crypton-2.1.3: cbits/s2n/arm/p256_montjmixadd_alt.S
// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT-0
// ----------------------------------------------------------------------------
// Point mixed addition on NIST curve P-256 in Montgomery-Jacobian coordinates
//
// extern void p256_montjmixadd_alt(uint64_t p3[static 12],
// const uint64_t p1[static 12],
// const uint64_t p2[static 8]);
//
// Does p3 := p1 + p2 where all points are regarded as Jacobian triples with
// each coordinate in the Montgomery domain, i.e. x' = (2^256 * x) mod p_256.
// A Jacobian triple (x',y',z') represents affine point (x/z^2,y/z^3).
// The "mixed" part means that p2 only has x and y coordinates, with the
// implicit z coordinate assumed to be the identity.
//
// Standard ARM ABI: X0 = p3, X1 = p1, X2 = p2
// ----------------------------------------------------------------------------
#include "_internal_s2n_bignum_arm.h"
S2N_BN_SYM_VISIBILITY_DIRECTIVE(p256_montjmixadd_alt)
S2N_BN_FUNCTION_TYPE_DIRECTIVE(p256_montjmixadd_alt)
S2N_BN_SYM_PRIVACY_DIRECTIVE(p256_montjmixadd_alt)
.text
.balign 4
// Size of individual field elements
#define NUMSIZE 32
// Stable homes for input arguments during main code sequence
#define input_z x15
#define input_x x16
#define input_y x17
// Pointer-offset pairs for inputs and outputs
#define x_1 input_x, #0
#define y_1 input_x, #NUMSIZE
#define z_1 input_x, #(2*NUMSIZE)
#define x_2 input_y, #0
#define y_2 input_y, #NUMSIZE
#define x_3 input_z, #0
#define y_3 input_z, #NUMSIZE
#define z_3 input_z, #(2*NUMSIZE)
// Pointer-offset pairs for temporaries, with some aliasing
// #NSPACE is the total stack needed for these temporaries
#define zp2 sp, #(NUMSIZE*0)
#define ww sp, #(NUMSIZE*0)
#define resx sp, #(NUMSIZE*0)
#define yd sp, #(NUMSIZE*1)
#define y2a sp, #(NUMSIZE*1)
#define x2a sp, #(NUMSIZE*2)
#define zzx2 sp, #(NUMSIZE*2)
#define zz sp, #(NUMSIZE*3)
#define t1 sp, #(NUMSIZE*3)
#define t2 sp, #(NUMSIZE*4)
#define zzx1 sp, #(NUMSIZE*4)
#define resy sp, #(NUMSIZE*4)
#define xd sp, #(NUMSIZE*5)
#define resz sp, #(NUMSIZE*5)
#define NSPACE NUMSIZE*6
// Corresponds to bignum_montmul_p256_alt except registers
#define montmul_p256(P0,P1,P2) \
ldp x3, x4, [P1] __LF \
ldp x7, x8, [P2] __LF \
mul x12, x3, x7 __LF \
umulh x13, x3, x7 __LF \
mul x11, x3, x8 __LF \
umulh x14, x3, x8 __LF \
adds x13, x13, x11 __LF \
ldp x9, x10, [P2+16] __LF \
mul x11, x3, x9 __LF \
umulh x0, x3, x9 __LF \
adcs x14, x14, x11 __LF \
mul x11, x3, x10 __LF \
umulh x1, x3, x10 __LF \
adcs x0, x0, x11 __LF \
adc x1, x1, xzr __LF \
ldp x5, x6, [P1+16] __LF \
mul x11, x4, x7 __LF \
adds x13, x13, x11 __LF \
mul x11, x4, x8 __LF \
adcs x14, x14, x11 __LF \
mul x11, x4, x9 __LF \
adcs x0, x0, x11 __LF \
mul x11, x4, x10 __LF \
adcs x1, x1, x11 __LF \
umulh x3, x4, x10 __LF \
adc x3, x3, xzr __LF \
umulh x11, x4, x7 __LF \
adds x14, x14, x11 __LF \
umulh x11, x4, x8 __LF \
adcs x0, x0, x11 __LF \
umulh x11, x4, x9 __LF \
adcs x1, x1, x11 __LF \
adc x3, x3, xzr __LF \
mul x11, x5, x7 __LF \
adds x14, x14, x11 __LF \
mul x11, x5, x8 __LF \
adcs x0, x0, x11 __LF \
mul x11, x5, x9 __LF \
adcs x1, x1, x11 __LF \
mul x11, x5, x10 __LF \
adcs x3, x3, x11 __LF \
umulh x4, x5, x10 __LF \
adc x4, x4, xzr __LF \
umulh x11, x5, x7 __LF \
adds x0, x0, x11 __LF \
umulh x11, x5, x8 __LF \
adcs x1, x1, x11 __LF \
umulh x11, x5, x9 __LF \
adcs x3, x3, x11 __LF \
adc x4, x4, xzr __LF \
mul x11, x6, x7 __LF \
adds x0, x0, x11 __LF \
mul x11, x6, x8 __LF \
adcs x1, x1, x11 __LF \
mul x11, x6, x9 __LF \
adcs x3, x3, x11 __LF \
mul x11, x6, x10 __LF \
adcs x4, x4, x11 __LF \
umulh x5, x6, x10 __LF \
adc x5, x5, xzr __LF \
mov x10, #0xffffffff00000001 __LF \
adds x13, x13, x12, lsl #32 __LF \
lsr x11, x12, #32 __LF \
adcs x14, x14, x11 __LF \
mul x11, x12, x10 __LF \
umulh x12, x12, x10 __LF \
adcs x0, x0, x11 __LF \
adc x12, x12, xzr __LF \
umulh x11, x6, x7 __LF \
adds x1, x1, x11 __LF \
umulh x11, x6, x8 __LF \
adcs x3, x3, x11 __LF \
umulh x11, x6, x9 __LF \
adcs x4, x4, x11 __LF \
adc x5, x5, xzr __LF \
adds x14, x14, x13, lsl #32 __LF \
lsr x11, x13, #32 __LF \
adcs x0, x0, x11 __LF \
mul x11, x13, x10 __LF \
umulh x13, x13, x10 __LF \
adcs x12, x12, x11 __LF \
adc x13, x13, xzr __LF \
adds x0, x0, x14, lsl #32 __LF \
lsr x11, x14, #32 __LF \
adcs x12, x12, x11 __LF \
mul x11, x14, x10 __LF \
umulh x14, x14, x10 __LF \
adcs x13, x13, x11 __LF \
adc x14, x14, xzr __LF \
adds x12, x12, x0, lsl #32 __LF \
lsr x11, x0, #32 __LF \
adcs x13, x13, x11 __LF \
mul x11, x0, x10 __LF \
umulh x0, x0, x10 __LF \
adcs x14, x14, x11 __LF \
adc x0, x0, xzr __LF \
adds x12, x12, x1 __LF \
adcs x13, x13, x3 __LF \
adcs x14, x14, x4 __LF \
adcs x0, x0, x5 __LF \
cset x8, cs __LF \
mov x11, #0xffffffff __LF \
adds x1, x12, #0x1 __LF \
sbcs x3, x13, x11 __LF \
sbcs x4, x14, xzr __LF \
sbcs x5, x0, x10 __LF \
sbcs xzr, x8, xzr __LF \
csel x12, x12, x1, cc __LF \
csel x13, x13, x3, cc __LF \
csel x14, x14, x4, cc __LF \
csel x0, x0, x5, cc __LF \
stp x12, x13, [P0] __LF \
stp x14, x0, [P0+16]
// Corresponds exactly to bignum_montsqr_p256_alt
#define montsqr_p256(P0,P1) \
ldp x2, x3, [P1] __LF \
mul x9, x2, x3 __LF \
umulh x10, x2, x3 __LF \
ldp x4, x5, [P1+16] __LF \
mul x11, x2, x5 __LF \
umulh x12, x2, x5 __LF \
mul x6, x2, x4 __LF \
umulh x7, x2, x4 __LF \
adds x10, x10, x6 __LF \
adcs x11, x11, x7 __LF \
mul x6, x3, x4 __LF \
umulh x7, x3, x4 __LF \
adc x7, x7, xzr __LF \
adds x11, x11, x6 __LF \
mul x13, x4, x5 __LF \
umulh x14, x4, x5 __LF \
adcs x12, x12, x7 __LF \
mul x6, x3, x5 __LF \
umulh x7, x3, x5 __LF \
adc x7, x7, xzr __LF \
adds x12, x12, x6 __LF \
adcs x13, x13, x7 __LF \
adc x14, x14, xzr __LF \
adds x9, x9, x9 __LF \
adcs x10, x10, x10 __LF \
adcs x11, x11, x11 __LF \
adcs x12, x12, x12 __LF \
adcs x13, x13, x13 __LF \
adcs x14, x14, x14 __LF \
cset x7, cs __LF \
umulh x6, x2, x2 __LF \
mul x8, x2, x2 __LF \
adds x9, x9, x6 __LF \
mul x6, x3, x3 __LF \
adcs x10, x10, x6 __LF \
umulh x6, x3, x3 __LF \
adcs x11, x11, x6 __LF \
mul x6, x4, x4 __LF \
adcs x12, x12, x6 __LF \
umulh x6, x4, x4 __LF \
adcs x13, x13, x6 __LF \
mul x6, x5, x5 __LF \
adcs x14, x14, x6 __LF \
umulh x6, x5, x5 __LF \
adc x7, x7, x6 __LF \
adds x9, x9, x8, lsl #32 __LF \
lsr x3, x8, #32 __LF \
adcs x10, x10, x3 __LF \
mov x3, #0xffffffff00000001 __LF \
mul x2, x8, x3 __LF \
umulh x8, x8, x3 __LF \
adcs x11, x11, x2 __LF \
adc x8, x8, xzr __LF \
adds x10, x10, x9, lsl #32 __LF \
lsr x3, x9, #32 __LF \
adcs x11, x11, x3 __LF \
mov x3, #0xffffffff00000001 __LF \
mul x2, x9, x3 __LF \
umulh x9, x9, x3 __LF \
adcs x8, x8, x2 __LF \
adc x9, x9, xzr __LF \
adds x11, x11, x10, lsl #32 __LF \
lsr x3, x10, #32 __LF \
adcs x8, x8, x3 __LF \
mov x3, #0xffffffff00000001 __LF \
mul x2, x10, x3 __LF \
umulh x10, x10, x3 __LF \
adcs x9, x9, x2 __LF \
adc x10, x10, xzr __LF \
adds x8, x8, x11, lsl #32 __LF \
lsr x3, x11, #32 __LF \
adcs x9, x9, x3 __LF \
mov x3, #0xffffffff00000001 __LF \
mul x2, x11, x3 __LF \
umulh x11, x11, x3 __LF \
adcs x10, x10, x2 __LF \
adc x11, x11, xzr __LF \
adds x8, x8, x12 __LF \
adcs x9, x9, x13 __LF \
adcs x10, x10, x14 __LF \
adcs x11, x11, x7 __LF \
cset x2, cs __LF \
mov x3, #0xffffffff __LF \
mov x5, #0xffffffff00000001 __LF \
adds x12, x8, #0x1 __LF \
sbcs x13, x9, x3 __LF \
sbcs x14, x10, xzr __LF \
sbcs x7, x11, x5 __LF \
sbcs xzr, x2, xzr __LF \
csel x8, x8, x12, cc __LF \
csel x9, x9, x13, cc __LF \
csel x10, x10, x14, cc __LF \
csel x11, x11, x7, cc __LF \
stp x8, x9, [P0] __LF \
stp x10, x11, [P0+16]
// Almost-Montgomery variant which we use when an input to other muls
// with the other argument fully reduced (which is always safe).
#define amontsqr_p256(P0,P1) \
ldp x2, x3, [P1] __LF \
mul x9, x2, x3 __LF \
umulh x10, x2, x3 __LF \
ldp x4, x5, [P1+16] __LF \
mul x11, x2, x5 __LF \
umulh x12, x2, x5 __LF \
mul x6, x2, x4 __LF \
umulh x7, x2, x4 __LF \
adds x10, x10, x6 __LF \
adcs x11, x11, x7 __LF \
mul x6, x3, x4 __LF \
umulh x7, x3, x4 __LF \
adc x7, x7, xzr __LF \
adds x11, x11, x6 __LF \
mul x13, x4, x5 __LF \
umulh x14, x4, x5 __LF \
adcs x12, x12, x7 __LF \
mul x6, x3, x5 __LF \
umulh x7, x3, x5 __LF \
adc x7, x7, xzr __LF \
adds x12, x12, x6 __LF \
adcs x13, x13, x7 __LF \
adc x14, x14, xzr __LF \
adds x9, x9, x9 __LF \
adcs x10, x10, x10 __LF \
adcs x11, x11, x11 __LF \
adcs x12, x12, x12 __LF \
adcs x13, x13, x13 __LF \
adcs x14, x14, x14 __LF \
cset x7, cs __LF \
umulh x6, x2, x2 __LF \
mul x8, x2, x2 __LF \
adds x9, x9, x6 __LF \
mul x6, x3, x3 __LF \
adcs x10, x10, x6 __LF \
umulh x6, x3, x3 __LF \
adcs x11, x11, x6 __LF \
mul x6, x4, x4 __LF \
adcs x12, x12, x6 __LF \
umulh x6, x4, x4 __LF \
adcs x13, x13, x6 __LF \
mul x6, x5, x5 __LF \
adcs x14, x14, x6 __LF \
umulh x6, x5, x5 __LF \
adc x7, x7, x6 __LF \
adds x9, x9, x8, lsl #32 __LF \
lsr x3, x8, #32 __LF \
adcs x10, x10, x3 __LF \
mov x3, #0xffffffff00000001 __LF \
mul x2, x8, x3 __LF \
umulh x8, x8, x3 __LF \
adcs x11, x11, x2 __LF \
adc x8, x8, xzr __LF \
adds x10, x10, x9, lsl #32 __LF \
lsr x3, x9, #32 __LF \
adcs x11, x11, x3 __LF \
mov x3, #0xffffffff00000001 __LF \
mul x2, x9, x3 __LF \
umulh x9, x9, x3 __LF \
adcs x8, x8, x2 __LF \
adc x9, x9, xzr __LF \
adds x11, x11, x10, lsl #32 __LF \
lsr x3, x10, #32 __LF \
adcs x8, x8, x3 __LF \
mov x3, #0xffffffff00000001 __LF \
mul x2, x10, x3 __LF \
umulh x10, x10, x3 __LF \
adcs x9, x9, x2 __LF \
adc x10, x10, xzr __LF \
adds x8, x8, x11, lsl #32 __LF \
lsr x3, x11, #32 __LF \
adcs x9, x9, x3 __LF \
mov x3, #0xffffffff00000001 __LF \
mul x2, x11, x3 __LF \
umulh x11, x11, x3 __LF \
adcs x10, x10, x2 __LF \
adc x11, x11, xzr __LF \
adds x8, x8, x12 __LF \
adcs x9, x9, x13 __LF \
adcs x10, x10, x14 __LF \
adcs x11, x11, x7 __LF \
mov x2, #0xffffffffffffffff __LF \
csel x2, xzr, x2, cc __LF \
mov x3, #0xffffffff __LF \
csel x3, xzr, x3, cc __LF \
mov x5, #0xffffffff00000001 __LF \
csel x5, xzr, x5, cc __LF \
subs x8, x8, x2 __LF \
sbcs x9, x9, x3 __LF \
sbcs x10, x10, xzr __LF \
sbc x11, x11, x5 __LF \
stp x8, x9, [P0] __LF \
stp x10, x11, [P0+16]
// Corresponds exactly to bignum_sub_p256
#define sub_p256(P0,P1,P2) \
ldp x5, x6, [P1] __LF \
ldp x4, x3, [P2] __LF \
subs x5, x5, x4 __LF \
sbcs x6, x6, x3 __LF \
ldp x7, x8, [P1+16] __LF \
ldp x4, x3, [P2+16] __LF \
sbcs x7, x7, x4 __LF \
sbcs x8, x8, x3 __LF \
csetm x3, cc __LF \
adds x5, x5, x3 __LF \
mov x4, #0xffffffff __LF \
and x4, x4, x3 __LF \
adcs x6, x6, x4 __LF \
adcs x7, x7, xzr __LF \
mov x4, #0xffffffff00000001 __LF \
and x4, x4, x3 __LF \
adc x8, x8, x4 __LF \
stp x5, x6, [P0] __LF \
stp x7, x8, [P0+16]
S2N_BN_SYMBOL(p256_montjmixadd_alt):
CFI_START
// Make room on stack for temporary variables
// Move the input arguments to stable places
CFI_DEC_SP(NSPACE)
mov input_z, x0
mov input_x, x1
mov input_y, x2
// Main code, just a sequence of basic field operations
// 8 * multiply + 3 * square + 7 * subtract
amontsqr_p256(zp2,z_1)
montmul_p256(y2a,z_1,y_2)
montmul_p256(x2a,zp2,x_2)
montmul_p256(y2a,zp2,y2a)
sub_p256(xd,x2a,x_1)
sub_p256(yd,y2a,y_1)
amontsqr_p256(zz,xd)
montsqr_p256(ww,yd)
montmul_p256(zzx1,zz,x_1)
montmul_p256(zzx2,zz,x2a)
sub_p256(resx,ww,zzx1)
sub_p256(t1,zzx2,zzx1)
montmul_p256(resz,xd,z_1)
sub_p256(resx,resx,zzx2)
sub_p256(t2,zzx1,resx)
montmul_p256(t1,t1,y_1)
montmul_p256(t2,yd,t2)
sub_p256(resy,t2,t1)
// Test if z_1 = 0 to decide if p1 = 0 (up to projective equivalence)
ldp x0, x1, [z_1]
ldp x2, x3, [z_1+16]
orr x4, x0, x1
orr x5, x2, x3
orr x4, x4, x5
cmp x4, xzr
// Multiplex: if p1 <> 0 just copy the computed result from the staging area.
// If p1 = 0 then return the point p2 augmented with a z = 1 coordinate (in
// Montgomery form so not the simple constant 1 but rather 2^256 - p_256),
// hence giving 0 + p2 = p2 for the final result.
ldp x0, x1, [resx]
ldp x12, x13, [x_2]
csel x0, x0, x12, ne
csel x1, x1, x13, ne
ldp x2, x3, [resx+16]
ldp x12, x13, [x_2+16]
csel x2, x2, x12, ne
csel x3, x3, x13, ne
ldp x4, x5, [resy]
ldp x12, x13, [y_2]
csel x4, x4, x12, ne
csel x5, x5, x13, ne
ldp x6, x7, [resy+16]
ldp x12, x13, [y_2+16]
csel x6, x6, x12, ne
csel x7, x7, x13, ne
ldp x8, x9, [resz]
mov x12, #0x0000000000000001
mov x13, #0xffffffff00000000
csel x8, x8, x12, ne
csel x9, x9, x13, ne
ldp x10, x11, [resz+16]
mov x12, #0xffffffffffffffff
mov x13, #0x00000000fffffffe
csel x10, x10, x12, ne
csel x11, x11, x13, ne
stp x0, x1, [x_3]
stp x2, x3, [x_3+16]
stp x4, x5, [y_3]
stp x6, x7, [y_3+16]
stp x8, x9, [z_3]
stp x10, x11, [z_3+16]
// Restore stack and return
CFI_INC_SP(NSPACE)
CFI_RET
S2N_BN_SIZE_DIRECTIVE(p256_montjmixadd_alt)
#if defined(__linux__) && defined(__ELF__)
.section .note.GNU-stack, "", %progbits
#endif