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P256-cortex-m4-ecdh-speedopt-gcc.s
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P256-cortex-m4-ecdh-speedopt-gcc.s
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.syntax unified
.thumb
// P-256 ECDH
// Author: Emil Lenngren
// Licensed under the BSD 2-clause license.
// Note on calling conventions: some of the local functions in this file use custom calling conventions.
// Exported symbols use the standard C calling conventions for ARM, which means that r4-r11 and sp are preserved and the other registers are clobbered.
// All integers are assumed to be in little endian
// Run time: 994k cycles
.text
// Field arithmetics for the prime field where p = 2^256 - 2^224 + 2^192 + 2^96 - 1
// Multiplication and Squaring use Montgomery Modular Multiplication where R = 2^256
// To convert a value to Montgomery class, use P256_mulmod(value, R^512 mod p)
// To convert a value from Montgomery class to standard form, use P256_mulmod(value, 1)
// If inputs are A*R mod p and B*R mod p, computes AB*R mod p
// *r1 = in1, *r2 = in2
// out: r0-r7
// clobbers all other registers
// cycles: 230
.type P256_mulmod, %function
P256_mulmod:
push {r2,lr}
//frame push {lr}
//frame address sp,8
sub sp,#36
//frame address sp,44
ldm r2,{r2,r3,r4,r5}
ldm r1!,{r0,r10,lr}
umull r6,r11,r2,r0
umull r7,r12,r3,r0
umaal r7,r11,r2,r10
push {r6,r7}
//frame address sp,52
umull r8,r6,r4,r0
umaal r8,r11,r3,r10
umull r9,r7,r5,r0
umaal r9,r11,r4,r10
umaal r11,r7,r5,r10
umaal r8,r12,r2,lr
umaal r9,r12,r3,lr
umaal r11,r12,r4,lr
umaal r12,r7,r5,lr
ldm r1!,{r0,r10,lr}
umaal r9,r6,r2,r0
umaal r11,r6,r3,r0
umaal r12,r6,r4,r0
umaal r6,r7,r5,r0
strd r8,r9,[sp,#8]
mov r9,#0
umaal r11,r9,r2,r10
umaal r12,r9,r3,r10
umaal r6,r9,r4,r10
umaal r7,r9,r5,r10
mov r10,#0
umaal r12,r10,r2,lr
umaal r6,r10,r3,lr
umaal r7,r10,r4,lr
umaal r9,r10,r5,lr
ldr r8,[r1],#4
mov lr,#0
umaal lr,r6,r2,r8
umaal r7,r6,r3,r8
umaal r9,r6,r4,r8
umaal r10,r6,r5,r8
//_ _ _ _ _ 6 10 9| 7 | lr 12 11 _ _ _ _
ldr r8,[r1],#-28
mov r0,#0
umaal r7,r0,r2,r8
umaal r9,r0,r3,r8
umaal r10,r0,r4,r8
umaal r6,r0,r5,r8
push {r0}
//frame address sp,56
//_ _ _ _ s 6 10 9| 7 | lr 12 11 _ _ _ _
ldr r2,[sp,#48]
adds r2,r2,#16
ldm r2,{r2,r3,r4,r5}
ldr r8,[r1],#4
mov r0,#0
umaal r11,r0,r2,r8
str r11,[sp,#16+4]
umaal r12,r0,r3,r8
umaal lr,r0,r4,r8
umaal r0,r7,r5,r8 // 7=carry for 9
//_ _ _ _ s 6 10 9+7| 0 | lr 12 _ _ _ _ _
ldr r8,[r1],#4
mov r11,#0
umaal r12,r11,r2,r8
str r12,[sp,#20+4]
umaal lr,r11,r3,r8
umaal r0,r11,r4,r8
umaal r11,r7,r5,r8 // 7=carry for 10
//_ _ _ _ s 6 10+7 9+11| 0 | lr _ _ _ _ _ _
ldr r8,[r1],#4
mov r12,#0
umaal lr,r12,r2,r8
str lr,[sp,#24+4]
umaal r0,r12,r3,r8
umaal r11,r12,r4,r8
umaal r10,r12,r5,r8 // 12=carry for 6
//_ _ _ _ s 6+12 10+7 9+11| 0 | _ _ _ _ _ _ _
ldr r8,[r1],#4
mov lr,#0
umaal r0,lr,r2,r8
str r0,[sp,#28+4]
umaal r11,lr,r3,r8
umaal r10,lr,r4,r8
umaal r6,lr,r5,r8 // lr=carry for saved
//_ _ _ _ s+lr 6+12 10+7 9+11| _ | _ _ _ _ _ _ _
ldm r1!,{r0,r8}
umaal r11,r9,r2,r0
str r11,[sp,#32+4]
umaal r9,r10,r3,r0
umaal r10,r6,r4,r0
pop {r11}
//frame address sp,52
umaal r11,r6,r5,r0 // 6=carry for next
//_ _ _ 6 11+lr 10+12 9+7 _ | _ | _ _ _ _ _ _ _
umaal r9,r7,r2,r8
umaal r10,r7,r3,r8
umaal r11,r7,r4,r8
umaal r6,r7,r5,r8
ldm r1!,{r0,r8}
umaal r10,r12,r2,r0
umaal r11,r12,r3,r0
umaal r6,r12,r4,r0
umaal r7,r12,r5,r0
umaal r11,lr,r2,r8
umaal lr,r6,r3,r8
umaal r6,r7,r4,r8
umaal r7,r12,r5,r8
// 12 7 6 lr 11 10 9 stack*9
strd r6,r7,[sp,#36]
str r12,[sp,#44]
pop {r0-r8}
//frame address sp,16
mov r12,#0
adds r3,r0
adcs r4,r1
adcs r5,r2
adcs r6,r0
adcs r7,r1
adcs r8,r0
adcs r9,r1
adcs r10,#0
adcs r11,#0
adcs r12,#0
adds r6,r3
adcs r7,r4 // r4 instead of 0
adcs r8,r2
adcs r9,r3
adcs r10,r2
adcs r11,r3
adcs r12,#0
subs r7,r0
sbcs r8,r1
sbcs r9,r2
sbcs r10,r3
sbcs r11,#0
sbcs r12,#0 // r12 is between 0 and 2
pop {r1-r3}
//frame address sp,4
adds r0,lr,r12
adcs r1,#0
mov r12,#0
adcs r12,#0
//adds r7,r4 (added above instead)
adcs r8,r5
adcs r9,r6
adcs r10,r4
adcs r11,r5
adcs r0,r4
adcs r1,r5
adcs r2,r12
adcs r3,#0
mov r12,#0
adcs r12,#0
adcs r10,r7
adcs r11,#0
adcs r0,r6
adcs r1,r7
adcs r2,r6
adcs r3,r7
adcs r12,#0
subs r11,r4
sbcs r0,r5
sbcs r1,r6
sbcs r2,r7
sbcs r3,#0
sbcs r12,#0
// now (T + mN) / R is
// 8 9 10 11 0 1 2 3 12 (lsb -> msb)
subs r8,r8,#0xffffffff
sbcs r9,r9,#0xffffffff
sbcs r10,r10,#0xffffffff
sbcs r11,r11,#0
sbcs r4,r0,#0
sbcs r5,r1,#0
sbcs r6,r2,#1
sbcs r7,r3,#0xffffffff
sbc r12,r12,#0
adds r0,r8,r12
adcs r1,r9,r12
adcs r2,r10,r12
adcs r3,r11,#0
adcs r4,r4,#0
adcs r5,r5,#0
adcs r6,r6,r12, lsr #31
adcs r7,r7,r12
pop {pc}
.size P256_mulmod, .-P256_mulmod
// 172 cycles
// If input is A*R mod p, computes A^2*R mod p
// in/out: r0-r7
// clobbers all other registers
.type P256_sqrmod, %function
P256_sqrmod:
push {lr}
//frame push {lr}
//mul 01, 00
umull r10,r9,r0,r0
umull r11,r12,r0,r1
adds r11,r11,r11
mov lr,#0
umaal r9,r11,lr,lr
//r9 r10 done
//r12 carry for 3rd before col
//r11+C carry for 3rd final col
push {r9,r10}
//frame address sp,12
//mul 02, 11
mov r9,#0
umaal r9,r12,r0,r2
adcs r9,r9,r9
umaal r9,r11,r1,r1
//r9 done (3rd col)
//r12 carry for 4th before col
//r11+C carry for 4th final col
//mul 03, 12
umull r8,r10,r0,r3
umaal r8,r12,r1,r2
adcs r8,r8,r8
umaal r8,r11,lr,lr
//r8 done (4th col)
//r10+r12 carry for 5th before col
//r11+C carry for 5th final col
push {r8,r9}
//frame address sp,20
//mul 04, 13, 22
mov r9,#0
umaal r9,r10,r0,r4
umaal r9,r12,r1,r3
adcs r9,r9,r9
umaal r9,r11,r2,r2
//r9 done (5th col)
//r10+r12 carry for 6th before col
//r11+C carry for 6th final col
push {r9}
//frame address sp,24
//mul 05, 14, 23
umull r9,r8,r0,r5
umaal r9,r10,r1,r4
umaal r9,r12,r2,r3
adcs r9,r9,r9
umaal r9,r11,lr,lr
//r9 done (6th col)
//r10+r12+r8 carry for 7th before col
//r11+C carry for 7th final col
push {r9}
//frame address sp,28
//mul 06, 15, 24, 33
mov r9,#0
umaal r9,r8,r1,r5
umaal r9,r12,r2,r4
umaal r9,r10,r0,r6
adcs r9,r9,r9
umaal r9,r11,r3,r3
//r9 done (7th col)
//r8+r10+r12 carry for 8th before col
//r11+C carry for 8th final col
push {r9}
//frame address sp,32
//mul 07, 16, 25, 34
umull r9,r0,r0,r7
umaal r9,r10,r1,r6
umaal r9,r12,r2,r5
umaal r9,r8,r3,r4
adcs r9,r9,r9
umaal r9,r11,lr,lr
//r9 done (8th col)
//r0+r8+r10+r12 carry for 9th before col
//r11+C carry for 9th final col
//mul 17, 26, 35, 44
umaal r0,r8,r1,r7 //r1 is now dead
umaal r0,r10,r2,r6
umaal r0,r12,r3,r5
adcs r0,r0,r0
umaal r11,r0,r4,r4
//r11 done (9th col)
//r8+r10+r12 carry for 10th before col
//r0+C carry for 10th final col
//mul 27, 36, 45
umaal r12,r8,r2,r7 //r2 is now dead
umaal r12,r10,r3,r6
movs r2,#0
umaal r12,r2,r4,r5
adcs r1,r12,r12
umaal r0,r1,lr,lr
//r0 done (10th col)
//r8+r10+r2 carry for 11th before col
//r1+C carry for 11th final col
//mul 37, 46, 55
umaal r2,r8,r3,r7 //r3 is now dead
umaal r2,r10,r4,r6
adcs r2,r2,r2
umaal r1,r2,r5,r5
//r1 done (11th col)
//r8+r10 carry for 12th before col
//r2+C carry for 12th final col
//mul 47, 56
movs r3,#0
umaal r3,r8,r4,r7 //r4 is now dead
umaal r3,r10,r5,r6
adcs r3,r3,r3
umaal r2,r3,lr,lr
//r2 done (12th col)
//r8+r10 carry for 13th before col
//r3+C carry for 13th final col
//mul 57, 66
umaal r8,r10,r5,r7 //r5 is now dead
adcs r8,r8,r8
umaal r3,r8,r6,r6
//r3 done (13th col)
//r10 carry for 14th before col
//r8+C carry for 14th final col
//mul 67
umull r4,r5,lr,lr // set 0
umaal r4,r10,r6,r7
adcs r4,r4,r4
umaal r4,r8,lr,lr
//r4 done (14th col)
//r10 carry for 15th before col
//r8+C carry for 15th final col
//mul 77
adcs r10,r10,r10
umaal r8,r10,r7,r7
adcs r10,r10,lr
//r8 done (15th col)
//r10 done (16th col)
//msb -> lsb: r10 r8 r4 r3 r2 r1 r0 r11 r9 sp sp+4 sp+8 sp+12 sp+16 sp+20 sp+24
//now do reduction
push {r4,r8,r10}
//frame address sp,44
add r4,sp,#12
ldm r4,{r4-r8,r10,r12}
//lr is already 0
X0 .req r12
X1 .req r10
X2 .req r8
X3 .req r7
X4 .req r6
X5 .req r5
X6 .req r4
X7 .req r9
X8 .req r11
X9 .req r0
X10 .req r1
X11 .req r2
X12 .req r3
X13 .req r7
X14 .req r8
X15 .req r10
adcs X3,X0
adcs X4,X1
adcs X5,X2
adcs X6,X0
adcs X7,X1
adcs X8,X0
adcs X9,X1
adcs X10,#0
adcs X11,#0
adcs lr,#0
adds X6,X3
adcs X7,X4 // X4 instead of 0
adcs X8,X2
adcs X9,X3
adcs X10,X2
adcs X11,X3
adcs lr,#0
subs X7,X0
sbcs X8,X1
sbcs X9,X2
sbcs X10,X3
sbcs X11,#0
sbcs lr,#0 // lr is between 0 and 2
pop {X13,X14,X15}
//frame address sp,32
adds X0,X12,lr
adcs X13,#0
mov lr,#0
adcs lr,#0
//adds X7,X4 (added above instead)
adcs X8,X5
adcs X9,X6
adcs X10,X4
adcs X11,X5
adcs X0,X4
adcs X13,X5
adcs X14,lr
adcs X15,#0
mov lr,#0
adcs lr,#0
adcs X10,X7
adcs X11,#0
adcs X0,X6
adcs X13,X7
adcs X14,X6
adcs X15,X7
adcs lr,#0
subs X11,X4
sbcs X0,X5
sbcs X13,X6
sbcs X14,X7
sbcs X15,#0
sbcs lr,#0
// now (T + mN) / R is
// X8 X9 X10 X11 X0 X13 X14 X15 lr (lsb -> msb)
// r11 r0 r1 r2 r12 r7 r8 r10 lr
subs r11,r11,#0xffffffff
sbcs r9,r0,#0xffffffff
sbcs r4,r1,#0xffffffff
sbcs r3,r2,#0
sbcs r6,r12,#0
sbcs r5,r7,#0
sbcs r12,r8,#1
sbcs r8,r10,#0xffffffff
sbcs r7,lr,#0
adds r0,r11,r7
adcs r1,r9,r7
adcs r2,r4,r7
adcs r3,r3,#0
adcs r4,r6,#0
adcs r5,r5,#0
adcs r6,r12,r7, lsr #31
adcs r7,r8,r7
add sp,#28
//frame address sp,4
pop {pc}
.size P256_sqrmod, .-P256_sqrmod
// in/out: r0-r7, r8: count, *r9: operand for final multiplication
.type P256_sqrmod_many_and_mulmod, %function
P256_sqrmod_many_and_mulmod:
push {r9,lr}
//frame push {r9,lr}
cmp r8,#0
beq 1f
0:
push {r8}
//frame address sp,12
bl P256_sqrmod
pop {r8}
//frame address sp,8
subs r8,#1
bne 0b
1:
push {r0-r7}
//frame address sp,40
mov r1,sp
ldr r2,[sp,#32]
bl P256_mulmod
add sp,#36
//frame address sp,4
pop {pc}
.size P256_sqrmod_many_and_mulmod, .-P256_sqrmod_many_and_mulmod
P256_invtbl:
.byte ((8-4)>>2)
.byte 32
.byte ((16-8)>>2)+128
.byte 0
.byte (16>>2)+128
.byte 0
.byte (32>>2)+128
.byte 5*32
.byte (192-64)>>2
.byte 0
.byte (224-192)>>2
.byte 0
.byte (240-224)>>2
.byte 32
.byte (248-240)>>2
.byte 64
.byte (252-248)>>2
.byte 128
.byte (256-252)>>2
.byte 96
.byte 0
.byte 5*32
// in: r0-r7 = value
// out: r0-r7
// for modinv, call input a, then if a = A * R % p, then it calculates A^-1 * R % p = (a/R)^-1 * R % p = R^2 / a % p
.type P256_modinv, %function
P256_modinv:
push {r0-r7,lr}
//frame push {r4-r7,lr}
//frame address sp,36
// t = a^2*a
mov r8,#1
mov r9,sp
bl P256_sqrmod_many_and_mulmod
push {r0-r7}
//frame address sp,68
// a4_2 = a2_0^(2^2)
bl P256_sqrmod
bl P256_sqrmod
push {r0-r7}
//frame address sp,100
// a4_0 = a4_2*a2_0
mov r1,sp
add r2,sp,#32
bl P256_mulmod
add r8,sp,#32
stm r8,{r0-r7}
mov r12,#0
0:
adr r9,P256_invtbl
ldrsb r10,[r9,r12]
add r9,#1
ldrb r9,[r9,r12]
lsls r8,r10,#2
bpl 1f
push {r0-r7}
1:
and r8,#0xff
add r9,sp
push {r12}
bl P256_sqrmod_many_and_mulmod
pop {r12}
add r12,#2
cmp r12,#22
bne 0b
add sp,#6*32
//frame address sp,4
pop {pc}
.size P256_modinv, .-P256_modinv
// 52 cycles
// Computes A + B mod p, assumes A, B < p
// in: *r1, *r2
// out: r0-r7
// clobbers all other registers
.type P256_addmod, %function
P256_addmod:
ldm r2,{r2-r9}
ldm r1!,{r0,r10,r11,r12}
adds r2,r0
adcs r3,r10
adcs r4,r11
adcs r5,r12
ldm r1,{r0,r1,r11,r12}
adcs r6,r0
adcs r7,r1
adcs r8,r11
adcs r9,r12
movs r10,#0
adcs r10,r10
subs r2,#0xffffffff
sbcs r3,#0xffffffff
sbcs r4,#0xffffffff
sbcs r5,#0
sbcs r6,#0
sbcs r7,#0
sbcs r8,#1
sbcs r9,#0xffffffff
sbcs r10,#0
adds r0,r2,r10
adcs r1,r3,r10
adcs r2,r4,r10
adcs r3,r5,#0
adcs r4,r6,#0
adcs r5,r7,#0
adcs r6,r8,r10, lsr #31
adcs r7,r9,r10
bx lr
.size P256_addmod, .-P256_addmod
// 42 cycles
// Computes A - B mod p, assumes A, B < p
// in: *r1, *r2
// out: r0-r7
// clobbers all other registers
.type P256_submod, %function
P256_submod:
ldm r1,{r3-r10}
ldm r2!,{r0,r1,r11,r12}
subs r3,r0
sbcs r4,r1
sbcs r5,r11
sbcs r6,r12
ldm r2,{r0,r1,r11,r12}
sbcs r7,r0
sbcs r8,r1
sbcs r9,r11
sbcs r10,r12
sbcs r11,r11
adds r0,r3,r11
adcs r1,r4,r11
adcs r2,r5,r11
adcs r3,r6,#0
adcs r4,r7,#0
adcs r5,r8,#0
adcs r6,r9,r11, lsr #31
adcs r7,r10,r11
bx lr
.size P256_submod, .-P256_submod
// 33 cycles
// in: r0-r7
.type P256_times2, %function
P256_times2:
adds r0,r0
adcs r1,r1
adcs r2,r2
adcs r3,r3
adcs r4,r4
adcs r5,r5
adcs r6,r6
adcs r7,r7
mov r8,#0
adcs r8,r8
subs r0,#0xffffffff
sbcs r1,#0xffffffff
sbcs r2,#0xffffffff
sbcs r3,#0
sbcs r4,#0
sbcs r5,#0
sbcs r6,#1
sbcs r7,#0xffffffff
sbcs r8,#0
adds r0,r8
adcs r1,r8
adcs r2,r8
adcs r3,#0
adcs r4,#0
adcs r5,#0
adcs r6,r6,r8, lsr #31
adcs r7,r8
bx lr
.size P256_times2, .-P256_times2
.align 2
// (2^256)^2 mod p
R2_mod_p:
.word 3
.word 0
.word 0xffffffff
.word 0xfffffffb
.word 0xfffffffe
.word 0xffffffff
.word 0xfffffffd
.word 4
// in: *r1
// out: *r0
.type P256_to_montgomery, %function
P256_to_montgomery:
push {r0,r4-r11,lr}
//frame push {r4-r11,lr}
//frame address sp,40
adr r2,R2_mod_p
bl P256_mulmod
pop {r8}
//frame address sp,36
stm r8,{r0-r7}
pop {r4-r11,pc}
.size P256_to_montgomery, .-P256_to_montgomery
// in: *r1
// out: *r0
.type P256_from_montgomery, %function
P256_from_montgomery:
push {r0,r4-r11,lr}
//frame push {r4-r11,lr}
//frame address sp,40
movs r2,#0
movs r3,#0
push {r2-r3}
//frame address sp,48
push {r2-r3}
//frame address sp,56
push {r2-r3}
//frame address sp,64
movs r2,#1
push {r2-r3}
//frame address sp,72
mov r2,sp
bl P256_mulmod
add sp,#32
//frame address sp,40
pop {r8}
//frame address sp,36
stm r8,{r0-r7}
pop {r4-r11,pc}
.size P256_from_montgomery, .-P256_from_montgomery
// Elliptic curve operations on the NIST curve P256
// Checks if a point is on curve
// in: *r0 = x, *r1 = y, in Montgomery form
// out: r0 = 1 if on curve, .else 0
.type P256_point_is_on_curve, %function
P256_point_is_on_curve:
push {r0,r4-r11,lr}
//frame push {r4-r11,lr}
//frame address sp,40
// We verify y^2 - (x^3 - 3x) = b
// y^2
ldm r1,{r0-r7}
bl P256_sqrmod
push {r0-r7}
//frame address sp,72
// x^2
ldr r0,[sp,#32]
ldm r0,{r0-r7}
bl P256_sqrmod
push {r0-r7}
//frame address sp,104
// x^3
ldr r1,[sp,#64]
mov r2,sp
bl P256_mulmod
stm sp,{r0-r7}
// x^3 - 3x
movs r0,#3
0:
push {r0}
//frame address sp,108
add r1,sp,#4
ldr r2,[sp,#68]
bl P256_submod
add r8,sp,#4
stm r8,{r0-r7}
pop {r0}
//frame address sp,104
subs r0,#1
bne 0b
// y^2 - (x^3 - 3x)
add r1,sp,#32
mov r2,sp
bl P256_submod
// compare with b
adr r8,P256_b_mont
ldm r8!,{r9-r12}
eors r0,r9
ittt eq
eorseq r1,r10
eorseq r2,r11
eorseq r3,r12
ldm r8,{r9-r12}
itttt eq
eorseq r4,r9
eorseq r5,r10
eorseq r6,r11
eorseq r7,r12
mov r0,#0
it eq
moveq r0,#1
add sp,#68
//frame address sp,36
pop {r4-r11,pc}
.size P256_point_is_on_curve, .-P256_point_is_on_curve
.align 2
P256_b_mont:
.word 0x29c4bddf
.word 0xd89cdf62
.word 0x78843090
.word 0xacf005cd
.word 0xf7212ed6
.word 0xe5a220ab
.word 0x04874834
.word 0xdc30061d
// Selects one of many values
// *r0 = output, *r1 = table, r2 = index to choose [0..7]
.type P256_select, %function
P256_select:
mov r3,r2
movs r2,#3
push {r0,r2,r3,r4-r11,lr}
//frame push {r4-r11,lr}
//frame address sp,48
0:
rsbs r3,#0
sbcs r3,r3
mvns r3,r3
ldm r1!,{r4-r11}
ands r4,r3
ands r5,r3
ands r6,r3
ands r7,r3
and r8,r3
and r9,r3
and r10,r3
and r11,r3
adds r1,#64
movs r3,#1
1:
ldr r0,[sp,#8]
eors r0,r3
mrs r0,apsr
lsrs r0,#30
ldm r1!,{r2,r12,lr}
umlal r4,r3,r0,r2
umlal r5,r2,r0,r12
umlal r6,r3,r0,lr
ldm r1!,{r2,r12,lr}
umlal r7,r3,r0,r2
umlal r8,r2,r0,r12
umlal r9,r3,r0,lr
ldm r1!,{r12,lr}
umlal r10,r2,r0,r12
umlal r11,r3,r0,lr
adds r1,#64
adds r3,#1
cmp r3,#8
bne 1b
ldm sp,{r0,r12}
stm r0!,{r4-r11}
str r0,[sp]
subs r1,#736
subs r12,#1
str r12,[sp,#4]
ldr r3,[sp,#8]
bne 0b
add sp,#12
//frame address sp,36
pop {r4-r11,pc}
.size P256_select, .-P256_select
// Doubles the point in Jacobian form (integers are in Montgomery form)
// *r0 = out, *r1 = in