blob: 26fd3863496cd16b92a459f7a5164a41a3f1c022 [file] [log] [blame]
use std::ops::{Add, Sub, Mul};
use std::cmp::{Eq, PartialEq,min};
use util::{fixed_time_eq};
use step_by::RangeExt;
/*
fe means field element.
Here the field is \Z/(2^255-19).
An element t, entries t[0]...t[9], represents the integer
t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
Bounds on each t[i] vary depending on context.
*/
#[derive(Clone, Copy)]
pub struct Fe(pub [i32; 10]);
impl PartialEq for Fe {
fn eq(&self, other: &Fe) -> bool {
let &Fe(self_elems) = self;
let &Fe(other_elems) = other;
self_elems.to_vec() == other_elems.to_vec()
}
}
impl Eq for Fe { }
static FE_ZERO : Fe = Fe([0,0,0,0,0,0,0,0,0,0]);
static FE_ONE : Fe = Fe([1,0,0,0,0,0,0,0,0,0]);
static FE_SQRTM1 : Fe = Fe([-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482]);
static FE_D : Fe = Fe([-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116]);
static FE_D2 : Fe = Fe([-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199]);
fn load_4u(s: &[u8]) -> u64 {
(s[0] as u64)
| ((s[1] as u64)<<8)
| ((s[2] as u64)<<16)
| ((s[3] as u64)<<24)
}
fn load_4i(s: &[u8]) -> i64 {
load_4u(s) as i64
}
fn load_3u(s: &[u8]) -> u64 {
(s[0] as u64)
| ((s[1] as u64)<<8)
| ((s[2] as u64)<<16)
}
fn load_3i(s: &[u8]) -> i64 {
load_3u(s) as i64
}
impl Add for Fe {
type Output = Fe;
/*
h = f + g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
fn add(self, _rhs: Fe) -> Fe {
let Fe(f) = self;
let Fe(g) = _rhs;
let f0 = f[0];
let f1 = f[1];
let f2 = f[2];
let f3 = f[3];
let f4 = f[4];
let f5 = f[5];
let f6 = f[6];
let f7 = f[7];
let f8 = f[8];
let f9 = f[9];
let g0 = g[0];
let g1 = g[1];
let g2 = g[2];
let g3 = g[3];
let g4 = g[4];
let g5 = g[5];
let g6 = g[6];
let g7 = g[7];
let g8 = g[8];
let g9 = g[9];
let h0 = f0 + g0;
let h1 = f1 + g1;
let h2 = f2 + g2;
let h3 = f3 + g3;
let h4 = f4 + g4;
let h5 = f5 + g5;
let h6 = f6 + g6;
let h7 = f7 + g7;
let h8 = f8 + g8;
let h9 = f9 + g9;
Fe([h0, h1, h2, h3, h4, h5, h6, h7, h8, h9])
}
}
impl Sub for Fe {
type Output = Fe;
/*
h = f - g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
fn sub(self, _rhs: Fe) -> Fe {
let Fe(f) = self;
let Fe(g) = _rhs;
let f0 = f[0];
let f1 = f[1];
let f2 = f[2];
let f3 = f[3];
let f4 = f[4];
let f5 = f[5];
let f6 = f[6];
let f7 = f[7];
let f8 = f[8];
let f9 = f[9];
let g0 = g[0];
let g1 = g[1];
let g2 = g[2];
let g3 = g[3];
let g4 = g[4];
let g5 = g[5];
let g6 = g[6];
let g7 = g[7];
let g8 = g[8];
let g9 = g[9];
let h0 = f0 - g0;
let h1 = f1 - g1;
let h2 = f2 - g2;
let h3 = f3 - g3;
let h4 = f4 - g4;
let h5 = f5 - g5;
let h6 = f6 - g6;
let h7 = f7 - g7;
let h8 = f8 - g8;
let h9 = f9 - g9;
Fe([h0, h1, h2, h3, h4, h5, h6, h7, h8, h9])
}
}
impl Mul for Fe {
type Output = Fe;
/*
h = f * g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
|g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
Postconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/
/*
Notes on implementation strategy:
Using schoolbook multiplication.
Karatsuba would save a little in some cost models.
Most multiplications by 2 and 19 are 32-bit precomputations;
cheaper than 64-bit postcomputations.
There is one remaining multiplication by 19 in the carry chain;
one *19 precomputation can be merged into this,
but the resulting data flow is considerably less clean.
There are 12 carries below.
10 of them are 2-way parallelizable and vectorizable.
Can get away with 11 carries, but then data flow is much deeper.
With tighter constraints on inputs can squeeze carries into int32.
*/
fn mul(self, _rhs: Fe) -> Fe {
let Fe(f) = self;
let Fe(g) = _rhs;
let f0 = f[0];
let f1 = f[1];
let f2 = f[2];
let f3 = f[3];
let f4 = f[4];
let f5 = f[5];
let f6 = f[6];
let f7 = f[7];
let f8 = f[8];
let f9 = f[9];
let g0 = g[0];
let g1 = g[1];
let g2 = g[2];
let g3 = g[3];
let g4 = g[4];
let g5 = g[5];
let g6 = g[6];
let g7 = g[7];
let g8 = g[8];
let g9 = g[9];
let g1_19 = 19 * g1; /* 1.4*2^29 */
let g2_19 = 19 * g2; /* 1.4*2^30; still ok */
let g3_19 = 19 * g3;
let g4_19 = 19 * g4;
let g5_19 = 19 * g5;
let g6_19 = 19 * g6;
let g7_19 = 19 * g7;
let g8_19 = 19 * g8;
let g9_19 = 19 * g9;
let f1_2 = 2 * f1;
let f3_2 = 2 * f3;
let f5_2 = 2 * f5;
let f7_2 = 2 * f7;
let f9_2 = 2 * f9;
let f0g0 = (f0 as i64) * (g0 as i64);
let f0g1 = (f0 as i64) * (g1 as i64);
let f0g2 = (f0 as i64) * (g2 as i64);
let f0g3 = (f0 as i64) * (g3 as i64);
let f0g4 = (f0 as i64) * (g4 as i64);
let f0g5 = (f0 as i64) * (g5 as i64);
let f0g6 = (f0 as i64) * (g6 as i64);
let f0g7 = (f0 as i64) * (g7 as i64);
let f0g8 = (f0 as i64) * (g8 as i64);
let f0g9 = (f0 as i64) * (g9 as i64);
let f1g0 = (f1 as i64) * (g0 as i64);
let f1g1_2 = (f1_2 as i64) * (g1 as i64);
let f1g2 = (f1 as i64) * (g2 as i64);
let f1g3_2 = (f1_2 as i64) * (g3 as i64);
let f1g4 = (f1 as i64) * (g4 as i64);
let f1g5_2 = (f1_2 as i64) * (g5 as i64);
let f1g6 = (f1 as i64) * (g6 as i64);
let f1g7_2 = (f1_2 as i64) * (g7 as i64);
let f1g8 = (f1 as i64) * (g8 as i64);
let f1g9_38 = (f1_2 as i64) * (g9_19 as i64);
let f2g0 = (f2 as i64) * (g0 as i64);
let f2g1 = (f2 as i64) * (g1 as i64);
let f2g2 = (f2 as i64) * (g2 as i64);
let f2g3 = (f2 as i64) * (g3 as i64);
let f2g4 = (f2 as i64) * (g4 as i64);
let f2g5 = (f2 as i64) * (g5 as i64);
let f2g6 = (f2 as i64) * (g6 as i64);
let f2g7 = (f2 as i64) * (g7 as i64);
let f2g8_19 = (f2 as i64) * (g8_19 as i64);
let f2g9_19 = (f2 as i64) * (g9_19 as i64);
let f3g0 = (f3 as i64) * (g0 as i64);
let f3g1_2 = (f3_2 as i64) * (g1 as i64);
let f3g2 = (f3 as i64) * (g2 as i64);
let f3g3_2 = (f3_2 as i64) * (g3 as i64);
let f3g4 = (f3 as i64) * (g4 as i64);
let f3g5_2 = (f3_2 as i64) * (g5 as i64);
let f3g6 = (f3 as i64) * (g6 as i64);
let f3g7_38 = (f3_2 as i64) * (g7_19 as i64);
let f3g8_19 = (f3 as i64) * (g8_19 as i64);
let f3g9_38 = (f3_2 as i64) * (g9_19 as i64);
let f4g0 = (f4 as i64) * (g0 as i64);
let f4g1 = (f4 as i64) * (g1 as i64);
let f4g2 = (f4 as i64) * (g2 as i64);
let f4g3 = (f4 as i64) * (g3 as i64);
let f4g4 = (f4 as i64) * (g4 as i64);
let f4g5 = (f4 as i64) * (g5 as i64);
let f4g6_19 = (f4 as i64) * (g6_19 as i64);
let f4g7_19 = (f4 as i64) * (g7_19 as i64);
let f4g8_19 = (f4 as i64) * (g8_19 as i64);
let f4g9_19 = (f4 as i64) * (g9_19 as i64);
let f5g0 = (f5 as i64) * (g0 as i64);
let f5g1_2 = (f5_2 as i64) * (g1 as i64);
let f5g2 = (f5 as i64) * (g2 as i64);
let f5g3_2 = (f5_2 as i64) * (g3 as i64);
let f5g4 = (f5 as i64) * (g4 as i64);
let f5g5_38 = (f5_2 as i64) * (g5_19 as i64);
let f5g6_19 = (f5 as i64) * (g6_19 as i64);
let f5g7_38 = (f5_2 as i64) * (g7_19 as i64);
let f5g8_19 = (f5 as i64) * (g8_19 as i64);
let f5g9_38 = (f5_2 as i64) * (g9_19 as i64);
let f6g0 = (f6 as i64) * (g0 as i64);
let f6g1 = (f6 as i64) * (g1 as i64);
let f6g2 = (f6 as i64) * (g2 as i64);
let f6g3 = (f6 as i64) * (g3 as i64);
let f6g4_19 = (f6 as i64) * (g4_19 as i64);
let f6g5_19 = (f6 as i64) * (g5_19 as i64);
let f6g6_19 = (f6 as i64) * (g6_19 as i64);
let f6g7_19 = (f6 as i64) * (g7_19 as i64);
let f6g8_19 = (f6 as i64) * (g8_19 as i64);
let f6g9_19 = (f6 as i64) * (g9_19 as i64);
let f7g0 = (f7 as i64) * (g0 as i64);
let f7g1_2 = (f7_2 as i64) * (g1 as i64);
let f7g2 = (f7 as i64) * (g2 as i64);
let f7g3_38 = (f7_2 as i64) * (g3_19 as i64);
let f7g4_19 = (f7 as i64) * (g4_19 as i64);
let f7g5_38 = (f7_2 as i64) * (g5_19 as i64);
let f7g6_19 = (f7 as i64) * (g6_19 as i64);
let f7g7_38 = (f7_2 as i64) * (g7_19 as i64);
let f7g8_19 = (f7 as i64) * (g8_19 as i64);
let f7g9_38 = (f7_2 as i64) * (g9_19 as i64);
let f8g0 = (f8 as i64) * (g0 as i64);
let f8g1 = (f8 as i64) * (g1 as i64);
let f8g2_19 = (f8 as i64) * (g2_19 as i64);
let f8g3_19 = (f8 as i64) * (g3_19 as i64);
let f8g4_19 = (f8 as i64) * (g4_19 as i64);
let f8g5_19 = (f8 as i64) * (g5_19 as i64);
let f8g6_19 = (f8 as i64) * (g6_19 as i64);
let f8g7_19 = (f8 as i64) * (g7_19 as i64);
let f8g8_19 = (f8 as i64) * (g8_19 as i64);
let f8g9_19 = (f8 as i64) * (g9_19 as i64);
let f9g0 = (f9 as i64) * (g0 as i64);
let f9g1_38 = (f9_2 as i64) * (g1_19 as i64);
let f9g2_19 = (f9 as i64) * (g2_19 as i64);
let f9g3_38 = (f9_2 as i64) * (g3_19 as i64);
let f9g4_19 = (f9 as i64) * (g4_19 as i64);
let f9g5_38 = (f9_2 as i64) * (g5_19 as i64);
let f9g6_19 = (f9 as i64) * (g6_19 as i64);
let f9g7_38 = (f9_2 as i64) * (g7_19 as i64);
let f9g8_19 = (f9 as i64) * (g8_19 as i64);
let f9g9_38 = (f9_2 as i64) * (g9_19 as i64);
let mut h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
let mut h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
let mut h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
let mut h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
let mut h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
let mut h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
let mut h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
let mut h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
let mut h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
let mut h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
let mut carry0;
let carry1;
let carry2;
let carry3;
let mut carry4;
let carry5;
let carry6;
let carry7;
let carry8;
let carry9;
/*
|h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
|h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
*/
carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.51*2^58 */
/* |h5| <= 1.51*2^58 */
carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.21*2^59 */
/* |h6| <= 1.21*2^59 */
carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.51*2^58 */
/* |h7| <= 1.51*2^58 */
carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.52*2^33 */
/* |h8| <= 1.52*2^33 */
carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.51*2^58 */
carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.8*2^37 */
carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
}
}
impl Fe {
pub fn from_bytes(s: &[u8]) -> Fe {
let mut h0 = load_4i(&s[0..4]);
let mut h1 = load_3i(&s[4..7]) << 6;
let mut h2 = load_3i(&s[7..10]) << 5;
let mut h3 = load_3i(&s[10..13]) << 3;
let mut h4 = load_3i(&s[13..16]) << 2;
let mut h5 = load_4i(&s[16..20]);
let mut h6 = load_3i(&s[20..23]) << 7;
let mut h7 = load_3i(&s[23..26]) << 5;
let mut h8 = load_3i(&s[26..29]) << 4;
let mut h9 = (load_3i(&s[29..32]) & 8388607) << 2;
let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
}
/*
Preconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
Write p=2^255-19; q=floor(h/p).
Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
Proof:
Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
Then 0<y<1.
Write r=h-pq.
Have 0<=r<=p-1=2^255-20.
Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
Write x=r+19(2^-255)r+y.
Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
*/
pub fn to_bytes(&self) -> [u8; 32] {
let &Fe(es) = self;
let mut h0 = es[0];
let mut h1 = es[1];
let mut h2 = es[2];
let mut h3 = es[3];
let mut h4 = es[4];
let mut h5 = es[5];
let mut h6 = es[6];
let mut h7 = es[7];
let mut h8 = es[8];
let mut h9 = es[9];
let mut q;
q = (19 * h9 + (1 << 24)) >> 25;
q = (h0 + q) >> 26;
q = (h1 + q) >> 25;
q = (h2 + q) >> 26;
q = (h3 + q) >> 25;
q = (h4 + q) >> 26;
q = (h5 + q) >> 25;
q = (h6 + q) >> 26;
q = (h7 + q) >> 25;
q = (h8 + q) >> 26;
q = (h9 + q) >> 25;
/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
h0 += 19 * q;
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
let carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
let carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
let carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
let carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
let carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
let carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
let carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
let carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
let carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
let carry9 = h9 >> 25; h9 -= carry9 << 25;
/* h10 = carry9 */
/*
Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
Have h0+...+2^230 h9 between 0 and 2^255-1;
evidently 2^255 h10-2^255 q = 0.
Goal: Output h0+...+2^230 h9.
*/
[
(h0 >> 0) as u8,
(h0 >> 8) as u8,
(h0 >> 16) as u8,
((h0 >> 24) | (h1 << 2)) as u8,
(h1 >> 6) as u8,
(h1 >> 14) as u8,
((h1 >> 22) | (h2 << 3)) as u8,
(h2 >> 5) as u8,
(h2 >> 13) as u8,
((h2 >> 21) | (h3 << 5)) as u8,
(h3 >> 3) as u8,
(h3 >> 11) as u8,
((h3 >> 19) | (h4 << 6)) as u8,
(h4 >> 2) as u8,
(h4 >> 10) as u8,
(h4 >> 18) as u8,
(h5 >> 0) as u8,
(h5 >> 8) as u8,
(h5 >> 16) as u8,
((h5 >> 24) | (h6 << 1)) as u8,
(h6 >> 7) as u8,
(h6 >> 15) as u8,
((h6 >> 23) | (h7 << 3)) as u8,
(h7 >> 5) as u8,
(h7 >> 13) as u8,
((h7 >> 21) | (h8 << 4)) as u8,
(h8 >> 4) as u8,
(h8 >> 12) as u8,
((h8 >> 20) | (h9 << 6)) as u8,
(h9 >> 2) as u8,
(h9 >> 10) as u8,
(h9 >> 18) as u8,
]
}
pub fn maybe_swap_with(&mut self, other: &mut Fe, do_swap: i32) {
let &mut Fe(f) = self;
let &mut Fe(g) = other;
let f0 = f[0];
let f1 = f[1];
let f2 = f[2];
let f3 = f[3];
let f4 = f[4];
let f5 = f[5];
let f6 = f[6];
let f7 = f[7];
let f8 = f[8];
let f9 = f[9];
let g0 = g[0];
let g1 = g[1];
let g2 = g[2];
let g3 = g[3];
let g4 = g[4];
let g5 = g[5];
let g6 = g[6];
let g7 = g[7];
let g8 = g[8];
let g9 = g[9];
let mut x0 = f0 ^ g0;
let mut x1 = f1 ^ g1;
let mut x2 = f2 ^ g2;
let mut x3 = f3 ^ g3;
let mut x4 = f4 ^ g4;
let mut x5 = f5 ^ g5;
let mut x6 = f6 ^ g6;
let mut x7 = f7 ^ g7;
let mut x8 = f8 ^ g8;
let mut x9 = f9 ^ g9;
let b = -do_swap;
x0 &= b;
x1 &= b;
x2 &= b;
x3 &= b;
x4 &= b;
x5 &= b;
x6 &= b;
x7 &= b;
x8 &= b;
x9 &= b;
*self = Fe([f0^x0, f1^x1, f2^x2, f3^x3, f4^x4,
f5^x5, f6^x6, f7^x7, f8^x8, f9^x9]);
*other = Fe([g0^x0, g1^x1, g2^x2, g3^x3, g4^x4,
g5^x5, g6^x6, g7^x7, g8^x8, g9^x9]);
}
pub fn maybe_set(&mut self, other: &Fe, do_swap: i32) {
let &mut Fe(f) = self;
let &Fe(g) = other;
let f0 = f[0];
let f1 = f[1];
let f2 = f[2];
let f3 = f[3];
let f4 = f[4];
let f5 = f[5];
let f6 = f[6];
let f7 = f[7];
let f8 = f[8];
let f9 = f[9];
let g0 = g[0];
let g1 = g[1];
let g2 = g[2];
let g3 = g[3];
let g4 = g[4];
let g5 = g[5];
let g6 = g[6];
let g7 = g[7];
let g8 = g[8];
let g9 = g[9];
let mut x0 = f0 ^ g0;
let mut x1 = f1 ^ g1;
let mut x2 = f2 ^ g2;
let mut x3 = f3 ^ g3;
let mut x4 = f4 ^ g4;
let mut x5 = f5 ^ g5;
let mut x6 = f6 ^ g6;
let mut x7 = f7 ^ g7;
let mut x8 = f8 ^ g8;
let mut x9 = f9 ^ g9;
let b = -do_swap;
x0 &= b;
x1 &= b;
x2 &= b;
x3 &= b;
x4 &= b;
x5 &= b;
x6 &= b;
x7 &= b;
x8 &= b;
x9 &= b;
*self = Fe([f0^x0, f1^x1, f2^x2, f3^x3, f4^x4,
f5^x5, f6^x6, f7^x7, f8^x8, f9^x9]);
}
/*
h = f * 121666
Can overlap h with f.
Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
Postconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/
fn mul_121666(&self) -> Fe {
let &Fe(f) = self;
let mut h0 = (f[0] as i64) * 121666;
let mut h1 = (f[1] as i64) * 121666;
let mut h2 = (f[2] as i64) * 121666;
let mut h3 = (f[3] as i64) * 121666;
let mut h4 = (f[4] as i64) * 121666;
let mut h5 = (f[5] as i64) * 121666;
let mut h6 = (f[6] as i64) * 121666;
let mut h7 = (f[7] as i64) * 121666;
let mut h8 = (f[8] as i64) * 121666;
let mut h9 = (f[9] as i64) * 121666;
let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
}
/*
h = f * f
Can overlap h with f.
Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
Postconditions:
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/
/*
See fe_mul.c for discussion of implementation strategy.
*/
fn square(&self) -> Fe {
let &Fe(f) = self;
let f0 = f[0];
let f1 = f[1];
let f2 = f[2];
let f3 = f[3];
let f4 = f[4];
let f5 = f[5];
let f6 = f[6];
let f7 = f[7];
let f8 = f[8];
let f9 = f[9];
let f0_2 = 2 * f0;
let f1_2 = 2 * f1;
let f2_2 = 2 * f2;
let f3_2 = 2 * f3;
let f4_2 = 2 * f4;
let f5_2 = 2 * f5;
let f6_2 = 2 * f6;
let f7_2 = 2 * f7;
let f5_38 = 38 * f5; /* 1.31*2^30 */
let f6_19 = 19 * f6; /* 1.31*2^30 */
let f7_38 = 38 * f7; /* 1.31*2^30 */
let f8_19 = 19 * f8; /* 1.31*2^30 */
let f9_38 = 38 * f9; /* 1.31*2^30 */
let f0f0 = (f0 as i64) * (f0 as i64);
let f0f1_2 = (f0_2 as i64) * (f1 as i64);
let f0f2_2 = (f0_2 as i64) * (f2 as i64);
let f0f3_2 = (f0_2 as i64) * (f3 as i64);
let f0f4_2 = (f0_2 as i64) * (f4 as i64);
let f0f5_2 = (f0_2 as i64) * (f5 as i64);
let f0f6_2 = (f0_2 as i64) * (f6 as i64);
let f0f7_2 = (f0_2 as i64) * (f7 as i64);
let f0f8_2 = (f0_2 as i64) * (f8 as i64);
let f0f9_2 = (f0_2 as i64) * (f9 as i64);
let f1f1_2 = (f1_2 as i64) * (f1 as i64);
let f1f2_2 = (f1_2 as i64) * (f2 as i64);
let f1f3_4 = (f1_2 as i64) * (f3_2 as i64);
let f1f4_2 = (f1_2 as i64) * (f4 as i64);
let f1f5_4 = (f1_2 as i64) * (f5_2 as i64);
let f1f6_2 = (f1_2 as i64) * (f6 as i64);
let f1f7_4 = (f1_2 as i64) * (f7_2 as i64);
let f1f8_2 = (f1_2 as i64) * (f8 as i64);
let f1f9_76 = (f1_2 as i64) * (f9_38 as i64);
let f2f2 = (f2 as i64) * (f2 as i64);
let f2f3_2 = (f2_2 as i64) * (f3 as i64);
let f2f4_2 = (f2_2 as i64) * (f4 as i64);
let f2f5_2 = (f2_2 as i64) * (f5 as i64);
let f2f6_2 = (f2_2 as i64) * (f6 as i64);
let f2f7_2 = (f2_2 as i64) * (f7 as i64);
let f2f8_38 = (f2_2 as i64) * (f8_19 as i64);
let f2f9_38 = (f2 as i64) * (f9_38 as i64);
let f3f3_2 = (f3_2 as i64) * (f3 as i64);
let f3f4_2 = (f3_2 as i64) * (f4 as i64);
let f3f5_4 = (f3_2 as i64) * (f5_2 as i64);
let f3f6_2 = (f3_2 as i64) * (f6 as i64);
let f3f7_76 = (f3_2 as i64) * (f7_38 as i64);
let f3f8_38 = (f3_2 as i64) * (f8_19 as i64);
let f3f9_76 = (f3_2 as i64) * (f9_38 as i64);
let f4f4 = (f4 as i64) * (f4 as i64);
let f4f5_2 = (f4_2 as i64) * (f5 as i64);
let f4f6_38 = (f4_2 as i64) * (f6_19 as i64);
let f4f7_38 = (f4 as i64) * (f7_38 as i64);
let f4f8_38 = (f4_2 as i64) * (f8_19 as i64);
let f4f9_38 = (f4 as i64) * (f9_38 as i64);
let f5f5_38 = (f5 as i64) * (f5_38 as i64);
let f5f6_38 = (f5_2 as i64) * (f6_19 as i64);
let f5f7_76 = (f5_2 as i64) * (f7_38 as i64);
let f5f8_38 = (f5_2 as i64) * (f8_19 as i64);
let f5f9_76 = (f5_2 as i64) * (f9_38 as i64);
let f6f6_19 = (f6 as i64) * (f6_19 as i64);
let f6f7_38 = (f6 as i64) * (f7_38 as i64);
let f6f8_38 = (f6_2 as i64) * (f8_19 as i64);
let f6f9_38 = (f6 as i64) * (f9_38 as i64);
let f7f7_38 = (f7 as i64) * (f7_38 as i64);
let f7f8_38 = (f7_2 as i64) * (f8_19 as i64);
let f7f9_76 = (f7_2 as i64) * (f9_38 as i64);
let f8f8_19 = (f8 as i64) * (f8_19 as i64);
let f8f9_38 = (f8 as i64) * (f9_38 as i64);
let f9f9_38 = (f9 as i64) * (f9_38 as i64);
let mut h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
let mut h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
let mut h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
let mut h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
let mut h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
let mut h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
let mut h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
let mut h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
let mut h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
let mut h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
let carrya = (h0 + (1<<25)) >> 26; h1 += carrya; h0 -= carrya << 26;
Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
}
fn square_and_double(&self) -> Fe {
let &Fe(f) = self;
let f0 = f[0];
let f1 = f[1];
let f2 = f[2];
let f3 = f[3];
let f4 = f[4];
let f5 = f[5];
let f6 = f[6];
let f7 = f[7];
let f8 = f[8];
let f9 = f[9];
let f0_2 = 2 * f0;
let f1_2 = 2 * f1;
let f2_2 = 2 * f2;
let f3_2 = 2 * f3;
let f4_2 = 2 * f4;
let f5_2 = 2 * f5;
let f6_2 = 2 * f6;
let f7_2 = 2 * f7;
let f5_38 = 38 * f5; /* 1.959375*2^30 */
let f6_19 = 19 * f6; /* 1.959375*2^30 */
let f7_38 = 38 * f7; /* 1.959375*2^30 */
let f8_19 = 19 * f8; /* 1.959375*2^30 */
let f9_38 = 38 * f9; /* 1.959375*2^30 */
let f0f0 = (f0 as i64) * (f0 as i64);
let f0f1_2 = (f0_2 as i64) * (f1 as i64);
let f0f2_2 = (f0_2 as i64) * (f2 as i64);
let f0f3_2 = (f0_2 as i64) * (f3 as i64);
let f0f4_2 = (f0_2 as i64) * (f4 as i64);
let f0f5_2 = (f0_2 as i64) * (f5 as i64);
let f0f6_2 = (f0_2 as i64) * (f6 as i64);
let f0f7_2 = (f0_2 as i64) * (f7 as i64);
let f0f8_2 = (f0_2 as i64) * (f8 as i64);
let f0f9_2 = (f0_2 as i64) * (f9 as i64);
let f1f1_2 = (f1_2 as i64) * (f1 as i64);
let f1f2_2 = (f1_2 as i64) * (f2 as i64);
let f1f3_4 = (f1_2 as i64) * (f3_2 as i64);
let f1f4_2 = (f1_2 as i64) * (f4 as i64);
let f1f5_4 = (f1_2 as i64) * (f5_2 as i64);
let f1f6_2 = (f1_2 as i64) * (f6 as i64);
let f1f7_4 = (f1_2 as i64) * (f7_2 as i64);
let f1f8_2 = (f1_2 as i64) * (f8 as i64);
let f1f9_76 = (f1_2 as i64) * (f9_38 as i64);
let f2f2 = (f2 as i64) * (f2 as i64);
let f2f3_2 = (f2_2 as i64) * (f3 as i64);
let f2f4_2 = (f2_2 as i64) * (f4 as i64);
let f2f5_2 = (f2_2 as i64) * (f5 as i64);
let f2f6_2 = (f2_2 as i64) * (f6 as i64);
let f2f7_2 = (f2_2 as i64) * (f7 as i64);
let f2f8_38 = (f2_2 as i64) * (f8_19 as i64);
let f2f9_38 = (f2 as i64) * (f9_38 as i64);
let f3f3_2 = (f3_2 as i64) * (f3 as i64);
let f3f4_2 = (f3_2 as i64) * (f4 as i64);
let f3f5_4 = (f3_2 as i64) * (f5_2 as i64);
let f3f6_2 = (f3_2 as i64) * (f6 as i64);
let f3f7_76 = (f3_2 as i64) * (f7_38 as i64);
let f3f8_38 = (f3_2 as i64) * (f8_19 as i64);
let f3f9_76 = (f3_2 as i64) * (f9_38 as i64);
let f4f4 = (f4 as i64) * (f4 as i64);
let f4f5_2 = (f4_2 as i64) * (f5 as i64);
let f4f6_38 = (f4_2 as i64) * (f6_19 as i64);
let f4f7_38 = (f4 as i64) * (f7_38 as i64);
let f4f8_38 = (f4_2 as i64) * (f8_19 as i64);
let f4f9_38 = (f4 as i64) * (f9_38 as i64);
let f5f5_38 = (f5 as i64) * (f5_38 as i64);
let f5f6_38 = (f5_2 as i64) * (f6_19 as i64);
let f5f7_76 = (f5_2 as i64) * (f7_38 as i64);
let f5f8_38 = (f5_2 as i64) * (f8_19 as i64);
let f5f9_76 = (f5_2 as i64) * (f9_38 as i64);
let f6f6_19 = (f6 as i64) * (f6_19 as i64);
let f6f7_38 = (f6 as i64) * (f7_38 as i64);
let f6f8_38 = (f6_2 as i64) * (f8_19 as i64);
let f6f9_38 = (f6 as i64) * (f9_38 as i64);
let f7f7_38 = (f7 as i64) * (f7_38 as i64);
let f7f8_38 = (f7_2 as i64) * (f8_19 as i64);
let f7f9_76 = (f7_2 as i64) * (f9_38 as i64);
let f8f8_19 = (f8 as i64) * (f8_19 as i64);
let f8f9_38 = (f8 as i64) * (f9_38 as i64);
let f9f9_38 = (f9 as i64) * (f9_38 as i64);
let mut h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
let mut h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
let mut h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
let mut h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
let mut h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
let mut h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
let mut h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
let mut h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
let mut h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
let mut h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
let mut carry0: i64;
let carry1: i64;
let carry2: i64;
let carry3: i64;
let mut carry4: i64;
let carry5: i64;
let carry6: i64;
let carry7: i64;
let carry8: i64;
let carry9: i64;
h0 += h0;
h1 += h1;
h2 += h2;
h3 += h3;
h4 += h4;
h5 += h5;
h6 += h6;
h7 += h7;
h8 += h8;
h9 += h9;
carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
}
pub fn invert(&self) -> Fe {
let z1 = *self;
/* qhasm: z2 = z1^2^1 */
let z2 = z1.square();
/* qhasm: z8 = z2^2^2 */
let z8 = z2.square().square();
/* qhasm: z9 = z1*z8 */
let z9 = z1*z8;
/* qhasm: z11 = z2*z9 */
let z11 = z2*z9;
/* qhasm: z22 = z11^2^1 */
let z22 = z11.square();
/* qhasm: z_5_0 = z9*z22 */
let z_5_0 = z9*z22;
/* qhasm: z_10_5 = z_5_0^2^5 */
let z_10_5 = (0..5).fold(z_5_0, |z_5_n, _| z_5_n.square());
/* qhasm: z_10_0 = z_10_5*z_5_0 */
let z_10_0 = z_10_5*z_5_0;
/* qhasm: z_20_10 = z_10_0^2^10 */
let z_20_10 = (0..10).fold(z_10_0, |x, _| x.square());
/* qhasm: z_20_0 = z_20_10*z_10_0 */
let z_20_0 = z_20_10*z_10_0;
/* qhasm: z_40_20 = z_20_0^2^20 */
let z_40_20 = (0..20).fold(z_20_0, |x, _| x.square());
/* qhasm: z_40_0 = z_40_20*z_20_0 */
let z_40_0 = z_40_20*z_20_0;
/* qhasm: z_50_10 = z_40_0^2^10 */
let z_50_10 = (0..10).fold(z_40_0, |x, _| x.square());
/* qhasm: z_50_0 = z_50_10*z_10_0 */
let z_50_0 = z_50_10*z_10_0;
/* qhasm: z_100_50 = z_50_0^2^50 */
let z_100_50 = (0..50).fold(z_50_0, |x, _| x.square());
/* qhasm: z_100_0 = z_100_50*z_50_0 */
let z_100_0 = z_100_50*z_50_0;
/* qhasm: z_200_100 = z_100_0^2^100 */
let z_200_100 = (0..100).fold(z_100_0, |x, _| x.square());
/* qhasm: z_200_0 = z_200_100*z_100_0 */
/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
let z_200_0 = z_200_100*z_100_0;
/* qhasm: z_250_50 = z_200_0^2^50 */
let z_250_50 = (0..50).fold(z_200_0, |x, _| x.square());
/* qhasm: z_250_0 = z_250_50*z_50_0 */
let z_250_0 = z_250_50*z_50_0;
/* qhasm: z_255_5 = z_250_0^2^5 */
let z_255_5 = (0..5).fold(z_250_0, |x, _| x.square());
/* qhasm: z_255_21 = z_255_5*z11 */
/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
let z_255_21 = z_255_5*z11;
z_255_21
}
fn is_nonzero(&self) -> bool {
let bs = self.to_bytes();
let zero = [0; 32];
!fixed_time_eq(bs.as_ref(), zero.as_ref())
}
fn is_negative(&self) -> bool {
(self.to_bytes()[0] & 1) != 0
}
fn neg(&self) -> Fe {
let &Fe(f) = self;
Fe([-f[0], -f[1], -f[2], -f[3], -f[4],
-f[5], -f[6], -f[7], -f[8], -f[9]])
}
fn pow25523(&self) -> Fe {
let z2 = self.square();
let z8 = (0..2).fold(z2, |x, _| x.square());
let z9 = *self * z8;
let z11 = z2 * z9;
let z22 = z11.square();
let z_5_0 = z9 * z22;
let z_10_5 = (0..5).fold(z_5_0, |x, _| x.square());
let z_10_0 = z_10_5 * z_5_0;
let z_20_10 = (0..10).fold(z_10_0, |x, _| x.square());
let z_20_0 = z_20_10 * z_10_0;
let z_40_20 = (0..20).fold(z_20_0, |x, _| x.square());
let z_40_0 = z_40_20 * z_20_0;
let z_50_10 = (0..10).fold(z_40_0, |x, _| x.square());
let z_50_0 = z_50_10 * z_10_0;
let z_100_50 = (0..50).fold(z_50_0, |x, _| x.square());
let z_100_0 = z_100_50 * z_50_0;
let z_200_100 = (0..100).fold(z_100_0, |x, _| x.square());
let z_200_0 = z_200_100 * z_100_0;
let z_250_50 = (0..50).fold(z_200_0, |x, _| x.square());
let z_250_0 = z_250_50 * z_50_0;
let z_252_2 = (0..2).fold(z_250_0, |x, _| x.square());
let z_252_3 = z_252_2 * *self;
z_252_3
}
}
#[derive(Clone, Copy)]
pub struct GeP2 {
x: Fe,
y: Fe,
z: Fe,
}
#[derive(Clone, Copy)]
pub struct GeP3 {
x: Fe,
y: Fe,
z: Fe,
t: Fe,
}
#[derive(Clone, Copy)]
pub struct GeP1P1 {
x: Fe,
y: Fe,
z: Fe,
t: Fe,
}
#[derive(Clone, Copy)]
pub struct GePrecomp {
y_plus_x: Fe,
y_minus_x: Fe,
xy2d: Fe,
}
#[derive(Clone, Copy)]
pub struct GeCached {
y_plus_x: Fe,
y_minus_x: Fe,
z: Fe,
t2d: Fe,
}
impl GeP1P1 {
fn to_p2(&self) -> GeP2 {
GeP2 {
x: self.x * self.t,
y: self.y * self.z,
z: self.z * self.t,
}
}
fn to_p3(&self) -> GeP3 {
GeP3 {
x: self.x * self.t,
y: self.y * self.z,
z: self.z * self.t,
t: self.x * self.y,
}
}
}
impl GeP2 {
fn zero() -> GeP2 {
GeP2 {
x: FE_ZERO,
y: FE_ONE,
z: FE_ONE,
}
}
pub fn to_bytes(&self) -> [u8; 32] {
let recip = self.z.invert();
let x = self.x * recip;
let y = self.y * recip;
let mut bs = y.to_bytes();
bs[31] ^= (if x.is_negative() { 1 } else { 0 }) << 7;
bs
}
fn dbl(&self) -> GeP1P1 {
let xx = self.x.square();
let yy = self.y.square();
let b = self.z.square_and_double();
let a = self.x + self.y;
let aa = a.square();
let y3 = yy + xx;
let z3 = yy - xx;
let x3 = aa - y3;
let t3 = b - z3;
GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
}
fn slide(a: &[u8]) -> [i8; 256] {
let mut r = [0i8; 256];
for i in 0..256 {
r[i] = (1 & (a[i >> 3] >> (i & 7))) as i8;
}
for i in 0..256 {
if r[i]!=0 {
for b in 1..min(7, 256-i) {
if r[i + b] != 0 {
if r[i] + (r[i + b] << b) <= 15 {
r[i] += r[i + b] << b; r[i + b] = 0;
} else if r[i] - (r[i + b] << b) >= -15 {
r[i] -= r[i + b] << b;
for k in i+b..256 {
if r[k]==0 {
r[k] = 1;
break;
}
r[k] = 0;
}
} else {
break;
}
}
}
}
}
r
}
/*
r = a * A + b * B
where a = a[0]+256*a[1]+...+256^31 a[31].
and b = b[0]+256*b[1]+...+256^31 b[31].
B is the Ed25519 base point (x,4/5) with x positive.
*/
pub fn double_scalarmult_vartime(a_scalar: &[u8], a_point: GeP3, b_scalar: &[u8]) -> GeP2 {
let aslide = GeP2::slide(a_scalar);
let bslide = GeP2::slide(b_scalar);
let mut ai = [GeCached{y_plus_x:FE_ZERO, y_minus_x: FE_ZERO, z: FE_ZERO, t2d: FE_ZERO}; 8]; /* A,3A,5A,7A,9A,11A,13A,15A */
ai[0] = a_point.to_cached();
let a2 = a_point.dbl().to_p3();
ai[1] = (a2 + ai[0]).to_p3().to_cached();
ai[2] = (a2 + ai[1]).to_p3().to_cached();
ai[3] = (a2 + ai[2]).to_p3().to_cached();
ai[4] = (a2 + ai[3]).to_p3().to_cached();
ai[5] = (a2 + ai[4]).to_p3().to_cached();
ai[6] = (a2 + ai[5]).to_p3().to_cached();
ai[7] = (a2 + ai[6]).to_p3().to_cached();
let mut r = GeP2::zero();
let mut i: usize = 255;
loop {
if aslide[i]!=0 || bslide[i]!=0 {
break;
}
if i==0 {
return r;
}
i -= 1;
}
loop {
let mut t = r.dbl();
if aslide[i] > 0 {
t = t.to_p3() + ai[(aslide[i]/2) as usize];
} else if aslide[i] < 0 {
t = t.to_p3() - ai[(-aslide[i]/2) as usize];
}
if bslide[i] > 0 {
t = t.to_p3() + BI[(bslide[i]/2) as usize];
} else if bslide[i] < 0 {
t = t.to_p3() - BI[(-bslide[i]/2) as usize];
}
r = t.to_p2();
if i==0 {
return r;
}
i -= 1;
}
}
}
impl GeP3 {
pub fn from_bytes_negate_vartime(s: &[u8]) -> Option<GeP3> {
let y = Fe::from_bytes(s);
let z = FE_ONE;
let y_squared = y.square();
let u = y_squared - FE_ONE;
let v = (y_squared * FE_D) + FE_ONE;
let v_raise_3 = v.square() * v;
let v_raise_7 = v_raise_3.square() * v;
let uv7 = v_raise_7 * u;// Is this commutative? u comes second in the code, but not in the notation...
let mut x = uv7.pow25523() * v_raise_3 * u;
let vxx = x.square() * v;
let check = vxx - u;
if check.is_nonzero() {
let check2 = vxx + u;
if check2.is_nonzero() {
return None;
}
x = x * FE_SQRTM1;
}
if x.is_negative() == ((s[31]>>7)!=0) {
x = x.neg();
}
let t = x * y;
Some(GeP3{x: x, y: y, z: z, t: t})
}
fn to_p2(&self) -> GeP2 {
GeP2 {
x: self.x,
y: self.y,
z: self.z,
}
}
fn to_cached(&self) -> GeCached {
GeCached {
y_plus_x: self.y + self.x,
y_minus_x: self.y - self.x,
z: self.z,
t2d: self.t * FE_D2
}
}
fn zero() -> GeP3 {
GeP3 {
x: FE_ZERO,
y: FE_ONE,
z: FE_ONE,
t: FE_ZERO,
}
}
fn dbl(&self) -> GeP1P1 {
self.to_p2().dbl()
}
pub fn to_bytes(&self) -> [u8; 32] {
let recip = self.z.invert();
let x = self.x * recip;
let y = self.y * recip;
let mut bs = y.to_bytes();
bs[31] ^= (if x.is_negative() { 1 } else { 0 }) << 7;
bs
}
}
impl Add<GeCached> for GeP3 {
type Output = GeP1P1;
fn add(self, _rhs: GeCached) -> GeP1P1 {
let y1_plus_x1 = self.y + self.x;
let y1_minus_x1 = self.y - self.x;
let a = y1_plus_x1 * _rhs.y_plus_x;
let b = y1_minus_x1 * _rhs.y_minus_x;
let c = _rhs.t2d * self.t;
let zz = self.z * _rhs.z;
let d = zz + zz;
let x3 = a - b;
let y3 = a + b;
let z3 = d + c;
let t3 = d - c;
GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
}
}
impl Add<GePrecomp> for GeP3 {
type Output = GeP1P1;
fn add(self, _rhs: GePrecomp) -> GeP1P1 {
let y1_plus_x1 = self.y + self.x;
let y1_minus_x1 = self.y - self.x;
let a = y1_plus_x1 * _rhs.y_plus_x;
let b = y1_minus_x1 * _rhs.y_minus_x;
let c = _rhs.xy2d * self.t;
let d = self.z + self.z;
let x3 = a - b;
let y3 = a + b;
let z3 = d + c;
let t3 = d - c;
GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
}
}
impl Sub<GeCached> for GeP3 {
type Output = GeP1P1;
fn sub(self, _rhs: GeCached) -> GeP1P1 {
let y1_plus_x1 = self.y + self.x;
let y1_minus_x1 = self.y - self.x;
let a = y1_plus_x1 * _rhs.y_minus_x;
let b = y1_minus_x1 * _rhs.y_plus_x;
let c = _rhs.t2d * self.t;
let zz = self.z * _rhs.z;
let d = zz + zz;
let x3 = a - b;
let y3 = a + b;
let z3 = d - c;
let t3 = d + c;
GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
}
}
impl Sub<GePrecomp> for GeP3 {
type Output = GeP1P1;
fn sub(self, _rhs: GePrecomp) -> GeP1P1 {
let y1_plus_x1 = self.y + self.x;
let y1_minus_x1 = self.y - self.x;
let a = y1_plus_x1 * _rhs.y_minus_x;
let b = y1_minus_x1 * _rhs.y_plus_x;
let c = _rhs.xy2d * self.t;
let d = self.z + self.z;
let x3 = a - b;
let y3 = a + b;
let z3 = d - c;
let t3 = d + c;
GeP1P1 { x: x3, y: y3, z: z3, t: t3 }
}
}
fn equal(b: u8, c: u8) -> i32 {
let x = b ^ c; /* 0: yes; 1..255: no */
let mut y = x as u32; /* 0: yes; 1..255: no */
y = y.wrapping_sub(1); /* 4294967295: yes; 0..254: no */
y >>= 31; /* 1: yes; 0: no */
y as i32
}
fn negative(b: i8) -> u8 {
let mut x = (b as i64) as u64;
x >>= 63; /* 1: yes; 0: no */
x as u8
}
impl GePrecomp {
fn zero() -> GePrecomp {
GePrecomp {
y_plus_x: FE_ONE,
y_minus_x: FE_ONE,
xy2d: FE_ZERO,
}
}
pub fn maybe_set(&mut self, other: &GePrecomp, do_swap: i32) {
self.y_plus_x.maybe_set(&other.y_plus_x, do_swap);
self.y_minus_x.maybe_set(&other.y_minus_x, do_swap);
self.xy2d.maybe_set(&other.xy2d, do_swap);
}
pub fn select(pos: usize, b: i8) -> GePrecomp {
let bnegative: u8 = negative(b);
let babs: u8 = (b - (((-(bnegative as i8)) & b) << 1)) as u8;
let mut t = GePrecomp::zero();
t.maybe_set(&GE_PRECOMP_BASE[pos][0], equal(babs, 1));
t.maybe_set(&GE_PRECOMP_BASE[pos][1], equal(babs, 2));
t.maybe_set(&GE_PRECOMP_BASE[pos][2], equal(babs, 3));
t.maybe_set(&GE_PRECOMP_BASE[pos][3], equal(babs, 4));
t.maybe_set(&GE_PRECOMP_BASE[pos][4], equal(babs, 5));
t.maybe_set(&GE_PRECOMP_BASE[pos][5], equal(babs, 6));
t.maybe_set(&GE_PRECOMP_BASE[pos][6], equal(babs, 7));
t.maybe_set(&GE_PRECOMP_BASE[pos][7], equal(babs, 8));
let minus_t = GePrecomp {
y_plus_x: t.y_minus_x,
y_minus_x: t.y_plus_x,
xy2d: t.xy2d.neg(),
};
t.maybe_set(&minus_t, bnegative as i32);
t
}
}
/*
h = a * B
where a = a[0]+256*a[1]+...+256^31 a[31]
B is the Ed25519 base point (x,4/5) with x positive.
Preconditions:
a[31] <= 127
*/
pub fn ge_scalarmult_base(a: &[u8]) -> GeP3 {
let mut es: [i8; 64] = [0; 64];
let mut r: GeP1P1;
let mut s: GeP2;
let mut t: GePrecomp;
for i in 0..32 {
es[2 * i + 0] = ((a[i] >> 0) & 15) as i8;
es[2 * i + 1] = ((a[i] >> 4) & 15) as i8;
}
/* each es[i] is between 0 and 15 */
/* es[63] is between 0 and 7 */
let mut carry: i8 = 0;
for i in 0..63 {
es[i] += carry;
carry = es[i] + 8;
carry >>= 4;
es[i] -= carry << 4;
}
es[63] += carry;
/* each es[i] is between -8 and 8 */
let mut h = GeP3::zero();
for i in (1..64).step_up(2) {
t = GePrecomp::select(i/2, es[i]);
r = h + t;
h = r.to_p3();
}
r = h.dbl(); s = r.to_p2();
r = s.dbl(); s = r.to_p2();
r = s.dbl(); s = r.to_p2();
r = s.dbl(); h = r.to_p3();
for i in (0..64).step_up(2) {
t = GePrecomp::select(i/2, es[i]);
r = h + t;
h = r.to_p3();
}
h
}
/*
Input:
s[0]+256*s[1]+...+256^63*s[63] = s
Output:
s[0]+256*s[1]+...+256^31*s[31] = s mod l
where l = 2^252 + 27742317777372353535851937790883648493.
Overwrites s in place.
*/
pub fn sc_reduce(s: &mut [u8]) {
let mut s0: i64 = 2097151 & load_3i(s);
let mut s1: i64 = 2097151 & (load_4i(&s[2..6]) >> 5);
let mut s2: i64 = 2097151 & (load_3i(&s[5..8]) >> 2);
let mut s3: i64 = 2097151 & (load_4i(&s[7..11]) >> 7);
let mut s4: i64 = 2097151 & (load_4i(&s[10..14]) >> 4);
let mut s5: i64 = 2097151 & (load_3i(&s[13..16]) >> 1);
let mut s6: i64 = 2097151 & (load_4i(&s[15..19]) >> 6);
let mut s7: i64 = 2097151 & (load_3i(&s[18..21]) >> 3);
let mut s8: i64 = 2097151 & load_3i(&s[21..24]);
let mut s9: i64 = 2097151 & (load_4i(&s[23..27]) >> 5);
let mut s10: i64 = 2097151 & (load_3i(&s[26..29]) >> 2);
let mut s11: i64 = 2097151 & (load_4i(&s[28..32]) >> 7);
let mut s12: i64 = 2097151 & (load_4i(&s[31..35]) >> 4);
let mut s13: i64 = 2097151 & (load_3i(&s[34..37]) >> 1);
let mut s14: i64 = 2097151 & (load_4i(&s[36..40]) >> 6);
let mut s15: i64 = 2097151 & (load_3i(&s[39..42]) >> 3);
let mut s16: i64 = 2097151 & load_3i(&s[42..45]);
let mut s17: i64 = 2097151 & (load_4i(&s[44..48]) >> 5);
let s18: i64 = 2097151 & (load_3i(&s[47..50]) >> 2);
let s19: i64 = 2097151 & (load_4i(&s[49..53]) >> 7);
let s20: i64 = 2097151 & (load_4i(&s[52..56]) >> 4);
let s21: i64 = 2097151 & (load_3i(&s[55..58]) >> 1);
let s22: i64 = 2097151 & (load_4i(&s[57..61]) >> 6);
let s23: i64 = load_4i(&s[60..64]) >> 3;
let mut carry0: i64;
let mut carry1: i64;
let mut carry2: i64;
let mut carry3: i64;
let mut carry4: i64;
let mut carry5: i64;
let mut carry6: i64;
let mut carry7: i64;
let mut carry8: i64;
let mut carry9: i64;
let mut carry10: i64;
let mut carry11: i64;
let carry12: i64;
let carry13: i64;
let carry14: i64;
let carry15: i64;
let carry16: i64;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
s[0] = (s0 >> 0) as u8;
s[1] = (s0 >> 8) as u8;
s[2] = ((s0 >> 16) | (s1 << 5)) as u8;
s[3] = (s1 >> 3) as u8;
s[4] = (s1 >> 11) as u8;
s[5] = ((s1 >> 19) | (s2 << 2)) as u8;
s[6] = (s2 >> 6) as u8;
s[7] = ((s2 >> 14) | (s3 << 7)) as u8;
s[8] = (s3 >> 1) as u8;
s[9] = (s3 >> 9) as u8;
s[10] = ((s3 >> 17) | (s4 << 4)) as u8;
s[11] = (s4 >> 4) as u8;
s[12] = (s4 >> 12) as u8;
s[13] = ((s4 >> 20) | (s5 << 1)) as u8;
s[14] = (s5 >> 7) as u8;
s[15] = ((s5 >> 15) | (s6 << 6)) as u8;
s[16] = (s6 >> 2) as u8;
s[17] = (s6 >> 10) as u8;
s[18] = ((s6 >> 18) | (s7 << 3)) as u8;
s[19] = (s7 >> 5) as u8;
s[20] = (s7 >> 13) as u8;
s[21] = (s8 >> 0) as u8;
s[22] = (s8 >> 8) as u8;
s[23] = ((s8 >> 16) | (s9 << 5)) as u8;
s[24] = (s9 >> 3) as u8;
s[25] = (s9 >> 11) as u8;
s[26] = ((s9 >> 19) | (s10 << 2)) as u8;
s[27] = (s10 >> 6) as u8;
s[28] = ((s10 >> 14) | (s11 << 7)) as u8;
s[29] = (s11 >> 1) as u8;
s[30] = (s11 >> 9) as u8;
s[31] = (s11 >> 17) as u8;
}
/*
Input:
a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
c[0]+256*c[1]+...+256^31*c[31] = c
Output:
s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
pub fn sc_muladd(s: &mut[u8], a: &[u8], b: &[u8], c: &[u8]) {
let a0 = 2097151 & load_3i(&a[0..3]);
let a1 = 2097151 & (load_4i(&a[2..6]) >> 5);
let a2 = 2097151 & (load_3i(&a[5..8]) >> 2);
let a3 = 2097151 & (load_4i(&a[7..11]) >> 7);
let a4 = 2097151 & (load_4i(&a[10..14]) >> 4);
let a5 = 2097151 & (load_3i(&a[13..16]) >> 1);
let a6 = 2097151 & (load_4i(&a[15..19]) >> 6);
let a7 = 2097151 & (load_3i(&a[18..21]) >> 3);
let a8 = 2097151 & load_3i(&a[21..24]);
let a9 = 2097151 & (load_4i(&a[23..27]) >> 5);
let a10 = 2097151 & (load_3i(&a[26..29]) >> 2);
let a11 = load_4i(&a[28..32]) >> 7;
let b0 = 2097151 & load_3i(&b[0..3]);
let b1 = 2097151 & (load_4i(&b[2..6]) >> 5);
let b2 = 2097151 & (load_3i(&b[5..8]) >> 2);
let b3 = 2097151 & (load_4i(&b[7..11]) >> 7);
let b4 = 2097151 & (load_4i(&b[10..14]) >> 4);
let b5 = 2097151 & (load_3i(&b[13..16]) >> 1);
let b6 = 2097151 & (load_4i(&b[15..19]) >> 6);
let b7 = 2097151 & (load_3i(&b[18..21]) >> 3);
let b8 = 2097151 & load_3i(&b[21..24]);
let b9 = 2097151 & (load_4i(&b[23..27]) >> 5);
let b10 = 2097151 & (load_3i(&b[26..29]) >> 2);
let b11 = load_4i(&b[28..32]) >> 7;
let c0 = 2097151 & load_3i(&c[0..3]);
let c1 = 2097151 & (load_4i(&c[2..6]) >> 5);
let c2 = 2097151 & (load_3i(&c[5..8]) >> 2);
let c3 = 2097151 & (load_4i(&c[7..11]) >> 7);
let c4 = 2097151 & (load_4i(&c[10..14]) >> 4);
let c5 = 2097151 & (load_3i(&c[13..16]) >> 1);
let c6 = 2097151 & (load_4i(&c[15..19]) >> 6);
let c7 = 2097151 & (load_3i(&c[18..21]) >> 3);
let c8 = 2097151 & load_3i(&c[21..24]);
let c9 = 2097151 & (load_4i(&c[23..27]) >> 5);
let c10 = 2097151 & (load_3i(&c[26..29]) >> 2);
let c11 = load_4i(&c[28..32]) >> 7;
let mut s0: i64;
let mut s1: i64;
let mut s2: i64;
let mut s3: i64;
let mut s4: i64;
let mut s5: i64;
let mut s6: i64;
let mut s7: i64;
let mut s8: i64;
let mut s9: i64;
let mut s10: i64;
let mut s11: i64;
let mut s12: i64;
let mut s13: i64;
let mut s14: i64;
let mut s15: i64;
let mut s16: i64;
let mut s17: i64;
let mut s18: i64;
let mut s19: i64;
let mut s20: i64;
let mut s21: i64;
let mut s22: i64;
let mut s23: i64;
let mut carry0: i64;
let mut carry1: i64;
let mut carry2: i64;
let mut carry3: i64;
let mut carry4: i64;
let mut carry5: i64;
let mut carry6: i64;
let mut carry7: i64;
let mut carry8: i64;
let mut carry9: i64;
let mut carry10: i64;
let mut carry11: i64;
let mut carry12: i64;
let mut carry13: i64;
let mut carry14: i64;
let mut carry15: i64;
let mut carry16: i64;
let carry17: i64;
let carry18: i64;
let carry19: i64;
let carry20: i64;
let carry21: i64;
let carry22: i64;
s0 = c0 + a0*b0;
s1 = c1 + a0*b1 + a1*b0;
s2 = c2 + a0*b2 + a1*b1 + a2*b0;
s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0;
s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0;
s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0;
s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0;
s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0;
s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0;
s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0;
s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0;
s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0;
s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1;
s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2;
s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3;
s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4;
s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5;
s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6;
s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7;
s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8;
s20 = a9*b11 + a10*b10 + a11*b9;
s21 = a10*b11 + a11*b10;
s22 = a11*b11;
s23 = 0;
carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;