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P256-cortex-m4-ecdh-sizeopt-keil.s
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P256-cortex-m4-ecdh-sizeopt-keil.s
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; 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: 1108k cycles
area |.text|, code, readonly
; 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)
P256_sqrmod ;label definition
mov r2,r1
; fallthrough
; If inputs are A*R mod p and B*R mod p, computes AB*R mod p
; input: *r0 = out, *r1 = in1, *r2 = in2
; output: *r8 = out
; clobbers all other registers
P256_mulmod proc
mov r3,r0
push {r2,r3,lr}
frame push {lr}
frame address sp,12
sub sp,#36
frame address sp,48
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,56
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,60
;_ _ _ _ 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,56
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,20
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,8
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 {r8}
frame address sp,4
stm r8,{r0-r7}
pop {pc}
endp
; 52 cycles
; Computes A + B mod p, assumes A, B < p
; in: *r1, *r2
; out: r0-r7
; clobbers all other registers
P256_addmod proc
push {r0}
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
pop {r8}
stm r8,{r0-r7}
bx lr
endp
; 42 cycles
; Computes A - B mod p, assumes A, B < p
; in: *r1, *r2
; out: r0-r7
; clobbers all other registers
P256_submod proc
push {r0}
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
pop {r8}
stm r8,{r0-r7}
bx lr
endp
; in: *r1
; out: *r0
P256_to_montgomery proc
push {r4-r11,lr}
frame push {r4-r11,lr}
adr r2,R2_mod_p
bl P256_mulmod
pop {r4-r11,pc}
endp
align 4
; (2^256)^2 mod p
R2_mod_p
dcd 3
dcd 0
dcd 0xffffffff
dcd 0xfffffffb
dcd 0xfffffffe
dcd 0xffffffff
dcd 0xfffffffd
dcd 4
; in: *r1
; out: *r0
P256_from_montgomery proc
push {r4-r11,lr}
frame push {r4-r11,lr}
movs r2,#0
movs r3,#0
push {r2-r3}
frame address sp,44
push {r2-r3}
frame address sp,52
push {r2-r3}
frame address sp,60
movs r2,#1
push {r2-r3}
frame address sp,68
mov r2,sp
bl P256_mulmod
add sp,#32
frame address sp,36
pop {r4-r11,pc}
endp
; 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
P256_point_is_on_curve proc
push {r0,r4-r11,lr}
frame push {r4-r11,lr}
frame address sp,40
; We verify y^2 - (x^3 - 3x) = b
; y^2
sub sp,#32
frame address sp,72
mov r0,sp
bl P256_sqrmod
; x^2
ldr r1,[sp,#32]
sub sp,#32
frame address sp,104
mov r0,sp
bl P256_sqrmod
; x^3
mov r0,sp
ldr r1,[sp,#64]
mov r2,sp
bl P256_mulmod
; x^3 - 3x
movs r0,#3
0
push {r0}
frame address sp,108
add r0,sp,#4
add r1,sp,#4
ldr r2,[sp,#68]
bl P256_submod
pop {r0}
frame address sp,104
subs r0,#1
bne %b0
; y^2 - (x^3 - 3x)
mov r0,sp
add r1,sp,#32
mov r2,sp
bl P256_submod
; compare with b
mov r0,sp
adr r1,P256_b_mont
bl P256_less_than
subs r0,#1
beq %f1
adr r0,P256_b_mont
mov r1,sp
bl P256_less_than
eor r0,#1
1
add sp,#68
frame address sp,36
pop {r4-r11,pc}
endp
align 4
P256_b_mont
dcd 0x29c4bddf
dcd 0xd89cdf62
dcd 0x78843090
dcd 0xacf005cd
dcd 0xf7212ed6
dcd 0xe5a220ab
dcd 0x04874834
dcd 0xdc30061d
; Selects one of many values
; *r0 = output, *r1 = table, r2 = index to choose [0..7]
P256_select proc
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 %b1
ldm sp,{r0,r12}
stm r0!,{r4-r11}
str r0,[sp] ; TODO: store r0,r12 together by push
subs r1,#736
subs r12,#1
str r12,[sp,#4]
ldr r3,[sp,#8]
bne %b0
add sp,#12
frame address sp,36
pop {r4-r11,pc}
endp
; Doubles the point in Jacobian form (integers are in Montgomery form)
; *r0 = out, *r1 = in
P256_double_j proc
push {r0,r1,r4-r11,lr}
frame push {r4-r11,lr}
frame address sp,44
; https://eprint.iacr.org/2014/130.pdf, algorithm 10
; t1 = Z1^2
sub sp,#32
frame address sp,76
mov r0,sp
adds r1,#64
bl P256_sqrmod
; Z2 = Y1 * Z1
ldrd r0,r1,[sp,#32]
adds r0,#64
adds r1,#32
add r2,r1,#32
bl P256_mulmod
; t2 = X1 + t1
ldr r1,[sp,#36]
mov r2,sp
sub sp,#32
frame address sp,108
mov r0,sp
bl P256_addmod
; t1 = X1 - t1
ldr r1,[sp,#68]
add r2,sp,#32
mov r0,r2
bl P256_submod
; t1 = t1 * t2
add r1,sp,#32
mov r2,sp
mov r0,r1
bl P256_mulmod
; t2 = t1 / 2
ldm r8,{r0-r7}
lsl r8,r0,#31
adds r0,r0,r8, asr #31
adcs r1,r1,r8, asr #31
adcs r2,r2,r8, asr #31
adcs r3,#0
adcs r4,#0
adcs r5,#0
adcs r6,r6,r8, lsr #31
adcs r7,r7,r8, asr #31
rrxs r7,r7
rrxs r6,r6
rrxs r5,r5
rrxs r4,r4
rrxs r3,r3
rrxs r2,r2
rrxs r1,r1
rrx r0,r0
stm sp,{r0-r7}
; t1 = t1 + t2
add r1,sp,#32
mov r2,sp
mov r0,r1
bl P256_addmod
; t2 = t1^2
mov r0,sp
add r1,sp,#32
bl P256_sqrmod
; Y2 = Y1^2
ldrd r0,r1,[sp,#64]
adds r0,#32
adds r1,#32
bl P256_sqrmod
; t3 = Y2^2
ldr r1,[sp,#64]
adds r1,#32
sub sp,#32
frame address sp,140
mov r0,sp
bl P256_sqrmod
; Y2 = X1 * Y2
ldrd r0,r1,[sp,#96]
adds r0,#32
mov r2,r0
bl P256_mulmod
mov r1,r8
; X2 = 2 * Y2
mov r2,r8
sub r0,r2,#32
bl P256_addmod
; X2 = t2 - X2
add r1,sp,#32
mov r2,r8
mov r0,r8
bl P256_submod
; t2 = Y2 - X2
mov r2,r8
add r1,r2,#32
add r0,sp,#32
bl P256_submod
; t1 = t1 * t2
add r0,sp,#64
add r1,sp,#64
add r2,sp,#32
bl P256_mulmod
; Y2 = t1 - t3
ldr r0,[sp,#96]
adds r0,#32
add r1,sp,#64
mov r2,sp
bl P256_submod
add sp,#104
frame address sp,36
pop {r4-r11,pc}
endp
; Adds or subtracts points in Jacobian form (integers are in Montgomery form)
; The first operand is located in *r0, the second in *r1 (may not overlap)
; The result is stored at *r0
;
; Requirements:
; - no operand is the point at infinity
; - both operand must be different
; - one operand must not be the negation of the other
; If requirements are not met, the returned Z point will be 0
P256_add_j proc
push {r0,r1,r4-r11,lr}
frame push {r4-r11,lr}
frame address sp,44
; Here a variant of
; https://www.hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-3/addition/add-1998-cmo-2.op3
; is used, but rearranged and uses less temporaries.
; The first operand to the function is both (X3,Y3,Z3) and (X2,Y2,Z2).
; The second operand to the function is (X1,Y1,Z1)
; Z1Z1 = Z1^2
sub sp,#32
frame address sp,76
mov r0,sp
adds r1,#64
bl P256_sqrmod
; U2 = X2*Z1Z1
ldr r1,[sp,#32]
mov r2,sp
mov r0,r1
bl P256_mulmod
; t1 = Z1*Z1Z1
ldr r1,[sp,#36]
adds r1,#64
mov r2,sp
mov r0,sp
bl P256_mulmod
; S2 = Y2*t1
ldr r1,[sp,#32]
adds r1,#32
mov r2,sp
mov r0,r1
bl P256_mulmod
; Z2Z2 = Z2^2
sub sp,#32
frame address sp,108
mov r0,sp
add r1,r8,#32
bl P256_sqrmod
; U1 = X1*Z2Z2
ldr r1,[sp,#68]
mov r2,sp
add r0,sp,#32
bl P256_mulmod
; t2 = Z2*Z2Z2
ldr r1,[sp,#64]
adds r1,#64
mov r2,sp
mov r0,sp
bl P256_mulmod
; S1 = Y1*t2
ldr r1,[sp,#68]
adds r1,#32
mov r2,sp
mov r0,sp
bl P256_mulmod
; H = U2-U1
ldr r1,[sp,#64]
add r2,sp,#32
mov r0,r1
bl P256_submod
; HH = H^2
mov r1,r8
sub sp,#32
frame address sp,140
mov r0,sp
bl P256_sqrmod
; Z3 = Z2*H
ldr r2,[sp,#96]
add r1,r2,#64
mov r0,r1
bl P256_mulmod
; Z3 = Z1*Z3
ldr r1,[sp,#100]
adds r1,#64
mov r2,r8
mov r0,r8
bl P256_mulmod
; HHH = H*HH
sub r1,r8,#64
mov r2,sp
mov r0,r1
bl P256_mulmod
; r = S2-S1
add r1,r8,#32
add r2,sp,#32
mov r0,r1
bl P256_submod
; V = U1*HH
add r1,sp,#64
mov r2,sp
mov r0,r1
bl P256_mulmod
; t3 = r^2
ldr r1,[sp,#96]
adds r1,#32
mov r0,sp
bl P256_sqrmod
; t2 = S1*HHH
add r1,sp,#32
ldr r2,[sp,#96]
add r0,sp,#32
bl P256_mulmod
; X3 = t3-HHH
mov r1,sp
ldr r2,[sp,#96]
mov r0,r2
bl P256_submod
; t3 = 2*V
add r1,sp,#64
add r2,sp,#64
mov r0,sp
bl P256_addmod
; X3 = X3-t3
ldr r1,[sp,#96]
mov r2,sp
mov r0,r1
bl P256_submod
; t3 = V-X3
add r1,sp,#64
mov r2,r8
mov r0,sp
bl P256_submod
; t3 = r*t3
ldr r1,[sp,#96]
adds r1,#32
mov r2,sp
mov r0,sp
bl P256_mulmod
; Y3 = t3-t2
mov r1,sp
add r2,sp,#32
ldr r0,[sp,#96]
adds r0,#32
bl P256_submod
add sp,#104
frame address sp,36
pop {r4-r11,pc}
endp
; in/out: r0-r7
P256_modinv proc
push {r0-r7,lr}
frame push {r4-r7,lr}
frame address sp,36
sub sp,#36
frame address sp,72
mov r0,sp
bl P256_load_1
mov r1,r0
bl P256_to_montgomery
adr r0,P256_p
ldm r0,{r0-r7}
subs r0,#2
push {r0-r7}
frame address sp,104
movs r0,#255
0
str r0,[sp,#64]
add r0,sp,#32
add r1,sp,#32
bl P256_sqrmod
ldr r0,[sp,#64]
lsrs r1,r0,#3
ldrb r1,[sp,r1]
and r2,r0,#7
lsrs r1,r2
tst r1,#1
beq %f1
add r0,sp,#32
add r1,sp,#32
add r2,sp,#68
bl P256_mulmod
1
ldr r0,[sp,#64]
subs r0,#1
bpl %b0
add sp,#32
frame address sp,72
pop {r0-r7}
frame address sp,40
add sp,#36
frame address sp,4
pop {pc}
endp
; *r0 = output affine montgomery, *r1 = input jacobian montgomery
P256_jacobian_to_affine proc
push {r0,r4-r11,lr}
frame push {r4-r11,lr}
frame address sp,40
adds r0,#64
ldm r0,{r0-r7}
bl P256_modinv
push {r0-r7}
frame address sp,72
mov r1,sp
sub sp,#32
frame address sp,104
mov r0,sp
bl P256_sqrmod
add r1,sp,#32
mov r2,sp
mov r0,r1
bl P256_mulmod
mov r1,sp
ldr r0,[sp,#64]
mov r2,r0
bl P256_mulmod
add r1,sp,#32
ldr r0,[sp,#64]
adds r0,#32
mov r2,r0
bl P256_mulmod
add sp,#68
frame address sp,36
pop {r4-r11,pc}
endp
; performs r0 := abs(r0)
P256_abs_int proc
rsbs r2,r0,#0
and r3,r2,r0, asr #31
and r0,r0,r2, asr #31
orrs r0,r0,r3
bx lr
endp
; input: *r0 = output (8 words)
; output: r0 is preserved
P256_load_1 proc
movs r1,#1
stm r0!,{r1}
movs r1,#0
umull r2,r3,r1,r1
stm r0!,{r1-r3}
stm r0!,{r1-r3}
stm r0!,{r1}
subs r0,#32
bx lr
endp
; input: *r0 = value, *r1 = limit
; output: 1 if value < limit, else 0
P256_less_than proc
push {r4-r5,lr}
frame push {r4-r5,lr}
subs r5,r5 ; set r5 to 0 and C to 1
movs r2,#8
0
ldm r0!,{r3}
ldm r1!,{r4}
sbcs r3,r4
sub r2,#1
cbz r2,%f1
b %b0
1
adcs r5,r5
eor r0,r5,#1
pop {r4-r5,pc}
endp
;P256_is_zero proc
; push {r4-r7,lr}
; ldm r0,{r0-r7}
; orrs r0,r1
; orrs r0,r2
; orrs r0,r3
; orrs r0,r4
; orrs r0,r5
; orrs r0,r6
; orrs r0,r7
; mrs r0,aprs
; lsrs r0,#30
; pop {r4-r7,pc}