,$s6 + umulh $t1,$s1,$s6 + adds $t4,$t4,$t0 + adcs $t6,$t6,$t1 + adcs $t7,$t7,xzr + + mul $t0,$s0,$s7 + umulh $t1,$s0,$s7 + adds $t4,$t4,$t0 + adcs $t6,$t6,$t1 + adcs $t7,$t7,xzr + +### s3*s5 + s2*s6 + s1*s7 ### + mul $t0,$s3,$s5 + umulh $t1,$s3,$s5 + adds $t6,$t6,$t0 + adcs $t7,$t7,$t1 + adcs $t8,xzr,xzr + + mul $t0,$s2,$s6 + umulh $t1,$s2,$s6 + adds $t6,$t6,$t0 + adcs $t7,$t7,$t1 + adcs $t8,$t8,xzr + + mul $t0,$s1,$s7 + umulh $t1,$s1,$s7 + adds $s4,$t6,$t0 + adcs $t7,$t7,$t1 + adcs $t8,$t8,xzr + +### s3*s6 + s2*s7 ### + mul $t0,$s3,$s6 + umulh $t1,$s3,$s6 + adds $t7,$t7,$t0 + adcs $t8,$t8,$t1 + adcs $t6,xzr,xzr + + mul $t0,$s2,$s7 + umulh $t1,$s2,$s7 + adds $s5,$t7,$t0 + adcs $t8,$t8,$t1 + adcs $t6,$t6,xzr + +### s3*s7 ### + mul $t0,$s3,$s7 + umulh $t1,$s3,$s7 + adds $s6,$t8,$t0 + adcs $s7,$t6,$t1 + + mov $s0,$t5 + mov $s1,$t2 + mov $s2,$t3 + mov $s3,$t4 + + # result of mul: s7 s6 s5 s4 s3 s2 s1 s0 + +### Reduction ### + RDC + + stp $s0,$s1,[x0] + stp $s2,$s3,[x0,#16] + + # Restore scalar registers + ldp x16,x17,[sp,#16] + ldp x18,x19,[sp,#64] + ldp x29,x30,[sp],#80 + + AARCH64_VALIDATE_LINK_REGISTER + ret +.size ecp_sm2p256_mul,.-ecp_sm2p256_mul + +// void ecp_sm2p256_sqr(BN_ULONG *r, const BN_ULONG *a); +.globl ecp_sm2p256_sqr +.type ecp_sm2p256_sqr,%function +.align 5 + +ecp_sm2p256_sqr: + AARCH64_SIGN_LINK_REGISTER + # Store scalar registers + stp x29,x30,[sp,#-80]! + add x29,sp,#0 + stp x16,x17,[sp,#16] + stp x18,x19,[sp,#64] + + # Load inputs + ldp $s4,$s5,[x1] + ldp $s6,$s7,[x1,#16] + +### square ### + # ======================== + # s7 s6 s5 s4 + # * s7 s6 s5 s4 + # ------------------------ + # + s4 s4 s4 s4 + # * * * * + # s7 s6 s5 s4 + # s5 s5 s5 s5 + # * * * * + # s7 s6 s5 s4 + # s6 s6 s6 s6 + # * * * * + # s7 s6 s5 s4 + # s7 s7 s7 s7 + # * * * * + # s7 s6 s5 s4 + # ------------------------ + # s7 s6 s5 s4 s3 s2 s1 s0 + # ======================== + +### s4*s5 ### + mul $s1,$s4,$s5 + umulh $s2,$s4,$s5 + +### s4*s6 ### + mul $t0,$s6,$s4 + umulh $s3,$s6,$s4 + adds $s2,$s2,$t0 + adcs $s3,$s3,xzr + +### s4*s7 + s5*s6 ### + mul $t0,$s7,$s4 + umulh $t1,$s7,$s4 + adds $s3,$s3,$t0 + adcs $s0,$t1,xzr + + mul $t0,$s6,$s5 + umulh $t1,$s6,$s5 + adds $s3,$s3,$t0 + adcs $s0,$s0,$t1 + adcs $t2,xzr,xzr + +### s5*s7 ### + mul $t0,$s7,$s5 + umulh $t1,$s7,$s5 + adds $s0,$s0,$t0 + adcs $t2,$t2,$t1 + +### s6*s7 ### + mul $t0,$s7,$s6 + umulh $t1,$s7,$s6 + adds $t2,$t2,$t0 + adcs $t3,$t1,xzr + +### 2*(t3,t2,s0,s3,s2,s1) ### + adds $s1,$s1,$s1 + adcs $s2,$s2,$s2 + adcs $s3,$s3,$s3 + adcs $s0,$s0,$s0 + adcs $t2,$t2,$t2 + adcs $t3,$t3,$t3 + adcs $t4,xzr,xzr + +### s4*s4 ### + mul $t5,$s4,$s4 + umulh $t6,$s4,$s4 + +### s5*s5 ### + mul $s4,$s5,$s5 + umulh $s5,$s5,$s5 + +### s6*s6 ### + mul $t0,$s6,$s6 + umulh $t1,$s6,$s6 + +### s7*s7 ### + mul $t7,$s7,$s7 + umulh $t8,$s7,$s7 + + adds $s1,$s1,$t6 + adcs $s2,$s2,$s4 + adcs $s3,$s3,$s5 + adcs $s0,$s0,$t0 + adcs $t2,$t2,$t1 + adcs $t3,$t3,$t7 + adcs $t4,$t4,$t8 + + mov $s4,$s0 + mov $s0,$t5 + mov $s5,$t2 + mov $s6,$t3 + mov $s7,$t4 + + # result of mul: s7 s6 s5 s4 s3 s2 s1 s0 + +### Reduction ### + RDC + + stp $s0,$s1,[x0] + stp $s2,$s3,[x0,#16] + + # Restore scalar registers + ldp x16,x17,[sp,#16] + ldp x18,x19,[sp,#64] + ldp x29,x30,[sp],#80 + + AARCH64_VALIDATE_LINK_REGISTER + ret +.size ecp_sm2p256_sqr,.-ecp_sm2p256_sqr +___ +} + +foreach (split("\n",$code)) { + s/\`([^\`]*)\`/eval $1/ge; + + print $_,"\n"; +} +close STDOUT or die "error closing STDOUT: $!"; # enforce flush diff --git a/crypto/ec/build.info b/crypto/ec/build.info index 4077bead7b..2f376a39c6 100644 --- a/crypto/ec/build.info +++ b/crypto/ec/build.info @@ -31,6 +31,13 @@ IF[{- !$disabled{asm} -}] $ECDEF_armv4=ECP_NISTZ256_ASM $ECASM_aarch64=ecp_nistz256.c ecp_nistz256-armv8.S $ECDEF_aarch64=ECP_NISTZ256_ASM + IF[{- !$disabled{'sm2'} -}] + $ECASM_aarch64=$ECASM_aarch64 ecp_sm2p256.c ecp_sm2p256-armv8.S + IF[{- !$disabled{'sm2-precomp'} -}] + $ECASM_aarch64=$ECASM_aarch64 ecp_sm2p256_table.c + ENDIF + $ECDEF_aarch64=$ECDEF_aarch64 ECP_SM2P256_ASM + ENDIF $ECASM_parisc11= $ECASM_parisc20_64= @@ -127,3 +134,8 @@ IF[{- !$disabled{'ecx'} -}] GENERATE[x25519-x86_64.s]=asm/x25519-x86_64.pl GENERATE[x25519-ppc64.s]=asm/x25519-ppc64.pl ENDIF + +IF[{- !$disabled{'sm2'} -}] + GENERATE[ecp_sm2p256-armv8.S]=asm/ecp_sm2p256-armv8.pl + INCLUDE[ecp_sm2p256-armv8.o]=.. +ENDIF diff --git a/crypto/ec/ec_curve.c b/crypto/ec/ec_curve.c index 724525a479..d703d16b3c 100644 --- a/crypto/ec/ec_curve.c +++ b/crypto/ec/ec_curve.c @@ -1,5 +1,5 @@ /* - * Copyright 2002-2021 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2002-2023 The OpenSSL Project Authors. All Rights Reserved. * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved * * Licensed under the Apache License 2.0 (the "License"). You may not use @@ -3111,8 +3111,13 @@ static const ec_list_element curve_list[] = { "RFC 5639 curve over a 512 bit prime field"}, {NID_brainpoolP512t1, &_EC_brainpoolP512t1.h, 0, "RFC 5639 curve over a 512 bit prime field"}, -# ifndef OPENSSL_NO_SM2 - {NID_sm2, &_EC_sm2p256v1.h, 0, +#ifndef OPENSSL_NO_SM2 + {NID_sm2, &_EC_sm2p256v1.h, +# ifdef ECP_SM2P256_ASM + EC_GFp_sm2p256_method, +# else + 0, +# endif "SM2 curve over a 256 bit prime field"}, # endif }; diff --git a/crypto/ec/ec_local.h b/crypto/ec/ec_local.h index 7181090fca..803786fdd2 100644 --- a/crypto/ec/ec_local.h +++ b/crypto/ec/ec_local.h @@ -653,6 +653,11 @@ int ossl_ec_key_simple_generate_key(EC_KEY *eckey); int ossl_ec_key_simple_generate_public_key(EC_KEY *eckey); int ossl_ec_key_simple_check_key(const EC_KEY *eckey); +#ifdef ECP_SM2P256_ASM +/* Returns optimized methods for SM2 */ +const EC_METHOD *EC_GFp_sm2p256_method(void); +#endif + int ossl_ec_curve_nid_from_params(const EC_GROUP *group, BN_CTX *ctx); /* EC_METHOD definitions */ diff --git a/crypto/ec/ecp_sm2p256.c b/crypto/ec/ecp_sm2p256.c new file mode 100644 index 0000000000..49fab47187 --- /dev/null +++ b/crypto/ec/ecp_sm2p256.c @@ -0,0 +1,800 @@ +/* + * Copyright 2023 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the Apache License 2.0 (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + * + */ + +/* + * SM2 low level APIs are deprecated for public use, but still ok for + * internal use. + */ +#include "internal/deprecated.h" + +#include <string.h> +#include <openssl/err.h> +#include "crypto/bn.h" +#include "ec_local.h" +#include "internal/constant_time.h" + +#if defined(__GNUC__) +# define ALIGN32 __attribute((aligned(32))) +# define ALIGN64 __attribute((aligned(64))) +#elif defined(_MSC_VER) +# define ALIGN32 __declspec(align(32)) +# define ALIGN64 __declspec(align(64)) +#else +# define ALIGN32 +# define ALIGN64 +#endif + +#define P256_LIMBS (256 / BN_BITS2) + +#if !defined(OPENSSL_NO_SM2_PRECOMP) +extern const BN_ULONG ecp_sm2p256_precomputed[8 * 32 * 256]; +#endif + +typedef struct { + BN_ULONG X[P256_LIMBS]; + BN_ULONG Y[P256_LIMBS]; + BN_ULONG Z[P256_LIMBS]; +} P256_POINT; + +typedef struct { + BN_ULONG X[P256_LIMBS]; + BN_ULONG Y[P256_LIMBS]; +} P256_POINT_AFFINE; + +#if !defined(OPENSSL_NO_SM2_PRECOMP) +/* Coordinates of G, for which we have precomputed tables */ +static const BN_ULONG def_xG[P256_LIMBS] ALIGN32 = { + 0x715a4589334c74c7, 0x8fe30bbff2660be1, + 0x5f9904466a39c994, 0x32c4ae2c1f198119 +}; + +static const BN_ULONG def_yG[P256_LIMBS] ALIGN32 = { + 0x02df32e52139f0a0, 0xd0a9877cc62a4740, + 0x59bdcee36b692153, 0xbc3736a2f4f6779c, +}; +#endif + +/* p and order for SM2 according to GB/T 32918.5-2017 */ +static const BN_ULONG def_p[P256_LIMBS] ALIGN32 = { + 0xffffffffffffffff, 0xffffffff00000000, + 0xffffffffffffffff, 0xfffffffeffffffff +}; +static const BN_ULONG def_ord[P256_LIMBS] ALIGN32 = { + 0x53bbf40939d54123, 0x7203df6b21c6052b, + 0xffffffffffffffff, 0xfffffffeffffffff +}; + +static const BN_ULONG ONE[P256_LIMBS] ALIGN32 = {1, 0, 0, 0}; + +/* Functions implemented in assembly */ +/* + * Most of below mentioned functions *preserve* the property of inputs + * being fully reduced, i.e. being in [0, modulus) range. Simply put if + * inputs are fully reduced, then output is too. + */ +/* Right shift: a >> 1 */ +void bn_rshift1(BN_ULONG *a); +/* Sub: r = a - b */ +void bn_sub(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b); +/* Modular div by 2: r = a / 2 mod p */ +void ecp_sm2p256_div_by_2(BN_ULONG *r, const BN_ULONG *a); +/* Modular div by 2: r = a / 2 mod n, where n = ord(p) */ +void ecp_sm2p256_div_by_2_mod_ord(BN_ULONG *r, const BN_ULONG *a); +/* Modular add: r = a + b mod p */ +void ecp_sm2p256_add(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b); +/* Modular sub: r = a - b mod p */ +void ecp_sm2p256_sub(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b); +/* Modular sub: r = a - b mod n, where n = ord(p) */ +void ecp_sm2p256_sub_mod_ord(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b); +/* Modular mul by 3: out = 3 * a mod p */ +void ecp_sm2p256_mul_by_3(BN_ULONG *r, const BN_ULONG *a); +/* Modular mul: r = a * b mod p */ +void ecp_sm2p256_mul(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b); +/* Modular sqr: r = a ^ 2 mod p */ +void ecp_sm2p256_sqr(BN_ULONG *r, const BN_ULONG *a); + +static ossl_inline BN_ULONG is_zeros(const BN_ULONG *a) +{ + BN_ULONG res; + + res = a[0] | a[1] | a[2] | a[3]; + + return constant_time_is_zero_64(res); +} + +static ossl_inline int is_equal(const BN_ULONG *a, const BN_ULONG *b) +{ + BN_ULONG res; + + res = a[0] ^ b[0]; + res |= a[1] ^ b[1]; + res |= a[2] ^ b[2]; + res |= a[3] ^ b[3]; + + return constant_time_is_zero_64(res); +} + +static ossl_inline int is_greater(const BN_ULONG *a, const BN_ULONG *b) +{ + int i; + + for (i = P256_LIMBS - 1; i >= 0; --i) { + if (a[i] > b[i]) + return 1; + if (a[i] < b[i]) + return -1; + } + + return 0; +} + +#define is_one(a) is_equal(a, ONE) +#define is_even(a) !(a[0] & 1) +#define is_point_equal(a, b) \ + is_equal(a->X, b->X) && \ + is_equal(a->Y, b->Y) && \ + is_equal(a->Z, b->Z) + +/* Bignum and field elements conversion */ +#define ecp_sm2p256_bignum_field_elem(out, in) \ + bn_copy_words(out, in, P256_LIMBS) + +/* Binary algorithm for inversion in Fp */ +#define BN_MOD_INV(out, in, mod_div, mod_sub, mod) \ + do { \ + BN_ULONG u[4] ALIGN32; \ + BN_ULONG v[4] ALIGN32; \ + BN_ULONG x1[4] ALIGN32 = {1, 0, 0, 0}; \ + BN_ULONG x2[4] ALIGN32 = {0}; \ + \ + if (is_zeros(in)) \ + return; \ + memcpy(u, in, 32); \ + memcpy(v, mod, 32); \ + while (!is_one(u) && !is_one(v)) { \ + while (is_even(u)) { \ + bn_rshift1(u); \ + mod_div(x1, x1); \ + } \ + while (is_even(v)) { \ + bn_rshift1(v); \ + mod_div(x2, x2); \ + } \ + if (is_greater(u, v) == 1) { \ + bn_sub(u, u, v); \ + mod_sub(x1, x1, x2); \ + } else { \ + bn_sub(v, v, u); \ + mod_sub(x2, x2, x1); \ + } \ + } \ + if (is_one(u)) \ + memcpy(out, x1, 32); \ + else \ + memcpy(out, x2, 32); \ + } while (0) + +/* Modular inverse |out| = |in|^(-1) mod |p|. */ +static ossl_inline void ecp_sm2p256_mod_inverse(BN_ULONG* out, + const BN_ULONG* in) { + BN_MOD_INV(out, in, ecp_sm2p256_div_by_2, ecp_sm2p256_sub, def_p); +} + +/* Modular inverse mod order |out| = |in|^(-1) % |ord|. */ +static ossl_inline void ecp_sm2p256_mod_ord_inverse(BN_ULONG* out, + const BN_ULONG* in) { + BN_MOD_INV(out, in, ecp_sm2p256_div_by_2_mod_ord, ecp_sm2p256_sub_mod_ord, + def_ord); +} + +/* Point double: R <- P + P */ +static void ecp_sm2p256_point_double(P256_POINT *R, const P256_POINT *P) +{ + unsigned int i; + BN_ULONG tmp0[P256_LIMBS] ALIGN32; + BN_ULONG tmp1[P256_LIMBS] ALIGN32; + BN_ULONG tmp2[P256_LIMBS] ALIGN32; + + /* zero-check P->Z */ + if (is_zeros(P->Z)) { + for (i = 0; i < P256_LIMBS; ++i) + R->Z[i] = 0; + + return; + } + + ecp_sm2p256_sqr(tmp0, P->Z); + ecp_sm2p256_sub(tmp1, P->X, tmp0); + ecp_sm2p256_add(tmp0, P->X, tmp0); + ecp_sm2p256_mul(tmp1, tmp1, tmp0); + ecp_sm2p256_mul_by_3(tmp1, tmp1); + ecp_sm2p256_add(R->Y, P->Y, P->Y); + ecp_sm2p256_mul(R->Z, R->Y, P->Z); + ecp_sm2p256_sqr(R->Y, R->Y); + ecp_sm2p256_mul(tmp2, R->Y, P->X); + ecp_sm2p256_sqr(R->Y, R->Y); + ecp_sm2p256_div_by_2(R->Y, R->Y); + ecp_sm2p256_sqr(R->X, tmp1); + ecp_sm2p256_add(tmp0, tmp2, tmp2); + ecp_sm2p256_sub(R->X, R->X, tmp0); + ecp_sm2p256_sub(tmp0, tmp2, R->X); + ecp_sm2p256_mul(tmp0, tmp0, tmp1); + ecp_sm2p256_sub(tmp1, tmp0, R->Y); + memcpy(R->Y, tmp1, 32); +} + +/* Point add affine: R <- P + Q */ +static void ecp_sm2p256_point_add_affine(P256_POINT *R, const P256_POINT *P, + const P256_POINT_AFFINE *Q) +{ + unsigned int i; + BN_ULONG tmp0[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG tmp1[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG tmp2[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG tmp3[P256_LIMBS] ALIGN32 = {0}; + + /* zero-check P->Z */ + if (is_zeros(P->Z)) { + for (i = 0; i < P256_LIMBS; ++i) { + R->X[i] = Q->X[i]; + R->Y[i] = Q->Y[i]; + R->Z[i] = 0; + } + R->Z[0] = 1; + + return; + } + + ecp_sm2p256_sqr(tmp0, P->Z); + ecp_sm2p256_mul(tmp1, tmp0, P->Z); + ecp_sm2p256_mul(tmp0, tmp0, Q->X); + ecp_sm2p256_mul(tmp1, tmp1, Q->Y); + ecp_sm2p256_sub(tmp0, tmp0, P->X); + ecp_sm2p256_sub(tmp1, tmp1, P->Y); + + /* zero-check tmp0, tmp1 */ + if (is_zeros(tmp0)) { + if (is_zeros(tmp1)) { + P256_POINT K; + + for (i = 0; i < P256_LIMBS; ++i) { + K.X[i] = Q->X[i]; + K.Y[i] = Q->Y[i]; + K.Z[i] = 0; + } + K.Z[0] = 1; + ecp_sm2p256_point_double(R, &K); + } else { + for (i = 0; i < P256_LIMBS; ++i) + R->Z[i] = 0; + } + + return; + } + + ecp_sm2p256_mul(R->Z, P->Z, tmp0); + ecp_sm2p256_sqr(tmp2, tmp0); + ecp_sm2p256_mul(tmp3, tmp2, tmp0); + ecp_sm2p256_mul(tmp2, tmp2, P->X); + ecp_sm2p256_add(tmp0, tmp2, tmp2); + ecp_sm2p256_sqr(R->X, tmp1); + ecp_sm2p256_sub(R->X, R->X, tmp0); + ecp_sm2p256_sub(R->X, R->X, tmp3); + ecp_sm2p256_sub(tmp2, tmp2, R->X); + ecp_sm2p256_mul(tmp2, tmp2, tmp1); + ecp_sm2p256_mul(tmp3, tmp3, P->Y); + ecp_sm2p256_sub(R->Y, tmp2, tmp3); +} + +/* Point add: R <- P + Q */ +static void ecp_sm2p256_point_add(P256_POINT *R, const P256_POINT *P, + const P256_POINT *Q) +{ + unsigned int i; + BN_ULONG tmp0[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG tmp1[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG tmp2[P256_LIMBS] ALIGN32 = {0}; + + /* zero-check P | Q ->Z */ + if (is_zeros(P->Z)) { + for (i = 0; i < P256_LIMBS; ++i) { + R->X[i] = Q->X[i]; + R->Y[i] = Q->Y[i]; + R->Z[i] = Q->Z[i]; + } + + return; + } else if (is_zeros(Q->Z)) { + for (i = 0; i < P256_LIMBS; ++i) { + R->X[i] = P->X[i]; + R->Y[i] = P->Y[i]; + R->Z[i] = P->Z[i]; + } + + return; + } else if (is_point_equal(P, Q)) { + ecp_sm2p256_point_double(R, Q); + + return; + } + + ecp_sm2p256_sqr(tmp0, P->Z); + ecp_sm2p256_mul(tmp1, tmp0, P->Z); + ecp_sm2p256_mul(tmp0, tmp0, Q->X); + ecp_sm2p256_mul(tmp1, tmp1, Q->Y); + ecp_sm2p256_mul(R->Y, P->Y, Q->Z); + ecp_sm2p256_mul(R->Z, Q->Z, P->Z); + ecp_sm2p256_sqr(tmp2, Q->Z); + ecp_sm2p256_mul(R->Y, tmp2, R->Y); + ecp_sm2p256_mul(R->X, tmp2, P->X); + ecp_sm2p256_sub(tmp0, tmp0, R->X); + ecp_sm2p256_mul(R->Z, tmp0, R->Z); + ecp_sm2p256_sub(tmp1, tmp1, R->Y); + ecp_sm2p256_sqr(tmp2, tmp0); + ecp_sm2p256_mul(tmp0, tmp0, tmp2); + ecp_sm2p256_mul(tmp2, tmp2, R->X); + ecp_sm2p256_sqr(R->X, tmp1); + ecp_sm2p256_sub(R->X, R->X, tmp2); + ecp_sm2p256_sub(R->X, R->X, tmp2); + ecp_sm2p256_sub(R->X, R->X, tmp0); + ecp_sm2p256_sub(tmp2, tmp2, R->X); + ecp_sm2p256_mul(tmp2, tmp1, tmp2); + ecp_sm2p256_mul(tmp0, tmp0, R->Y); + ecp_sm2p256_sub(R->Y, tmp2, tmp0); +} + +#if !defined(OPENSSL_NO_SM2_PRECOMP) +/* Base point mul by scalar: k - scalar, G - base point */ +static void ecp_sm2p256_point_G_mul_by_scalar(P256_POINT *R, const BN_ULONG *k) +{ + unsigned int i, index, mask = 0xff; + P256_POINT_AFFINE Q; + + memset(R, 0, sizeof(P256_POINT)); + + if (is_zeros(k)) + return; + + index = k[0] & mask; + if (index) { + index = index * 8; + memcpy(R->X, ecp_sm2p256_precomputed + index, 32); + memcpy(R->Y, ecp_sm2p256_precomputed + index + P256_LIMBS, 32); + R->Z[0] = 1; + } + + for (i = 1; i < 32; ++i) { + index = (k[i / 8] >> (8 * (i % 8))) & mask; + + if (index) { + index = index + i * 256; + index = index * 8; + memcpy(Q.X, ecp_sm2p256_precomputed + index, 32); + memcpy(Q.Y, ecp_sm2p256_precomputed + index + P256_LIMBS, 32); + ecp_sm2p256_point_add_affine(R, R, &Q); + } + } +} +#endif + +/* + * Affine point mul by scalar: k - scalar, P - affine point + */ +static void ecp_sm2p256_point_P_mul_by_scalar(P256_POINT *R, const BN_ULONG *k, + P256_POINT_AFFINE P) +{ + int i, init = 0; + unsigned int index, mask = 0x0f; + P256_POINT precomputed[16] ALIGN64; + + memset(R, 0, sizeof(P256_POINT)); + + if (is_zeros(k)) + return; + + /* The first value of the precomputed table is P. */ + memcpy(precomputed[1].X, P.X, 32); + memcpy(precomputed[1].Y, P.Y, 32); + precomputed[1].Z[0] = 1; + precomputed[1].Z[1] = 0; + precomputed[1].Z[2] = 0; + precomputed[1].Z[3] = 0; + + /* The second value of the precomputed table is 2P. */ + ecp_sm2p256_point_double(&precomputed[2], &precomputed[1]); + + /* The subsequent elements are 3P, 4P, and so on. */ + for (i = 3; i < 16; ++i) + ecp_sm2p256_point_add_affine(&precomputed[i], &precomputed[i - 1], &P); + + for (i = 64 - 1; i >= 0; --i) { + index = (k[i / 16] >> (4 * (i % 16))) & mask; + + if (init == 0) { + if (index) { + memcpy(R, &precomputed[index], sizeof(P256_POINT)); + init = 1; + } + } else { + ecp_sm2p256_point_double(R, R); + ecp_sm2p256_point_double(R, R); + ecp_sm2p256_point_double(R, R); + ecp_sm2p256_point_double(R, R); + if (index) + ecp_sm2p256_point_add(R, R, &precomputed[index]); + } + } +} + +/* Get affine point */ +static void ecp_sm2p256_point_get_affine(P256_POINT_AFFINE *R, + const P256_POINT *P) +{ + BN_ULONG z_inv3[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG z_inv2[P256_LIMBS] ALIGN32 = {0}; + + if (is_one(P->Z)) { + memcpy(R->X, P->X, 32); + memcpy(R->Y, P->Y, 32); + return; + } + + ecp_sm2p256_mod_inverse(z_inv3, P->Z); + ecp_sm2p256_sqr(z_inv2, z_inv3); + ecp_sm2p256_mul(R->X, P->X, z_inv2); + ecp_sm2p256_mul(z_inv3, z_inv3, z_inv2); + ecp_sm2p256_mul(R->Y, P->Y, z_inv3); +} + +#if !defined(OPENSSL_NO_SM2_PRECOMP) +static int ecp_sm2p256_is_affine_G(const EC_POINT *generator) +{ + return (bn_get_top(generator->X) == P256_LIMBS) + && (bn_get_top(generator->Y) == P256_LIMBS) + && is_equal(bn_get_words(generator->X), def_xG) + && is_equal(bn_get_words(generator->Y), def_yG) + && (generator->Z_is_one == 1); +} +#endif + +/* + * Convert Jacobian coordinate point into affine coordinate (x,y) + */ +static int ecp_sm2p256_get_affine(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, BN_CTX *ctx) +{ + BN_ULONG z_inv2[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG z_inv3[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG x_aff[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG y_aff[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG point_x[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG point_y[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG point_z[P256_LIMBS] ALIGN32 = {0}; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(ERR_LIB_EC, EC_R_POINT_AT_INFINITY); + return 0; + } + + if (ecp_sm2p256_bignum_field_elem(point_x, point->X) <= 0 + || ecp_sm2p256_bignum_field_elem(point_y, point->Y) <= 0 + || ecp_sm2p256_bignum_field_elem(point_z, point->Z) <= 0) { + ECerr(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); + return 0; + } + + ecp_sm2p256_mod_inverse(z_inv3, point_z); + ecp_sm2p256_sqr(z_inv2, z_inv3); + + if (x != NULL) { + ecp_sm2p256_mul(x_aff, point_x, z_inv2); + if (!bn_set_words(x, x_aff, P256_LIMBS)) + return 0; + } + + if (y != NULL) { + ecp_sm2p256_mul(z_inv3, z_inv3, z_inv2); + ecp_sm2p256_mul(y_aff, point_y, z_inv3); + if (!bn_set_words(y, y_aff, P256_LIMBS)) + return 0; + } + + return 1; +} + +/* r = sum(scalar[i]*point[i]) */ +static int ecp_sm2p256_windowed_mul(const EC_GROUP *group, + P256_POINT *r, + const BIGNUM **scalar, + const EC_POINT **point, + size_t num, BN_CTX *ctx) +{ + unsigned int i; + int ret = 0; + const BIGNUM **scalars = NULL; + BN_ULONG k[P256_LIMBS] ALIGN32 = {0}; + P256_POINT kP; + ALIGN32 union { + P256_POINT p; + P256_POINT_AFFINE a; + } t, p; + + if (num > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT) + || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) { + ECerr(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); + goto err; + } + + memset(r, 0, sizeof(P256_POINT)); + + for (i = 0; i < num; i++) { + if (EC_POINT_is_at_infinity(group, point[i])) + continue; + + if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) { + BIGNUM *tmp; + + if ((tmp = BN_CTX_get(ctx)) == NULL) + goto err; + if (!BN_nnmod(tmp, scalar[i], group->order, ctx)) { + ECerr(ERR_LIB_EC, ERR_R_BN_LIB); + goto err; + } + scalars[i] = tmp; + } else { + scalars[i] = scalar[i]; + } + + if (ecp_sm2p256_bignum_field_elem(k, scalars[i]) <= 0 + || ecp_sm2p256_bignum_field_elem(p.p.X, point[i]->X) <= 0 + || ecp_sm2p256_bignum_field_elem(p.p.Y, point[i]->Y) <= 0 + || ecp_sm2p256_bignum_field_elem(p.p.Z, point[i]->Z) <= 0) { + ECerr(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); + goto err; + } + + ecp_sm2p256_point_get_affine(&t.a, &p.p); + ecp_sm2p256_point_P_mul_by_scalar(&kP, k, t.a); + ecp_sm2p256_point_add(r, r, &kP); + } + + ret = 1; +err: + OPENSSL_free(scalars); + return ret; +} + +/* r = scalar*G + sum(scalars[i]*points[i]) */ +static int ecp_sm2p256_points_mul(const EC_GROUP *group, + EC_POINT *r, + const BIGNUM *scalar, + size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + int ret = 0, p_is_infinity = 0; + const EC_POINT *generator = NULL; + BN_ULONG k[P256_LIMBS] ALIGN32 = {0}; + ALIGN32 union { + P256_POINT p; + P256_POINT_AFFINE a; + } t, p; + + if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) { + ECerr(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); + goto err; + } + + BN_CTX_start(ctx); + + if (scalar) { + generator = EC_GROUP_get0_generator(group); + if (generator == NULL) { + ECerr(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR); + goto err; + } + + if (!ecp_sm2p256_bignum_field_elem(k, scalar)) { + ECerr(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); + goto err; + } +#if !defined(OPENSSL_NO_SM2_PRECOMP) + if (ecp_sm2p256_is_affine_G(generator)) { + ecp_sm2p256_point_G_mul_by_scalar(&p.p, k); + } else +#endif + { + /* if no precomputed table */ + const EC_POINT *new_generator[1]; + const BIGNUM *g_scalars[1]; + + new_generator[0] = generator; + g_scalars[0] = scalar; + + if (!ecp_sm2p256_windowed_mul(group, &p.p, g_scalars, new_generator, + (new_generator[0] != NULL + && g_scalars[0] != NULL), ctx)) + goto err; + } + } else { + p_is_infinity = 1; + } + if (num) { + P256_POINT *out = &t.p; + + if (p_is_infinity) + out = &p.p; + + if (!ecp_sm2p256_windowed_mul(group, out, scalars, points, num, ctx)) + goto err; + + if (!p_is_infinity) + ecp_sm2p256_point_add(&p.p, &p.p, out); + } + + /* Not constant-time, but we're only operating on the public output. */ + if (!bn_set_words(r->X, p.p.X, P256_LIMBS) + || !bn_set_words(r->Y, p.p.Y, P256_LIMBS) + || !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) + goto err; + r->Z_is_one = is_equal(bn_get_words(r->Z), ONE) & 1; + + ret = 1; +err: + BN_CTX_end(ctx); + return ret; +} + +static int ecp_sm2p256_field_mul(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ + BN_ULONG a_fe[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG b_fe[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG r_fe[P256_LIMBS] ALIGN32 = {0}; + + if (a == NULL || b == NULL || r == NULL) + return 0; + + if (!ecp_sm2p256_bignum_field_elem(a_fe, a) + || !ecp_sm2p256_bignum_field_elem(b_fe, b)) { + ECerr(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); + return 0; + } + + ecp_sm2p256_mul(r_fe, a_fe, b_fe); + + if (!bn_set_words(r, r_fe, P256_LIMBS)) + return 0; + + return 1; +} + +static int ecp_sm2p256_field_sqr(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, BN_CTX *ctx) +{ + BN_ULONG a_fe[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG r_fe[P256_LIMBS] ALIGN32 = {0}; + + if (a == NULL || r == NULL) + return 0; + + if (!ecp_sm2p256_bignum_field_elem(a_fe, a)) { + ECerr(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); + return 0; + } + + ecp_sm2p256_sqr(r_fe, a_fe); + + if (!bn_set_words(r, r_fe, P256_LIMBS)) + return 0; + + return 1; +} + +static int ecp_sm2p256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *x, BN_CTX *ctx) +{ + int ret = 0; + BN_ULONG t[P256_LIMBS] ALIGN32 = {0}; + BN_ULONG out[P256_LIMBS] ALIGN32 = {0}; + + if (bn_wexpand(r, P256_LIMBS) == NULL) { + ECerr(ERR_LIB_EC, ERR_R_BN_LIB); + goto err; + } + + if ((BN_num_bits(x) > 256) || BN_is_negative(x)) { + BIGNUM *tmp; + + if ((tmp = BN_CTX_get(ctx)) == NULL + || !BN_nnmod(tmp, x, group->order, ctx)) { + ECerr(ERR_LIB_EC, ERR_R_BN_LIB); + goto err; + } + x = tmp; + } + + if (!ecp_sm2p256_bignum_field_elem(t, x)) { + ECerr(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); + goto err; + } + + ecp_sm2p256_mod_ord_inverse(out, t); + + if (!bn_set_words(r, out, P256_LIMBS)) + goto err; + + ret = 1; +err: + return ret; +} + +const EC_METHOD *EC_GFp_sm2p256_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ossl_ec_GFp_simple_group_init, + ossl_ec_GFp_simple_group_finish, + ossl_ec_GFp_simple_group_clear_finish, + ossl_ec_GFp_simple_group_copy, + ossl_ec_GFp_simple_group_set_curve, + ossl_ec_GFp_simple_group_get_curve, + ossl_ec_GFp_simple_group_get_degree, + ossl_ec_group_simple_order_bits, + ossl_ec_GFp_simple_group_check_discriminant, + ossl_ec_GFp_simple_point_init, + ossl_ec_GFp_simple_point_finish, + ossl_ec_GFp_simple_point_clear_finish, + ossl_ec_GFp_simple_point_copy, + ossl_ec_GFp_simple_point_set_to_infinity, + ossl_ec_GFp_simple_point_set_affine_coordinates, + ecp_sm2p256_get_affine, + 0, 0, 0, + ossl_ec_GFp_simple_add, + ossl_ec_GFp_simple_dbl, + ossl_ec_GFp_simple_invert, + ossl_ec_GFp_simple_is_at_infinity, + ossl_ec_GFp_simple_is_on_curve, + ossl_ec_GFp_simple_cmp, + ossl_ec_GFp_simple_make_affine, + ossl_ec_GFp_simple_points_make_affine, + ecp_sm2p256_points_mul, /* mul */ + 0 /* precompute_mult */, + 0 /* have_precompute_mult */, + ecp_sm2p256_field_mul, + ecp_sm2p256_field_sqr, + 0 /* field_div */, + 0 /* field_inv */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */, + ossl_ec_key_simple_priv2oct, + ossl_ec_key_simple_oct2priv, + 0, /* set private */ + ossl_ec_key_simple_generate_key, + ossl_ec_key_simple_check_key, + ossl_ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ossl_ecdh_simple_compute_key, + ossl_ecdsa_simple_sign_setup, + ossl_ecdsa_simple_sign_sig, + ossl_ecdsa_simple_verify_sig, + ecp_sm2p256_inv_mod_ord, + 0, /* blind_coordinates */ + 0, /* ladder_pre */ + 0, /* ladder_step */ + 0 /* ladder_post */ + }; + + return &ret; +} diff --git a/crypto/ec/ecp_sm2p256_table.c b/crypto/ec/ecp_sm2p256_table.c new file mode 100644 index 0000000000..e19df48f55 --- /dev/null +++ b/crypto/ec/ecp_sm2p256_table.c @@ -0,0 +1,16387 @@ +/* + * Copyright 2023 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the Apache License 2.0 (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* + * This is the precomputed table for the code in ecp_sm2p256.c, for the default + * generator. The table consists of 32 subtables, each subtable contains 256 + * affine points. + * subtable 0: 0* (2^0)*G, 1* (2^0)*G, 2* (2^0)*G, ... , 255* (2^0)*G, + * subtable 1: 0* (2^8)*G, 1* (2^8)*G, 2* (2^8)*G, ... , 255* (2^8)*G, + * subtable 2: 0* (2^16)*G, 1* (2^16)*G, 2* (2^16)*G, ... , 255* (2^16)*G, + * ... + * subtable 31: 0*(2^248)*G, 1*(2^248)*G, 2*(2^248)*G, ... , 255*(2^248)*G, + * + * The affine points are encoded as eight uint64's, four for the + * x coordinate and four for the y. Both values are in little-endian order. + */ + +#include <openssl/bn.h> + +#if defined(__GNUC__) +__attribute((aligned(4096))) +#elif defined(_MSC_VER) +__declspec(align(4096)) +#elif defined(__SUNPRO_C) +# pragma align 4096(ecp_sm2p256_precomputed) +#endif +extern const BN_ULONG ecp_sm2p256_precomputed[8 * 32 * 256]; +const BN_ULONG ecp_sm2p256_precomputed[8 * 32 * 256] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x715a4589334c74c7, 0x8fe30bbff2660be1, 0x5f9904466a39c994, 0x32c4ae2c1f198119, + 0x02df32e52139f0a0, 0xd0a9877cc62a4740, 0x59bdcee36b692153, 0xbc3736a2f4f6779c, + 0x495c2e1da3f2bd52, 0x9c0dfa08c08a7331, 0x0d58ef57fa73ba4d, 0x56cefd60d7c87c00, + 0x6f780d3a970a23c3, 0x6de84c182f6c8e71, 0x68535ce0f8eaf1bd, 0x31b7e7e6cc8189f6, + 0xe26918f1d0509ebf, 0xa13f6bd945302244, 0xbe2daa8cdb41e24c, 0xa97f7cd4b3c993b4, + 0xaaacdd037458f6e6, 0x7c400ee5cd045292, 0xccc5cec08a72150f, 0x530b5dd88c688ef5, + 0xb21646cd34a0ced5, 0x009a084ad5cc937d, 0x2a81052ff641ed69, 0xc239507105c68324, + 0x7a253666cb66e009, 0x6bee2e96ab8c71fb, 0x35f1294ac0db1968, 0xb1bf7ec4080f3c87, + 0xa575da57cc372a9e, 0x344a417b7fce19db, 0x040e008fdd5eb77a, 0xc749061668652e26, + 0xa6976eff5fbe6480, 0x5006206eb579ff7d, 0x4504c622b51cf38f, 0xf2df5db2d144e945, + 0x2c8b1a1a3c4b0d30, 0x05ff8856a6601689, 0xbb17c93e71f22a31, 0x0927afb57d93483b, + 0xd572103000088f63, 0x81adf1f0855a064d, 0xac1c0ef6ebf26645, 0x150c6b1ab4d1fc7e, + 0xcd27e384d9fcaf15, 0xa80198337744ee78, 0xfdbe86a75c139906, 0xddf092555409c19d, + 0x223b949657e52bc1, 0x037937707d6a49a2, 0x5cd6b6e9c12d2922, 0x847d18ffb38e8706, + 0x675d822ded0bb916, 0xd4ea35d60c1c29bb, 0x3db4333d4e860e64, 0xb9c3faeb4b161071, + 0x3c286da2cfd31a3e, 0x0366a8a03024b3e0, 0x2491d2de9accf2be, 0xc519b309ecf7269c, + 0x173472a58cca247e, 0xfe8d59cb43619e4f, 0x0b4a2444a46a74c5, 0xa27233f3a5959508, + 0x85227940922c02e9, 0xc3a8433140d1ebca, 0x768f7689b210f45f, 0x379e72f63722c924, + 0x84a04814db522756, 0xb2d0d065cd219e32, 0x21666061f65c3e32, 0xd3f94862519621c1, + 0x47d46fb2bab82a14, 0xf6b743f64d1482d1, 0x2ebd57d146dca428, 0x4b9030cf676f6a74, + 0x668c74d78ce20ace, 0x125dcdd589c2ff82, 0x7c1aab770f67f543, 0x04b3cb10c9c6d8e2, + 0x739a8fd805174a4b, 0x0c94816e63c4bc72, 0x4918e5c02e2b0b93, 0x63516355287e39fe, + 0x9c9f042d0279270a, 0x5f7b516c5bdaddad, 0xd89058ca059be46e, 0xbfc2df6bb17f971a, + 0xb5fbf87b64af3c26, 0x73c9fc6fd150aaaa, 0xcef696b67939bd7b, 0xb145513f59636106, + 0x2b834f1d509b9cd0, 0x7bea65c6421e189e, 0xfa804513275f58aa, 0x952072d6ff9c65bd, + 0x03891e105e009b00, 0x58d1434ae934ba75, 0x1a473f8d9748f238, 0xe6bb9804458bb70f, + 0x0a44248a36bb0a07, 0xef22ea28be9d44de, 0x4aaf81826982d748, 0x83b4a4de96a4d70f, + 0x2e663cd4373a2f24, 0x3e707c8a43852949, 0xeeb6d6c6d7e74f8e, 0xe481c0d9ee8a98d4, + 0x461b1bbcb80f829c, 0x3b424f35f0ecce4c, 0x3291676c38d39324, 0xf73b839f13912c1a, + 0x4c3533771db0955e, 0xdc2e788fb170aa14, 0x5ee9fab985c12455, 0x32ec7722695dc7cf, + 0x55645bbc8704fb68, 0xea133cd248a93e25, 0xbbce44ef5db3e419, 0x35648233f554ae51, + 0x4411a9a30eca2046, 0x154b1870a6a65166, 0x6117bca9ce885dd6, 0x04d7ac60f6d975ef, + 0x36969f8b77125e6a, 0xbf5113ab85b5ed44, 0x1c993f01115c57f7, 0xdd18aa4aec26eac4, + 0xe0180d54d4ae2221, 0x6cce6001d7c0b853, 0x3361493f76fac50f, 0x161e5851969da822, + 0x427e33ae8ed9c317, 0xa3448557a24554db, 0x221ea8657781ce71, 0x69fdf8a436fd8e5d, + 0x71e35709341fdcab, 0xeb7b1ad657c155f5, 0x6b0a9658b33b347b, 0xbaa856d1cad68af3, + 0x1323f252e493952a, 0xf7c96c55940a4726, 0xe2e0586bb5dc9419, 0xa68b2ec49d1921d0, + 0xfd4520a63f5cc585, 0xb95f2de69200269e, 0x933ef442fca7a734, 0x96f361a23b3deb99, + 0x0588fdd88abdee94, 0xabbb1ea1417f958d, 0x7575e3cb2fa9092d, 0x08314765e44847eb, + 0x5eeb0e99c2eb61e9, 0x7de3a53937e8a75f, 0x6b443ab436095378, 0xdf922344fa592a98, + 0xe1de5f100950c8ab, 0x5b551c86a8976933, 0x137cbf4e8aa50535, 0x6407be639bc5b738, + 0xf945321148e90344, 0x60fcfd988fff6dec, 0x12a9423fd80dea54, 0x141caee612e7ab07, + 0x0755a352dafa1e1d, 0x3e7307f46fa550d1, 0x1835a4d0f3e5e299, 0xe61120569974c0bc, + 0x3b86cc142850b0f3, 0x02855e18d12379b4, 0xd08fc10e5056e4bc, 0xcfe30aa2c3877e52, + 0x4dbb2fcd069d45db, 0xbb570a9f430ea7f6, 0x15c07a8c04226fe3, 0xac8df677299e8288, + 0x7bd8b7c847718ce5, 0x0e9b9643d766da33, 0x30c43be69b23cc14, 0xaef82cf361db1c71, + 0xd7240a35d1f4ffed, 0xec268911ccb79283, 0x314fa6c814c7bda8, 0xdf8a74f904d1715e, + 0xbcb60a9e82017c30, 0xe1c80e7752bd6499, 0x7a7606ef148aa5fb, 0x0fed448a3f263918, + 0x0263b20d539e4139, 0x7e8581fbbcf5de01, 0xce1564c3df7d67ea, 0x178d1f6bd584afcc, + 0x9b499a7da7820bf9, 0x7021aafc29ac8e86, 0x53da45cec1caada1, 0xf575f34e5f6c63c6, + 0x8e6a9e4fdf895290, 0x73783ef304251e74, 0xbcf26fe238a102c2, 0xa0a1a4fbeb476576, + 0xe54f7f3a4896d9d3, 0xec73068587361b34, 0x0d09c3f281d4c41c, 0x8dfdd7cd150d2564, + 0xce37e84fc9541b4b, 0x02a85a7410754529, 0xd7a1f169475b4ddf, 0xec6f34ceacaa73a0, + 0x73306a0ff0485872, 0xe607f33be20135ea, 0x6f251c63fbbd2927, 0x3c85cf62a744817e, + 0x6cb2f058c747d33f, 0x36f0dfe49113c16e, 0x94ed53ed581d191d, 0x91cb72dc55f84346, + 0x3ea6aace93921f31, 0xf4c600e8b5dfe811, 0xf7efb07682931f88, 0x1957ad4cfffd491e, + 0x9dd4ef421635b9dc, 0xc9816be068be66db, 0x625773cae69bbe05, 0x28221c36398c4c3a, + 0x2995225e66b162ba, 0x64c77a81858d4ca1, 0xab2012c41627cd81, 0x3b4d172d6963510b, + 0xfd23ea021da51c9d, 0x8b1ac02e98d543ce, 0xc315796922bf1343, 0x17a5f74d533ae724, + 0x57d2e81dbb945dfe, 0x7befa4db8c8d3eff, 0xb9038823d9ad0d5f, 0x498470ec6752b2ec, + 0xac995c5066bdaaa5, 0x27d053c0f150fe10, 0xd6b48259b69e8530, 0x08daae840b2a43eb, + 0x2458b9e3c73bf657, 0xf7dc310560bbe83a, 0xc1b8e58150da662d, 0x80cc0a980495af87, + 0xa32641e56024666c, 0x791734cd03e5565c, 0xa6d5c2b5817f2329, 0x25d3debd0950d180, + 0xd39e100303fa10a2, 0x0458895120e208b4, 0xb938c406dd5cb0e1, 0x92d99a70679d61ef, + 0x6d69b1bd07837dc9, 0x451641e8455eedb6, 0x4624f85fe9b7cb83, 0xa1aa7f4a42808908, + 0xc3c8bd75b5fe25de, 0x6e67fd81941c6a60, 0xeb15fccc63694830, 0x3d420dee447499cf, + 0x37a60fce33247b4c, 0x1afddac4a9667094, 0x72e11351388e9d3d, 0x87e13ab96307c971, + 0x217ed12bbc413d35, 0xd7ac6191958240c7, 0xadb32c8ad1d8a615, 0x3ff4e73fac0283e5, + 0x549786448c4f3f4d, 0xbaf30f4638d2231b, 0x46dab2eba04afd78, 0x68126a90b051062b, + 0x5a8ce092c6b7c016, 0xe7fec8984be51251, 0x35ecf208bdec5980, 0x7e72f70a2eaf1bf4, + 0xfa2f46cf90a47d2b, 0xe7579164cc5a233c, 0xcdd2cc00d6ce411e, 0x323159ac22478ac2, + 0x939227b1d05f49ba, 0xa94c472c0089e4b4, 0x7e7a32282a0c2900, 0xe488cf88fe83acfc, + 0x31f8514dc6115cb5, 0x8c641a6cb43ae7da, 0x8b8f45b58a12e6cc, 0x3242e1de1fa494c5, + 0x7dab7b373c8f551b, 0x56ab9bcf11b6f25a, 0xaa27b4380a8333ad, 0xcbf18ef2f229c025, + 0xb7d6af71fb640a75, 0x47a9f7f697a28e0b, 0x6b663188dc931a44, 0x7f404379407b0976, + 0xf500974f78295571, 0xc7652177fdfae41b, 0x860bec0a6c78c5d0, 0x3178d1bb1435c9af, + 0xcd1bb864637cf4f9, 0x10e34d63f48c5ed4, 0x5b075be3c412ad03, 0xe6857f7fc3345385, + 0x1ca28a8ee15f1878, 0x5d72264551d68eae, 0x581dfa7d2b4c09e3, 0x6b61903f2ba03769, + 0x2bed704f6dff2150, 0x3b66f17073149664, 0x2a722a8a3b798a66, 0x376bf9e5403eedb7, + 0x95c769d2fc372cd9, 0x35698578596b792f, 0x2670a8f2e7f7a641, 0xf6f8ca3c58d3089e, + 0x47d58af32a91ddc2, 0x30abb6eab3f02921, 0x490df25e43f73f13, 0xf537773939d38a9b, + 0xf9099fa3212d8fc1, 0x63ae367eb959d9f8, 0x8e2e511cce74be18, 0xbeb6132d28ff4099, + 0xc88b69c57731c07e, 0x52ed6a3d227ff763, 0x52cd70822173c59f, 0xd0d299040f1250d8, + 0x5769c965f01be7a3, 0xf6db21dd26bbf942, 0x648ab14004516e12, 0xabfc349e2f1d2118, + 0x0180bb9d84d7141b, 0x134911d8e4bbaaec, 0x4b92b8f64e804905, 0x897da7bb358b6d21, + 0x38ecb2e51caf0aae, 0x6543e7e5a787f93d, 0xf571032510364cd2, 0x995b4a9a20d88c89, + 0xdd379996725be125, 0xb1df2f7a4fcad9d2, 0xa7b5fa7d47457508, 0x2575c600187cec18, + 0x1e259e3d752b00d1, 0x83580245568efa73, 0xed22d2e0508647f4, 0x84442dfc92fb06ff, + 0x3d24524ac4d2c465, 0x0462308a30d9d3e5, 0x45254a01baae8a2e, 0xd2593661cf6daf12, + 0x5dca599abe435bf0, 0xa169da8afcb3a620, 0x6cf13824af9f6508, 0x416b602161b2bbf6, + 0x5c4b342a0ead84ed, 0x654b3a33c67ed63d, 0xa31dbd4bffd8c960, 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