// Copyright 2018 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// This file contains constant-time, 64-bit assembly implementation of
// P256. The optimizations performed here are described in detail in:
// S.Gueron and V.Krasnov, "Fast prime field elliptic-curve cryptography with
// 256-bit primes"
// http://link.springer.com/article/10.1007%2Fs13389-014-0090-x
// https://eprint.iacr.org/2013/816.pdf
#include "textflag.h"
#define res_ptr R0
#define a_ptr R1
#define b_ptr R2
#define acc0 R3
#define acc1 R4
#define acc2 R5
#define acc3 R6
#define acc4 R7
#define acc5 R8
#define acc6 R9
#define acc7 R10
#define t0 R11
#define t1 R12
#define t2 R13
#define t3 R14
#define const0 R15
#define const1 R16
#define hlp0 R17
#define hlp1 res_ptr
#define x0 R19
#define x1 R20
#define x2 R21
#define x3 R22
#define y0 R23
#define y1 R24
#define y2 R25
#define y3 R26
#define const2 t2
#define const3 t3
DATA p256const0<>+0x00(SB)/8, $0x00000000ffffffff
DATA p256const1<>+0x00(SB)/8, $0xffffffff00000001
DATA p256ordK0<>+0x00(SB)/8, $0xccd1c8aaee00bc4f
DATA p256ord<>+0x00(SB)/8, $0xf3b9cac2fc632551
DATA p256ord<>+0x08(SB)/8, $0xbce6faada7179e84
DATA p256ord<>+0x10(SB)/8, $0xffffffffffffffff
DATA p256ord<>+0x18(SB)/8, $0xffffffff00000000
DATA p256one<>+0x00(SB)/8, $0x0000000000000001
DATA p256one<>+0x08(SB)/8, $0xffffffff00000000
DATA p256one<>+0x10(SB)/8, $0xffffffffffffffff
DATA p256one<>+0x18(SB)/8, $0x00000000fffffffe
GLOBL p256const0<>(SB), 8, $8
GLOBL p256const1<>(SB), 8, $8
GLOBL p256ordK0<>(SB), 8, $8
GLOBL p256ord<>(SB), 8, $32
GLOBL p256one<>(SB), 8, $32
/* ---------------------------------------*/
// func p256LittleToBig(res []byte, in []uint64)
TEXT ·p256LittleToBig(SB),NOSPLIT,$0
JMP ·p256BigToLittle(SB)
/* ---------------------------------------*/
// func p256BigToLittle(res []uint64, in []byte)
TEXT ·p256BigToLittle(SB),NOSPLIT,$0
MOVD res+0(FP), res_ptr
MOVD in+24(FP), a_ptr
LDP 0*16(a_ptr), (acc0, acc1)
LDP 1*16(a_ptr), (acc2, acc3)
REV acc0, acc0
REV acc1, acc1
REV acc2, acc2
REV acc3, acc3
STP (acc3, acc2), 0*16(res_ptr)
STP (acc1, acc0), 1*16(res_ptr)
RET
/* ---------------------------------------*/
// func p256MovCond(res, a, b []uint64, cond int)
// If cond == 0 res=b, else res=a
TEXT ·p256MovCond(SB),NOSPLIT,$0
MOVD res+0(FP), res_ptr
MOVD a+24(FP), a_ptr
MOVD b+48(FP), b_ptr
MOVD cond+72(FP), R3
CMP $0, R3
// Two remarks:
// 1) Will want to revisit NEON, when support is better
// 2) CSEL might not be constant time on all ARM processors
LDP 0*16(a_ptr), (R4, R5)
LDP 1*16(a_ptr), (R6, R7)
LDP 2*16(a_ptr), (R8, R9)
LDP 0*16(b_ptr), (R16, R17)
LDP 1*16(b_ptr), (R19, R20)
LDP 2*16(b_ptr), (R21, R22)
CSEL EQ, R16, R4, R4
CSEL EQ, R17, R5, R5
CSEL EQ, R19, R6, R6
CSEL EQ, R20, R7, R7
CSEL EQ, R21, R8, R8
CSEL EQ, R22, R9, R9
STP (R4, R5), 0*16(res_ptr)
STP (R6, R7), 1*16(res_ptr)
STP (R8, R9), 2*16(res_ptr)
LDP 3*16(a_ptr), (R4, R5)
LDP 4*16(a_ptr), (R6, R7)
LDP 5*16(a_ptr), (R8, R9)
LDP 3*16(b_ptr), (R16, R17)
LDP 4*16(b_ptr), (R19, R20)
LDP 5*16(b_ptr), (R21, R22)
CSEL EQ, R16, R4, R4
CSEL EQ, R17, R5, R5
CSEL EQ, R19, R6, R6
CSEL EQ, R20, R7, R7
CSEL EQ, R21, R8, R8
CSEL EQ, R22, R9, R9
STP (R4, R5), 3*16(res_ptr)
STP (R6, R7), 4*16(res_ptr)
STP (R8, R9), 5*16(res_ptr)
RET
/* ---------------------------------------*/
// func p256NegCond(val []uint64, cond int)
TEXT ·p256NegCond(SB),NOSPLIT,$0
MOVD val+0(FP), a_ptr
MOVD cond+24(FP), hlp0
MOVD a_ptr, res_ptr
// acc = poly
MOVD $-1, acc0
MOVD p256const0<>(SB), acc1
MOVD $0, acc2
MOVD p256const1<>(SB), acc3
// Load the original value
LDP 0*16(a_ptr), (t0, t1)
LDP 1*16(a_ptr), (t2, t3)
// Speculatively subtract
SUBS t0, acc0
SBCS t1, acc1
SBCS t2, acc2
SBC t3, acc3
// If condition is 0, keep original value
CMP $0, hlp0
CSEL EQ, t0, acc0, acc0
CSEL EQ, t1, acc1, acc1
CSEL EQ, t2, acc2, acc2
CSEL EQ, t3, acc3, acc3
// Store result
STP (acc0, acc1), 0*16(res_ptr)
STP (acc2, acc3), 1*16(res_ptr)
RET
/* ---------------------------------------*/
// func p256Sqr(res, in []uint64, n int)
TEXT ·p256Sqr(SB),NOSPLIT,$0
MOVD res+0(FP), res_ptr
MOVD in+24(FP), a_ptr
MOVD n+48(FP), b_ptr
MOVD p256const0<>(SB), const0
MOVD p256const1<>(SB), const1
LDP 0*16(a_ptr), (x0, x1)
LDP 1*16(a_ptr), (x2, x3)
sqrLoop:
SUB $1, b_ptr
CALL p256SqrInternal<>(SB)
MOVD y0, x0
MOVD y1, x1
MOVD y2, x2
MOVD y3, x3
CBNZ b_ptr, sqrLoop
STP (y0, y1), 0*16(res_ptr)
STP (y2, y3), 1*16(res_ptr)
RET
/* ---------------------------------------*/
// func p256Mul(res, in1, in2 []uint64)
TEXT ·p256Mul(SB),NOSPLIT,$0
MOVD res+0(FP), res_ptr
MOVD in1+24(FP), a_ptr
MOVD in2+48(FP), b_ptr
MOVD p256const0<>(SB), const0
MOVD p256const1<>(SB), const1
LDP 0*16(a_ptr), (x0, x1)
LDP 1*16(a_ptr), (x2, x3)
LDP 0*16(b_ptr), (y0, y1)
LDP 1*16(b_ptr), (y2, y3)
CALL p256MulInternal<>(SB)
STP (y0, y1), 0*16(res_ptr)
STP (y2, y3), 1*16(res_ptr)
RET
/* ---------------------------------------*/
// func p256FromMont(res, in []uint64)
TEXT ·p256FromMont(SB),NOSPLIT,$0
MOVD res+0(FP), res_ptr
MOVD in+24(FP), a_ptr
MOVD p256const0<>(SB), const0
MOVD p256const1<>(SB), const1
LDP 0*16(a_ptr), (acc0, acc1)
LDP 1*16(a_ptr), (acc2, acc3)
// Only reduce, no multiplications are needed
// First reduction step
ADDS acc0<<32, acc1, acc1
LSR $32, acc0, t0
MUL acc0, const1, t1
UMULH acc0, const1, acc0
ADCS t0, acc2
ADCS t1, acc3
ADC $0, acc0
// Second reduction step
ADDS acc1<<32, acc2, acc2
LSR $32, acc1, t0
MUL acc1, const1, t1
UMULH acc1, const1, acc1
ADCS t0, acc3
ADCS t1, acc0
ADC $0, acc1
// Third reduction step
ADDS acc2<<32, acc3, acc3
LSR $32, acc2, t0
MUL acc2, const1, t1
UMULH acc2, const1, acc2
ADCS t0, acc0
ADCS t1, acc1
ADC $0, acc2
// Last reduction step
ADDS acc3<<32, acc0, acc0
LSR $32, acc3, t0
MUL acc3, const1, t1
UMULH acc3, const1, acc3
ADCS t0, acc1
ADCS t1, acc2
ADC $0, acc3
SUBS $-1, acc0, t0
SBCS const0, acc1, t1
SBCS $0, acc2, t2
SBCS const1, acc3, t3
CSEL CS, t0, acc0, acc0
CSEL CS, t1, acc1, acc1
CSEL CS, t2, acc2, acc2
CSEL CS, t3, acc3, acc3
STP (acc0, acc1), 0*16(res_ptr)
STP (acc2, acc3), 1*16(res_ptr)
RET
/* ---------------------------------------*/
// Constant time point access to arbitrary point table.
// Indexed from 1 to 15, with -1 offset
// (index 0 is implicitly point at infinity)
// func p256Select(point, table []uint64, idx int)
TEXT ·p256Select(SB),NOSPLIT,$0
MOVD idx+48(FP), const0
MOVD table+24(FP), b_ptr
MOVD point+0(FP), res_ptr
EOR x0, x0, x0
EOR x1, x1, x1
EOR x2, x2, x2
EOR x3, x3, x3
EOR y0, y0, y0
EOR y1, y1, y1
EOR y2, y2, y2
EOR y3, y3, y3
EOR t0, t0, t0
EOR t1, t1, t1
EOR t2, t2, t2
EOR t3, t3, t3
MOVD $0, const1
loop_select:
ADD $1, const1
CMP const0, const1
LDP.P 16(b_ptr), (acc0, acc1)
CSEL EQ, acc0, x0, x0
CSEL EQ, acc1, x1, x1
LDP.P 16(b_ptr), (acc2, acc3)
CSEL EQ, acc2, x2, x2
CSEL EQ, acc3, x3, x3
LDP.P 16(b_ptr), (acc4, acc5)
CSEL EQ, acc4, y0, y0
CSEL EQ, acc5, y1, y1
LDP.P 16(b_ptr), (acc6, acc7)
CSEL EQ, acc6, y2, y2
CSEL EQ, acc7, y3, y3
LDP.P 16(b_ptr), (acc0, acc1)
CSEL EQ, acc0, t0, t0
CSEL EQ, acc1, t1, t1
LDP.P 16(b_ptr), (acc2, acc3)
CSEL EQ, acc2, t2, t2
CSEL EQ, acc3, t3, t3
CMP $16, const1
BNE loop_select
STP (x0, x1), 0*16(res_ptr)
STP (x2, x3), 1*16(res_ptr)
STP (y0, y1), 2*16(res_ptr)
STP (y2, y3), 3*16(res_ptr)
STP (t0, t1), 4*16(res_ptr)
STP (t2, t3), 5*16(res_ptr)
RET
/* ---------------------------------------*/
// Constant time point access to base point table.
// func p256SelectBase(point, table []uint64, idx int)
TEXT ·p256SelectBase(SB),NOSPLIT,$0
MOVD idx+48(FP), t0
MOVD table+24(FP), t1
MOVD point+0(FP), res_ptr
EOR x0, x0, x0
EOR x1, x1, x1
EOR x2, x2, x2
EOR x3, x3, x3
EOR y0, y0, y0
EOR y1, y1, y1
EOR y2, y2, y2
EOR y3, y3, y3
MOVD $0, t2
loop_select:
ADD $1, t2
CMP t0, t2
LDP.P 16(t1), (acc0, acc1)
CSEL EQ, acc0, x0, x0
CSEL EQ, acc1, x1, x1
LDP.P 16(t1), (acc2, acc3)
CSEL EQ, acc2, x2, x2
CSEL EQ, acc3, x3, x3
LDP.P 16(t1), (acc4, acc5)
CSEL EQ, acc4, y0, y0
CSEL EQ, acc5, y1, y1
LDP.P 16(t1), (acc6, acc7)
CSEL EQ, acc6, y2, y2
CSEL EQ, acc7, y3, y3
CMP $32, t2
BNE loop_select
STP (x0, x1), 0*16(res_ptr)
STP (x2, x3), 1*16(res_ptr)
STP (y0, y1), 2*16(res_ptr)
STP (y2, y3), 3*16(res_ptr)
RET
/* ---------------------------------------*/
// func p256OrdSqr(res, in []uint64, n int)
TEXT ·p256OrdSqr(SB),NOSPLIT,$0
MOVD in+24(FP), a_ptr
MOVD n+48(FP), b_ptr
MOVD p256ordK0<>(SB), hlp1
LDP p256ord<>+0x00(SB), (const0, const1)
LDP p256ord<>+0x10(SB), (const2, const3)
LDP 0*16(a_ptr), (x0, x1)
LDP 1*16(a_ptr), (x2, x3)
ordSqrLoop:
SUB $1, b_ptr
// x[1:] * x[0]
MUL x0, x1, acc1
UMULH x0, x1, acc2
MUL x0, x2, t0
ADDS t0, acc2, acc2
UMULH x0, x2, acc3
MUL x0, x3, t0
ADCS t0, acc3, acc3
UMULH x0, x3, acc4
ADC $0, acc4, acc4
// x[2:] * x[1]
MUL x1, x2, t0
ADDS t0, acc3
UMULH x1, x2, t1
ADCS t1, acc4
ADC $0, ZR, acc5
MUL x1, x3, t0
ADDS t0, acc4
UMULH x1, x3, t1
ADC t1, acc5
// x[3] * x[2]
MUL x2, x3, t0
ADDS t0, acc5
UMULH x2, x3, acc6
ADC $0, acc6
MOVD $0, acc7
// *2
ADDS acc1, acc1
ADCS acc2, acc2
ADCS acc3, acc3
ADCS acc4, acc4
ADCS acc5, acc5
ADCS acc6, acc6
ADC $0, acc7
// Missing products
MUL x0, x0, acc0
UMULH x0, x0, t0
ADDS t0, acc1, acc1
MUL x1, x1, t0
ADCS t0, acc2, acc2
UMULH x1, x1, t1
ADCS t1, acc3, acc3
MUL x2, x2, t0
ADCS t0, acc4, acc4
UMULH x2, x2, t1
ADCS t1, acc5, acc5
MUL x3, x3, t0
ADCS t0, acc6, acc6
UMULH x3, x3, t1
ADC t1, acc7, acc7
// First reduction step
MUL acc0, hlp1, hlp0
MUL const0, hlp1, t0
ADDS t0, acc0, acc0
UMULH const0, hlp0, t1
MUL const1, hlp0, t0
ADCS t0, acc1, acc1
UMULH const1, hlp0, y0
MUL const2, hlp0, t0
ADCS t0, acc2, acc2
UMULH const2, hlp0, acc0
MUL const3, hlp0, t0
ADCS t0, acc3, acc3
UMULH const3, hlp0, hlp0
ADC $0, hlp0
ADDS t1, acc1, acc1
ADCS y0, acc2, acc2
ADCS acc0, acc3, acc3
ADC $0, hlp0, acc0
// Second reduction step
MUL acc1, hlp1, hlp0
MUL const0, hlp1, t0
ADDS t0, acc1, acc1
UMULH const0, hlp0, t1
MUL const1, hlp0, t0
ADCS t0, acc2, acc2
UMULH const1, hlp0, y0
MUL const2, hlp0, t0
ADCS t0, acc3, acc3
UMULH const2, hlp0, acc1
MUL const3, hlp0, t0
ADCS t0, acc0, acc0
UMULH const3, hlp0, hlp0
ADC $0, hlp0
ADDS t1, acc2, acc2
ADCS y0, acc3, acc3
ADCS acc1, acc0, acc0
ADC $0, hlp0, acc1
// Third reduction step
MUL acc2, hlp1, hlp0
MUL const0, hlp1, t0
ADDS t0, acc2, acc2
UMULH const0, hlp0, t1
MUL const1, hlp0, t0
ADCS t0, acc3, acc3
UMULH const1, hlp0, y0
MUL const2, hlp0, t0
ADCS t0, acc0, acc0
UMULH const2, hlp0, acc2
MUL const3, hlp0, t0
ADCS t0, acc1, acc1
UMULH const3, hlp0, hlp0
ADC $0, hlp0
ADDS t1, acc3, acc3
ADCS y0, acc0, acc0
ADCS acc2, acc1, acc1
ADC $0, hlp0, acc2
// Last reduction step
MUL acc3, hlp1, hlp0
MUL const0, hlp1, t0
ADDS t0, acc3, acc3
UMULH const0, hlp0, t1
MUL const1, hlp0, t0
ADCS t0, acc0, acc0
UMULH const1, hlp0, y0
MUL const2, hlp0, t0
ADCS t0, acc1, acc1
UMULH const2, hlp0, acc3
MUL const3, hlp0, t0
ADCS t0, acc2, acc2
UMULH const3, hlp0, hlp0
ADC $0, acc7
ADDS t1, acc0, acc0
ADCS y0, acc1, acc1
ADCS acc3, acc2, acc2
ADC $0, hlp0, acc3
ADDS acc4, acc0, acc0
ADCS acc5, acc1, acc1
ADCS acc6, acc2, acc2
ADCS acc7, acc3, acc3
ADC $0, ZR, acc4
SUBS const0, acc0, y0
SBCS const1, acc1, y1
SBCS const2, acc2, y2
SBCS const3, acc3, y3
SBCS $0, acc4, acc4
CSEL CS, y0, acc0, x0
CSEL CS, y1, acc1, x1
CSEL CS, y2, acc2, x2
CSEL CS, y3, acc3, x3
CBNZ b_ptr, ordSqrLoop
MOVD res+0(FP), res_ptr
STP (x0, x1), 0*16(res_ptr)
STP (x2, x3), 1*16(res_ptr)
RET
/* ---------------------------------------*/
// func p256OrdMul(res, in1, in2 []uint64)
TEXT ·p256OrdMul(SB),NOSPLIT,$0
MOVD in1+24(FP), a_ptr
MOVD in2+48(FP), b_ptr
MOVD p256ordK0<>(SB), hlp1
LDP p256ord<>+0x00(SB), (const0, const1)
LDP p256ord<>+0x10(SB), (const2, const3)
LDP 0*16(a_ptr), (x0, x1)
LDP 1*16(a_ptr), (x2, x3)
LDP 0*16(b_ptr), (y0, y1)
LDP 1*16(b_ptr), (y2, y3)
// y[0] * x
MUL y0, x0, acc0
UMULH y0, x0, acc1
MUL y0, x1, t0
ADDS t0, acc1
UMULH y0, x1, acc2
MUL y0, x2, t0
ADCS t0, acc2
UMULH y0, x2, acc3
MUL y0, x3, t0
ADCS t0, acc3
UMULH y0, x3, acc4
ADC $0, acc4
// First reduction step
MUL acc0, hlp1, hlp0
MUL const0, hlp1, t0
ADDS t0, acc0, acc0
UMULH const0, hlp0, t1
MUL const1, hlp0, t0
ADCS t0, acc1, acc1
UMULH const1, hlp0, y0
MUL const2, hlp0, t0
ADCS t0, acc2, acc2
UMULH const2, hlp0, acc0
MUL const3, hlp0, t0
ADCS t0, acc3, acc3
UMULH const3, hlp0, hlp0
ADC $0, acc4
ADDS t1, acc1, acc1
ADCS y0, acc2, acc2
ADCS acc0, acc3, acc3
ADC $0, hlp0, acc0
// y[1] * x
MUL y1, x0, t0
ADDS t0, acc1
UMULH y1, x0, t1
MUL y1, x1, t0
ADCS t0, acc2
UMULH y1, x1, hlp0
MUL y1, x2, t0
ADCS t0, acc3
UMULH y1, x2, y0
MUL y1, x3, t0
ADCS t0, acc4
UMULH y1, x3, y1
ADC $0, ZR, acc5
ADDS t1, acc2
ADCS hlp0, acc3
ADCS y0, acc4
ADC y1, acc5
// Second reduction step
MUL acc1, hlp1, hlp0
MUL const0, hlp1, t0
ADDS t0, acc1, acc1
UMULH const0, hlp0, t1
MUL const1, hlp0, t0
ADCS t0, acc2, acc2
UMULH const1, hlp0, y0
MUL const2, hlp0, t0
ADCS t0, acc3, acc3
UMULH const2, hlp0, acc1
MUL const3, hlp0, t0
ADCS t0, acc0, acc0
UMULH const3, hlp0, hlp0
ADC $0, acc5
ADDS t1, acc2, acc2
ADCS y0, acc3, acc3
ADCS acc1, acc0, acc0
ADC $0, hlp0, acc1
// y[2] * x
MUL y2, x0, t0
ADDS t0, acc2
UMULH y2, x0, t1
MUL y2, x1, t0
ADCS t0, acc3
UMULH y2, x1, hlp0
MUL y2, x2, t0
ADCS t0, acc4
UMULH y2, x2, y0
MUL y2, x3, t0
ADCS t0, acc5
UMULH y2, x3, y1
ADC $0, ZR, acc6
ADDS t1, acc3
ADCS hlp0, acc4
ADCS y0, acc5
ADC y1, acc6
// Third reduction step
MUL acc2, hlp1, hlp0
MUL const0, hlp1, t0
ADDS t0, acc2, acc2
UMULH const0, hlp0, t1
MUL const1, hlp0, t0
ADCS t0, acc3, acc3
UMULH const1, hlp0, y0
MUL const2, hlp0, t0
ADCS t0, acc0, acc0
UMULH const2, hlp0, acc2
MUL const3, hlp0, t0
ADCS t0, acc1, acc1
UMULH const3, hlp0, hlp0
ADC $0, acc6
ADDS t1, acc3, acc3
ADCS y0, acc0, acc0
ADCS acc2, acc1, acc1
ADC $0, hlp0, acc2
// y[3] * x
MUL y3, x0, t0
ADDS t0, acc3
UMULH y3, x0, t1
MUL y3, x1, t0
ADCS t0, acc4
UMULH y3, x1, hlp0
MUL y3, x2, t0
ADCS t0, acc5
UMULH y3, x2, y0
MUL y3, x3, t0
ADCS t0, acc6
UMULH y3, x3, y1
ADC $0, ZR, acc7
ADDS t1, acc4
ADCS hlp0, acc5
ADCS y0, acc6
ADC y1, acc7
// Last reduction step
MUL acc3, hlp1, hlp0
MUL const0, hlp1, t0
ADDS t0, acc3, acc3
UMULH const0, hlp0, t1
MUL const1, hlp0, t0
ADCS t0, acc0, acc0
UMULH const1, hlp0, y0
MUL const2, hlp0, t0
ADCS t0, acc1, acc1
UMULH const2, hlp0, acc3
MUL const3, hlp0, t0
ADCS t0, acc2, acc2
UMULH const3, hlp0, hlp0
ADC $0, acc7
ADDS t1, acc0, acc0
ADCS y0, acc1, acc1
ADCS acc3, acc2, acc2
ADC $0, hlp0, acc3
ADDS acc4, acc0, acc0
ADCS acc5, acc1, acc1
ADCS acc6, acc2, acc2
ADCS acc7, acc3, acc3
ADC $0, ZR, acc4
SUBS const0, acc0, t0
SBCS const1, acc1, t1
SBCS const2, acc2, t2
SBCS const3, acc3, t3
SBCS $0, acc4, acc4
CSEL CS, t0, acc0, acc0
CSEL CS, t1, acc1, acc1
CSEL CS, t2, acc2, acc2
CSEL CS, t3, acc3, acc3
MOVD res+0(FP), res_ptr
STP (acc0, acc1), 0*16(res_ptr)
STP (acc2, acc3), 1*16(res_ptr)
RET
/* ---------------------------------------*/
TEXT p256SubInternal<>(SB),NOSPLIT,$0
SUBS x0, y0, acc0
SBCS x1, y1, acc1
SBCS x2, y2, acc2
SBCS x3, y3, acc3
SBC $0, ZR, t0
ADDS $-1, acc0, acc4
ADCS const0, acc1, acc5
ADCS $0, acc2, acc6
ADC const1, acc3, acc7
ANDS $1, t0
CSEL EQ, acc0, acc4, x0
CSEL EQ, acc1, acc5, x1
CSEL EQ, acc2, acc6, x2
CSEL EQ, acc3, acc7, x3
RET
/* ---------------------------------------*/
TEXT p256SqrInternal<>(SB),NOSPLIT,$0
// x[1:] * x[0]
MUL x0, x1, acc1
UMULH x0, x1, acc2
MUL x0, x2, t0
ADDS t0, acc2, acc2
UMULH x0, x2, acc3
MUL x0, x3, t0
ADCS t0, acc3, acc3
UMULH x0, x3, acc4
ADC $0, acc4, acc4
// x[2:] * x[1]
MUL x1, x2, t0
ADDS t0, acc3
UMULH x1, x2, t1
ADCS t1, acc4
ADC $0, ZR, acc5
MUL x1, x3, t0
ADDS t0, acc4
UMULH x1, x3, t1
ADC t1, acc5
// x[3] * x[2]
MUL x2, x3, t0
ADDS t0, acc5
UMULH x2, x3, acc6
ADC $0, acc6
MOVD $0, acc7
// *2
ADDS acc1, acc1
ADCS acc2, acc2
ADCS acc3, acc3
ADCS acc4, acc4
ADCS acc5, acc5
ADCS acc6, acc6
ADC $0, acc7
// Missing products
MUL x0, x0, acc0
UMULH x0, x0, t0
ADDS t0, acc1, acc1
MUL x1, x1, t0
ADCS t0, acc2, acc2
UMULH x1, x1, t1
ADCS t1, acc3, acc3
MUL x2, x2, t0
ADCS t0, acc4, acc4
UMULH x2, x2, t1
ADCS t1, acc5, acc5
MUL x3, x3, t0
ADCS t0, acc6, acc6
UMULH x3, x3, t1
ADCS t1, acc7, acc7
// First reduction step
ADDS acc0<<32, acc1, acc1
LSR $32, acc0, t0
MUL acc0, const1, t1
UMULH acc0, const1, acc0
ADCS t0, acc2, acc2
ADCS t1, acc3, acc3
ADC $0, acc0, acc0
// Second reduction step
ADDS acc1<<32, acc2, acc2
LSR $32, acc1, t0
MUL acc1, const1, t1
UMULH acc1, const1, acc1
ADCS t0, acc3, acc3
ADCS t1, acc0, acc0
ADC $0, acc1, acc1
// Third reduction step
ADDS acc2<<32, acc3, acc3
LSR $32, acc2, t0
MUL acc2, const1, t1
UMULH acc2, const1, acc2
ADCS t0, acc0, acc0
ADCS t1, acc1, acc1
ADC $0, acc2, acc2
// Last reduction step
ADDS acc3<<32, acc0, acc0
LSR $32, acc3, t0
MUL acc3, const1, t1
UMULH acc3, const1, acc3
ADCS t0, acc1, acc1
ADCS t1, acc2, acc2
ADC $0, acc3, acc3
// Add bits [511:256] of the sqr result
ADDS acc4, acc0, acc0
ADCS acc5, acc1, acc1
ADCS acc6, acc2, acc2
ADCS acc7, acc3, acc3
ADC $0, ZR, acc4
SUBS $-1, acc0, t0
SBCS const0, acc1, t1
SBCS $0, acc2, t2
SBCS const1, acc3, t3
SBCS $0, acc4, acc4
CSEL CS, t0, acc0, y0
CSEL CS, t1, acc1, y1
CSEL CS, t2, acc2, y2
CSEL CS, t3, acc3, y3
RET
/* ---------------------------------------*/
TEXT p256MulInternal<>(SB),NOSPLIT,$0
// y[0] * x
MUL y0, x0, acc0
UMULH y0, x0, acc1
MUL y0, x1, t0
ADDS t0, acc1
UMULH y0, x1, acc2
MUL y0, x2, t0
ADCS t0, acc2
UMULH y0, x2, acc3
MUL y0, x3, t0
ADCS t0, acc3
UMULH y0, x3, acc4
ADC $0, acc4
// First reduction step
ADDS acc0<<32, acc1, acc1
LSR $32, acc0, t0
MUL acc0, const1, t1
UMULH acc0, const1, acc0
ADCS t0, acc2
ADCS t1, acc3
ADC $0, acc0
// y[1] * x
MUL y1, x0, t0
ADDS t0, acc1
UMULH y1, x0, t1
MUL y1, x1, t0
ADCS t0, acc2
UMULH y1, x1, t2
MUL y1, x2, t0
ADCS t0, acc3
UMULH y1, x2, t3
MUL y1, x3, t0
ADCS t0, acc4
UMULH y1, x3, hlp0
ADC $0, ZR, acc5
ADDS t1, acc2
ADCS t2, acc3
ADCS t3, acc4
ADC hlp0, acc5
// Second reduction step
ADDS acc1<<32, acc2, acc2
LSR $32, acc1, t0
MUL acc1, const1, t1
UMULH acc1, const1, acc1
ADCS t0, acc3
ADCS t1, acc0
ADC $0, acc1
// y[2] * x
MUL y2, x0, t0
ADDS t0, acc2
UMULH y2, x0, t1
MUL y2, x1, t0
ADCS t0, acc3
UMULH y2, x1, t2
MUL y2, x2, t0
ADCS t0, acc4
UMULH y2, x2, t3
MUL y2, x3, t0
ADCS t0, acc5
UMULH y2, x3, hlp0
ADC $0, ZR, acc6
ADDS t1, acc3
ADCS t2, acc4
ADCS t3, acc5
ADC hlp0, acc6
// Third reduction step
ADDS acc2<<32, acc3, acc3
LSR $32, acc2, t0
MUL acc2, const1, t1
UMULH acc2, const1, acc2
ADCS t0, acc0
ADCS t1, acc1
ADC $0, acc2
// y[3] * x
MUL y3, x0, t0
ADDS t0, acc3
UMULH y3, x0, t1
MUL y3, x1, t0
ADCS t0, acc4
UMULH y3, x1, t2
MUL y3, x2, t0
ADCS t0, acc5
UMULH y3, x2, t3
MUL y3, x3, t0
ADCS t0, acc6
UMULH y3, x3, hlp0
ADC $0, ZR, acc7
ADDS t1, acc4
ADCS t2, acc5
ADCS t3, acc6
ADC hlp0, acc7
// Last reduction step
ADDS acc3<<32, acc0, acc0
LSR $32, acc3, t0
MUL acc3, const1, t1
UMULH acc3, const1, acc3
ADCS t0, acc1
ADCS t1, acc2
ADC $0, acc3
// Add bits [511:256] of the mul result
ADDS acc4, acc0, acc0
ADCS acc5, acc1, acc1
ADCS acc6, acc2, acc2
ADCS acc7, acc3, acc3
ADC $0, ZR, acc4
SUBS $-1, acc0, t0
SBCS const0, acc1, t1
SBCS $0, acc2, t2
SBCS const1, acc3, t3
SBCS $0, acc4, acc4
CSEL CS, t0, acc0, y0
CSEL CS, t1, acc1, y1
CSEL CS, t2, acc2, y2
CSEL CS, t3, acc3, y3
RET
/* ---------------------------------------*/
#define p256MulBy2Inline \
ADDS y0, y0, x0; \
ADCS y1, y1, x1; \
ADCS y2, y2, x2; \
ADCS y3, y3, x3; \
ADC $0, ZR, hlp0; \
SUBS $-1, x0, t0; \
SBCS const0, x1, t1;\
SBCS $0, x2, t2; \
SBCS const1, x3, t3;\
SBCS $0, hlp0, hlp0;\
CSEL CC, x0, t0, x0;\
CSEL CC, x1, t1, x1;\
CSEL CC, x2, t2, x2;\
CSEL CC, x3, t3, x3;
/* ---------------------------------------*/
#define x1in(off) (off)(a_ptr)
#define y1in(off) (off + 32)(a_ptr)
#define z1in(off) (off + 64)(a_ptr)
#define x2in(off) (off)(b_ptr)
#define z2in(off) (off + 64)(b_ptr)
#define x3out(off) (off)(res_ptr)
#define y3out(off) (off + 32)(res_ptr)
#define z3out(off) (off + 64)(res_ptr)
#define LDx(src) LDP src(0), (x0, x1); LDP src(16), (x2, x3)
#define LDy(src) LDP src(0), (y0, y1); LDP src(16), (y2, y3)
#define STx(src) STP (x0, x1), src(0); STP (x2, x3), src(16)
#define STy(src) STP (y0, y1), src(0); STP (y2, y3), src(16)
/* ---------------------------------------*/
#define y2in(off) (32*0 + 8 + off)(RSP)
#define s2(off) (32*1 + 8 + off)(RSP)
#define z1sqr(off) (32*2 + 8 + off)(RSP)
#define h(off) (32*3 + 8 + off)(RSP)
#define r(off) (32*4 + 8 + off)(RSP)
#define hsqr(off) (32*5 + 8 + off)(RSP)
#define rsqr(off) (32*6 + 8 + off)(RSP)
#define hcub(off) (32*7 + 8 + off)(RSP)
#define z2sqr(off) (32*8 + 8 + off)(RSP)
#define s1(off) (32*9 + 8 + off)(RSP)
#define u1(off) (32*10 + 8 + off)(RSP)
#define u2(off) (32*11 + 8 + off)(RSP)
// func p256PointAddAffineAsm(res, in1, in2 []uint64, sign, sel, zero int)
TEXT ·p256PointAddAffineAsm(SB),0,$264-96
MOVD in1+24(FP), a_ptr
MOVD in2+48(FP), b_ptr
MOVD sign+72(FP), hlp0
MOVD sel+80(FP), hlp1
MOVD zero+88(FP), t2
MOVD $1, t0
CMP $0, t2
CSEL EQ, ZR, t0, t2
CMP $0, hlp1
CSEL EQ, ZR, t0, hlp1
MOVD p256const0<>(SB), const0
MOVD p256const1<>(SB), const1
EOR t2<<1, hlp1
// Negate y2in based on sign
LDP 2*16(b_ptr), (y0, y1)
LDP 3*16(b_ptr), (y2, y3)
MOVD $-1, acc0
SUBS y0, acc0, acc0
SBCS y1, const0, acc1
SBCS y2, ZR, acc2
SBCS y3, const1, acc3
SBC $0, ZR, t0
ADDS $-1, acc0, acc4
ADCS const0, acc1, acc5
ADCS $0, acc2, acc6
ADCS const1, acc3, acc7
ADC $0, t0, t0
CMP $0, t0
CSEL EQ, acc4, acc0, acc0
CSEL EQ, acc5, acc1, acc1
CSEL EQ, acc6, acc2, acc2
CSEL EQ, acc7, acc3, acc3
// If condition is 0, keep original value
CMP $0, hlp0
CSEL EQ, y0, acc0, y0
CSEL EQ, y1, acc1, y1
CSEL EQ, y2, acc2, y2
CSEL EQ, y3, acc3, y3
// Store result
STy(y2in)
// Begin point add
LDx(z1in)
CALL p256SqrInternal<>(SB) // z1ˆ2
STy(z1sqr)
LDx(x2in)
CALL p256MulInternal<>(SB) // x2 * z1ˆ2
LDx(x1in)
CALL p256SubInternal<>(SB) // h = u2 - u1
STx(h)
LDy(z1in)
CALL p256MulInternal<>(SB) // z3 = h * z1
LDP 4*16(a_ptr), (acc0, acc1)// iff select[0] == 0, z3 = z1
LDP 5*16(a_ptr), (acc2, acc3)
ANDS $1, hlp1, ZR
CSEL EQ, acc0, y0, y0
CSEL EQ, acc1, y1, y1
CSEL EQ, acc2, y2, y2
CSEL EQ, acc3, y3, y3
LDP p256one<>+0x00(SB), (acc0, acc1)
LDP p256one<>+0x10(SB), (acc2, acc3)
ANDS $2, hlp1, ZR // iff select[1] == 0, z3 = 1
CSEL EQ, acc0, y0, y0
CSEL EQ, acc1, y1, y1
CSEL EQ, acc2, y2, y2
CSEL EQ, acc3, y3, y3
LDx(z1in)
MOVD res+0(FP), t0
STP (y0, y1), 4*16(t0)
STP (y2, y3), 5*16(t0)
LDy(z1sqr)
CALL p256MulInternal<>(SB) // z1 ^ 3
LDx(y2in)
CALL p256MulInternal<>(SB) // s2 = y2 * z1ˆ3
STy(s2)
LDx(y1in)
CALL p256SubInternal<>(SB) // r = s2 - s1
STx(r)
CALL p256SqrInternal<>(SB) // rsqr = rˆ2
STy (rsqr)
LDx(h)
CALL p256SqrInternal<>(SB) // hsqr = hˆ2
STy(hsqr)
CALL p256MulInternal<>(SB) // hcub = hˆ3
STy(hcub)
LDx(y1in)
CALL p256MulInternal<>(SB) // y1 * hˆ3
STy(s2)
LDP hsqr(0*8), (x0, x1)
LDP hsqr(2*8), (x2, x3)
LDP 0*16(a_ptr), (y0, y1)
LDP 1*16(a_ptr), (y2, y3)
CALL p256MulInternal<>(SB) // u1 * hˆ2
STP (y0, y1), h(0*8)
STP (y2, y3), h(2*8)
p256MulBy2Inline // u1 * hˆ2 * 2, inline
LDy(rsqr)
CALL p256SubInternal<>(SB) // rˆ2 - u1 * hˆ2 * 2
MOVD x0, y0
MOVD x1, y1
MOVD x2, y2
MOVD x3, y3
LDx(hcub)
CALL p256SubInternal<>(SB)
LDP 0*16(a_ptr), (acc0, acc1)
LDP 1*16(a_ptr), (acc2, acc3)
ANDS $1, hlp1, ZR // iff select[0] == 0, x3 = x1
CSEL EQ, acc0, x0, x0
CSEL EQ, acc1, x1, x1
CSEL EQ, acc2, x2, x2
CSEL EQ, acc3, x3, x3
LDP 0*16(b_ptr), (acc0, acc1)
LDP 1*16(b_ptr), (acc2, acc3)
ANDS $2, hlp1, ZR // iff select[1] == 0, x3 = x2
CSEL EQ, acc0, x0, x0
CSEL EQ, acc1, x1, x1
CSEL EQ, acc2, x2, x2
CSEL EQ, acc3, x3, x3
MOVD res+0(FP), t0
STP (x0, x1), 0*16(t0)
STP (x2, x3), 1*16(t0)
LDP h(0*8), (y0, y1)
LDP h(2*8), (y2, y3)
CALL p256SubInternal<>(SB)
LDP r(0*8), (y0, y1)
LDP r(2*8), (y2, y3)
CALL p256MulInternal<>(SB)
LDP s2(0*8), (x0, x1)
LDP s2(2*8), (x2, x3)
CALL p256SubInternal<>(SB)
LDP 2*16(a_ptr), (acc0, acc1)
LDP 3*16(a_ptr), (acc2, acc3)
ANDS $1, hlp1, ZR // iff select[0] == 0, y3 = y1
CSEL EQ, acc0, x0, x0
CSEL EQ, acc1, x1, x1
CSEL EQ, acc2, x2, x2
CSEL EQ, acc3, x3, x3
LDP y2in(0*8), (acc0, acc1)
LDP y2in(2*8), (acc2, acc3)
ANDS $2, hlp1, ZR // iff select[1] == 0, y3 = y2
CSEL EQ, acc0, x0, x0
CSEL EQ, acc1, x1, x1
CSEL EQ, acc2, x2, x2
CSEL EQ, acc3, x3, x3
MOVD res+0(FP), t0
STP (x0, x1), 2*16(t0)
STP (x2, x3), 3*16(t0)
RET
#define p256AddInline \
ADDS y0, x0, x0; \
ADCS y1, x1, x1; \
ADCS y2, x2, x2; \
ADCS y3, x3, x3; \
ADC $0, ZR, hlp0; \
SUBS $-1, x0, t0; \
SBCS const0, x1, t1;\
SBCS $0, x2, t2; \
SBCS const1, x3, t3;\
SBCS $0, hlp0, hlp0;\
CSEL CC, x0, t0, x0;\
CSEL CC, x1, t1, x1;\
CSEL CC, x2, t2, x2;\
CSEL CC, x3, t3, x3;
#define s(off) (32*0 + 8 + off)(RSP)
#define m(off) (32*1 + 8 + off)(RSP)
#define zsqr(off) (32*2 + 8 + off)(RSP)
#define tmp(off) (32*3 + 8 + off)(RSP)
//func p256PointDoubleAsm(res, in []uint64)
TEXT ·p256PointDoubleAsm(SB),NOSPLIT,$136-48
MOVD res+0(FP), res_ptr
MOVD in+24(FP), a_ptr
MOVD p256const0<>(SB), const0
MOVD p256const1<>(SB), const1
// Begin point double
LDP 4*16(a_ptr), (x0, x1)
LDP 5*16(a_ptr), (x2, x3)
CALL p256SqrInternal<>(SB)
STP (y0, y1), zsqr(0*8)
STP (y2, y3), zsqr(2*8)
LDP 0*16(a_ptr), (x0, x1)
LDP 1*16(a_ptr), (x2, x3)
p256AddInline
STx(m)
LDx(z1in)
LDy(y1in)
CALL p256MulInternal<>(SB)
p256MulBy2Inline
STx(z3out)
LDy(x1in)
LDx(zsqr)
CALL p256SubInternal<>(SB)
LDy(m)
CALL p256MulInternal<>(SB)
// Multiply by 3
p256MulBy2Inline
p256AddInline
STx(m)
LDy(y1in)
p256MulBy2Inline
CALL p256SqrInternal<>(SB)
STy(s)
MOVD y0, x0
MOVD y1, x1
MOVD y2, x2
MOVD y3, x3
CALL p256SqrInternal<>(SB)
// Divide by 2
ADDS $-1, y0, t0
ADCS const0, y1, t1
ADCS $0, y2, t2
ADCS const1, y3, t3
ADC $0, ZR, hlp0
ANDS $1, y0, ZR
CSEL EQ, y0, t0, t0
CSEL EQ, y1, t1, t1
CSEL EQ, y2, t2, t2
CSEL EQ, y3, t3, t3
AND y0, hlp0, hlp0
EXTR $1, t0, t1, y0
EXTR $1, t1, t2, y1
EXTR $1, t2, t3, y2
EXTR $1, t3, hlp0, y3
STy(y3out)
LDx(x1in)
LDy(s)
CALL p256MulInternal<>(SB)
STy(s)
p256MulBy2Inline
STx(tmp)
LDx(m)
CALL p256SqrInternal<>(SB)
LDx(tmp)
CALL p256SubInternal<>(SB)
STx(x3out)
LDy(s)
CALL p256SubInternal<>(SB)
LDy(m)
CALL p256MulInternal<>(SB)
LDx(y3out)
CALL p256SubInternal<>(SB)
STx(y3out)
RET
/* ---------------------------------------*/
#undef y2in
#undef x3out
#undef y3out
#undef z3out
#define y2in(off) (off + 32)(b_ptr)
#define x3out(off) (off)(b_ptr)
#define y3out(off) (off + 32)(b_ptr)
#define z3out(off) (off + 64)(b_ptr)
//func p256PointAddAsm(res, in1, in2 []uint64) int
TEXT ·p256PointAddAsm(SB),0,$392-80
// See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
// Move input to stack in order to free registers
MOVD in1+24(FP), a_ptr
MOVD in2+48(FP), b_ptr
MOVD p256const0<>(SB), const0
MOVD p256const1<>(SB), const1
// Begin point add
LDx(z2in)
CALL p256SqrInternal<>(SB) // z2^2
STy(z2sqr)
CALL p256MulInternal<>(SB) // z2^3
LDx(y1in)
CALL p256MulInternal<>(SB) // s1 = z2ˆ3*y1
STy(s1)
LDx(z1in)
CALL p256SqrInternal<>(SB) // z1^2
STy(z1sqr)
CALL p256MulInternal<>(SB) // z1^3
LDx(y2in)
CALL p256MulInternal<>(SB) // s2 = z1ˆ3*y2
LDx(s1)
CALL p256SubInternal<>(SB) // r = s2 - s1
STx(r)
MOVD $1, t2
ORR x0, x1, t0 // Check if zero mod p256
ORR x2, x3, t1
ORR t1, t0, t0
CMP $0, t0
CSEL EQ, t2, ZR, hlp1
EOR $-1, x0, t0
EOR const0, x1, t1
EOR const1, x3, t3
ORR t0, t1, t0
ORR x2, t3, t1
ORR t1, t0, t0
CMP $0, t0
CSEL EQ, t2, hlp1, hlp1
LDx(z2sqr)
LDy(x1in)
CALL p256MulInternal<>(SB) // u1 = x1 * z2ˆ2
STy(u1)
LDx(z1sqr)
LDy(x2in)
CALL p256MulInternal<>(SB) // u2 = x2 * z1ˆ2
STy(u2)
LDx(u1)
CALL p256SubInternal<>(SB) // h = u2 - u1
STx(h)
MOVD $1, t2
ORR x0, x1, t0 // Check if zero mod p256
ORR x2, x3, t1
ORR t1, t0, t0
CMP $0, t0
CSEL EQ, t2, ZR, hlp0
EOR $-1, x0, t0
EOR const0, x1, t1
EOR const1, x3, t3
ORR t0, t1, t0
ORR x2, t3, t1
ORR t1, t0, t0
CMP $0, t0
CSEL EQ, t2, hlp0, hlp0
AND hlp0, hlp1, hlp1
LDx(r)
CALL p256SqrInternal<>(SB) // rsqr = rˆ2
STy(rsqr)
LDx(h)
CALL p256SqrInternal<>(SB) // hsqr = hˆ2
STy(hsqr)
LDx(h)
CALL p256MulInternal<>(SB) // hcub = hˆ3
STy(hcub)
LDx(s1)
CALL p256MulInternal<>(SB)
STy(s2)
LDx(z1in)
LDy(z2in)
CALL p256MulInternal<>(SB) // z1 * z2
LDx(h)
CALL p256MulInternal<>(SB) // z1 * z2 * h
MOVD res+0(FP), b_ptr
STy(z3out)
LDx(hsqr)
LDy(u1)
CALL p256MulInternal<>(SB) // hˆ2 * u1
STy(u2)
p256MulBy2Inline // u1 * hˆ2 * 2, inline
LDy(rsqr)
CALL p256SubInternal<>(SB) // rˆ2 - u1 * hˆ2 * 2
MOVD x0, y0
MOVD x1, y1
MOVD x2, y2
MOVD x3, y3
LDx(hcub)
CALL p256SubInternal<>(SB)
STx(x3out)
LDy(u2)
CALL p256SubInternal<>(SB)
LDy(r)
CALL p256MulInternal<>(SB)
LDx(s2)
CALL p256SubInternal<>(SB)
STx(y3out)
MOVD hlp1, R0
MOVD R0, ret+72(FP)
RET
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