Skip to content

Reduce amount of modular reduction calls in point add/double #12

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
capito27 wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Reduce amount of modular reduction calls in point add/double #12

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
8 changes: 4 additions & 4 deletions src/edwards/point.rs
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -76,10 +76,10 @@ impl Point {
let bb = y1 * y2; // B = Y1 * Y2
let cc = d_ec * t1 * t2; // C = d*T1 * T2
let dd = z1 * z2; // D = Z1 * Z2
let ee = (x1 + y1) * (x2 + y2) - &aa - &bb; // E = (X1 + Y1 ) * (X2 + Y2 ) - A - B
let ff = &dd - &cc; // F = D - C
let gg = dd + cc; // G = D + C
let hh = bb - aa * a_ec; // H = B - a*A
let ee = (x1.add_nomod(y1) * x2.add_nomod(y2)).sub_nomod(&aa).sub_nomod(&bb); // E = (X1 + Y1 ) * (X2 + Y2 ) - A - B
let ff = dd.sub_nomod(&cc); // F = D - C
let gg = dd.add_nomod(&cc); // G = D + C
let hh = bb.sub_nomod(&(&aa * a_ec)); // H = B - a*A
let x3 = &ee * &ff; // X3 = E * F
let y3 = &gg * &hh; // Y3 = G * H
let t3 = ee * hh; // T3 = E * H
Expand Down
16 changes: 8 additions & 8 deletions src/montgomery/point.rs
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -85,14 +85,14 @@ impl Point {
let (t3, t4) = (x1 * y2, x2 * y1);
let (t5, t6) = (y1 * z2, y2 * z1);
let (t7, t8) = (x1 * z2, x2 * z1);
let t9 = &t7 + &t8;
let ta = &t9 + &(&t0 * a_ec);
let rr = &t5 + &t6;
let tt = &ta - &t1;
let vv = t9 * a_ec + &t0 + &t0 + &t0 + &t2;
let ss = (&t3 - &t4) * s_ec + t0 - t2;
let uu = (t7 - t8) * s_ec - t3 - t4;
let ww = (t5 - t6) * s_ec + ta + t1;
let t9 = t7.add_nomod(&t8);
let ta = t9.add_nomod(&(&t0 * a_ec));
let rr = t5.add_nomod(&t6);
let tt = ta.sub_nomod(&t1);
let vv = (t9 * a_ec).add_nomod(&t0).add_nomod(&t0).add_nomod(&t0).add_nomod(&t2);
let ss = (t3.sub_nomod(&t4) * s_ec).add_nomod(&t0).sub_nomod(&t2);
let uu = (t7.sub_nomod(&t8) * s_ec).sub_nomod(&t3).sub_nomod(&t4);
let ww = (t5.sub_nomod(&t6) * s_ec).add_nomod(&ta).add_nomod(&t1);
let x3 = &rr * &ss - &tt * &uu;
let y3 = tt * &ww - &vv * &ss;
let z3 = vv * uu - rr * ww;
Expand Down
27 changes: 27 additions & 0 deletions src/primefield/mod.rs
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -194,6 +194,32 @@ impl FpElt {
}
}

impl FpElt {
// Add crate addition function that doesn't reduce the result every time.
// Useful when doing the point addition or doubling functions, since add, at worst, will increase bit usage by 1,
// thus increase variable memory size by one in average once every 8 calls, which is perfectly acceptable
pub(crate) fn add_nomod(&self, other: &FpElt) -> FpElt {
assert!(self.f == other.f);
FpElt{ n: &self.n + &other.n, f: self.f.clone() }
}
// Same as above, but inplace
pub(crate) fn add_nomod_inplace(&mut self, other: &FpElt) -> &FpElt {
assert!(self.f == other.f);
self.n += &other.n;
self
}
pub(crate) fn sub_nomod(&self, other: &FpElt) -> FpElt {
assert!(self.f == other.f);
FpElt{ n: &self.n - &other.n, f: self.f.clone() }
}
// Same as above, but inplace
pub(crate) fn sub_nomod_inplace(&mut self, other: &FpElt) -> &FpElt {
assert!(self.f == other.f);
self.n -= &other.n;
self
}
}

impl_op_ex!(+|a: FpElt, b: &FpElt| -> FpElt {
do_if_eq!(a.f == b.f, a.red(&a.n + &b.n), ERR_BIN_OP)
});
Expand Down Expand Up @@ -252,6 +278,7 @@ enum SqrtPrecmp {
P9MOD16,
P1MOD16,
}

impl Fp {
fn get_sqrt_precmp(&self) -> SqrtPrecmp {
self.0
Expand Down
171 changes: 94 additions & 77 deletions src/weierstrass/point.rs
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -31,11 +31,13 @@ pub struct Point {
}

impl ScMulRef<Scalar> for Point {}

impl EcPoint<Scalar> for Point {
fn is_zero(&self) -> bool {
self.c.x.is_zero() && !self.c.y.is_zero() && self.c.z.is_zero()
}
}

impl Encode for Point {
fn encode(&self, compress: bool) -> Vec<u8> {
// normalize the point to ensure that z = 1
Expand Down Expand Up @@ -87,52 +89,61 @@ impl Point {
// Costello-Renes-Batina. [Alg.1] (eprint.iacr.org/2015/1060).
fn core_add(&self, p: &<Curve as EllipticCurve>::Point) -> <Curve as EllipticCurve>::Point {
let a = &self.e.a;
let b3 = &self.e.b + &self.e.b + &self.e.b;
let b3 = &self.e.b.add_nomod(&self.e.b).add_nomod(&self.e.b);
let (x1, x2) = (&self.c.x, &p.c.x);
let (y1, y2) = (&self.c.y, &p.c.y);
let (z1, z2) = (&self.c.z, &p.c.z);
let (mut x3, mut y3, mut z3);
let (mut t0, mut t1, mut t2, mut t3, mut t4, mut t5);
t0 = x1 * x2; // 1. t0 = X1 * X2
t1 = y1 * y2; // 2. t1 = Y1 * Y2
t2 = z1 * z2; // 3. t2 = Z1 * Z2
t3 = x1 + y1; // 4. t3 = X1 + Y1
t4 = x2 + y2; // 5. t4 = X2 + Y2
t3 = &t3 * &t4; // 6. t3 = t3 * t4
t4 = &t0 + &t1; // 7. t4 = t0 + t1
t3 = &t3 - &t4; // 8. t3 = t3 - t4
t4 = x1 + z1; // 9. t4 = X1 + Z1
t5 = x2 + z2; // 10. t5 = X2 + Z2
t4 = &t4 * &t5; // 11. t4 = t4 * t5
t5 = &t0 + &t2; // 12. t5 = t0 + t2
t4 = &t4 - &t5; // 13. t4 = t4 - t5
t5 = y1 + z1; // 14. t5 = Y1 + Z1
x3 = y2 + z2; // 15. X3 = Y2 + Z2
t5 = &t5 * &x3; // 16. t5 = t5 * X3
x3 = &t1 + &t2; // 17. X3 = t1 + t2
t5 = &t5 - &x3; // 18. t5 = t5 - X3
z3 = a * &t4; // 19. Z3 = a * t4
x3 = &b3 * &t2; // 20. X3 = b3 * t2
z3 = x3 + &z3; // 21. Z3 = X3 + Z3
x3 = &t1 - &z3; // 22. X3 = t1 - Z3
z3 = &t1 + &z3; // 23. Z3 = t1 + Z3
y3 = &x3 * &z3; // 24. Y3 = X3 * Z3
t1 = &t0 + &t0; // 25. t1 = t0 + t0
t1 = &t1 + &t0; // 26. t1 = t1 + t0
t2 = a * &t2; // 27. t2 = a * t2
t4 = b3 * &t4; // 28. t4 = b3 * t4
t1 = &t1 + &t2; // 29. t1 = t1 + t2
t2 = &t0 - &t2; // 30. t2 = t0 - t2
t2 = a * &t2; // 31. t2 = a * t2
t4 = &t4 + t2; // 32. t4 = t4 + t2
t0 = &t1 * &t4; // 33. t0 = t1 * t4
y3 = y3 + &t0; // 34. Y3 = Y3 + t0
t0 = &t5 * t4; // 35. t0 = t5 * t4
x3 = &t3 * &x3; // 36. X3 = t3 * X3
x3 = x3 - &t0; // 37. X3 = X3 - t0
t0 = t3 * t1; // 38. t0 = t3 * t1
z3 = t5 * z3; // 39. Z3 = t5 * Z3
z3 = z3 + t0; // 40. Z3 = Z3 + t0
let mut x3: FpElt;
let mut y3: FpElt;
let mut z3: FpElt;

let mut t0: FpElt;
let mut t1: FpElt;
let mut t2: FpElt;
let mut t3: FpElt;
let mut t4: FpElt;
let mut t5: FpElt;

t0 = x1 * x2; // 1. t0 = X1 * X2
t1 = y1 * y2; // 2. t1 = Y1 * Y2
t2 = z1 * z2; // 3. t2 = Z1 * Z2
t3 = x1.add_nomod(y1); // 4. t3 = X1 + Y1
t4 = x2.add_nomod(y2); // 5. t4 = X2 + Y2
t3 = &t3 * &t4; // 6. t3 = t3 * t4
t4 = t0.add_nomod(&t1); // 7. t4 = t0 + t1
t3.sub_nomod_inplace(&t4); // 8. t3 = t3 - t4
t4 = x1.add_nomod(z1); // 9. t4 = X1 + Z1
t5 = x2.add_nomod(z2); // 10. t5 = X2 + Z2
t4 = &t4 * &t5; // 11. t4 = t4 * t5
t5 = t0.add_nomod(&t2); // 12. t5 = t0 + t2
t4.sub_nomod_inplace(&t5); // 13. t4 = t4 - t5
t5 = y1.add_nomod(z1); // 14. t5 = Y1 + Z1
x3 = y2.add_nomod(z2); // 15. X3 = Y2 + Z2
t5 = &t5 * &x3; // 16. t5 = t5 * X3
x3 = t1.add_nomod(&t2); // 17. X3 = t1 + t2
t5.sub_nomod_inplace(&x3); // 18. t5 = t5 - X3
z3 = a * &t4; // 19. Z3 = a * t4
x3 = b3 * &t2; // 20. X3 = b3 * t2
z3.add_nomod_inplace(&x3); // 21. Z3 = X3 + Z3
x3 = t1.sub_nomod(&z3); // 22. X3 = t1 - Z3
z3.add_nomod_inplace(&t1); // 23. Z3 = t1 + Z3
y3 = &x3 * &z3; // 24. Y3 = X3 * Z3
t1 = t0.add_nomod(&t0); // 25. t1 = t0 + t0
t1.add_nomod_inplace(&t0); // 26. t1 = t1 + t0
t2 = a * &t2; // 27. t2 = a * t2
t4 = b3 * &t4; // 28. t4 = b3 * t4
t1.add_nomod_inplace(&t2); // 29. t1 = t1 + t2
t2 = t0.sub_nomod(&t2); // 30. t2 = t0 - t2
t2 = a * &t2; // 31. t2 = a * t2
t4.add_nomod_inplace(&t2); // 32. t4 = t4 + t2
t0 = &t1 * &t4; // 33. t0 = t1 * t4
y3.add_nomod_inplace(&t0); // 34. Y3 = Y3 + t0
t0 = &t5 * t4; // 35. t0 = t5 * t4
x3 = &t3 * &x3; // 36. X3 = t3 * X3
x3.sub_nomod_inplace(&t0); // 37. X3 = X3 - t0
t0 = t3 * t1; // 38. t0 = t3 * t1
z3 = t5 * z3; // 39. Z3 = t5 * Z3
z3.add_nomod_inplace(&t0); // 40. Z3 = Z3 + t0
self.e.new_proy_point(ProyCoordinates {
x: x3,
y: y3,
Expand All @@ -144,43 +155,49 @@ impl Point {
// Costello-Renes-Batina. [Alg.3] (eprint.iacr.org/2015/1060).
fn core_doubling(&self) -> <Curve as EllipticCurve>::Point {
let a = &self.e.a;
let b3 = &self.e.b + &self.e.b + &self.e.b;
let b3 = &self.e.b.add_nomod(&self.e.b).add_nomod(&self.e.b);
let x = &self.c.x;
let y = &self.c.y;
let z = &self.c.z;
let (mut x3, mut y3, mut z3);
let (mut t0, t1, mut t2, mut t3);
t0 = x * x; // 1. t0 = X * X
t1 = y * y; // 2. t1 = Y * Y
t2 = z * z; // 3. t2 = Z * Z
t3 = x * y; // 4. t3 = X * Y
t3 = &t3 + &t3; // 5. t3 = t3 + t3
z3 = x * z; // 6. Z3 = X * Z
z3 = &z3 + &z3; // 7. Z3 = Z3 + Z3
x3 = a * &z3; // 8. X3 = a * Z3
y3 = &b3 * &t2; // 9. Y3 = b3 * t2
y3 = &x3 + &y3; // 10. Y3 = X3 + Y3
x3 = &t1 - &y3; // 11. X3 = t1 - Y3
y3 = &t1 + &y3; // 12. Y3 = t1 + Y3
y3 = &x3 * &y3; // 13. Y3 = X3 * Y3
x3 = &t3 * &x3; // 14. X3 = t3 * X3
z3 = &b3 * &z3; // 15. Z3 = b3 * Z3
t2 = a * &t2; // 16. t2 = a * t2
t3 = &t0 - &t2; // 17. t3 = t0 - t2
t3 = a * &t3; // 18. t3 = a * t3
t3 = &t3 + &z3; // 19. t3 = t3 + Z3
z3 = &t0 + &t0; // 20. Z3 = t0 + t0
t0 = &z3 + &t0; // 21. t0 = Z3 + t0
t0 = &t0 + &t2; // 22. t0 = t0 + t2
t0 = &t0 * &t3; // 23. t0 = t0 * t3
y3 = &y3 + &t0; // 24. Y3 = Y3 + t0
t2 = y * z; // 25. t2 = Y * Z
t2 = &t2 + &t2; // 26. t2 = t2 + t2
t0 = &t2 * &t3; // 27. t2 = t2 * t3
x3 = &x3 - &t0; // 28. X3 = X3 - t0
z3 = &t2 * &t1; // 29. Z3 = t2 * t1
z3 = &z3 + &z3; // 30. Z3 = Z3 + Z3
z3 = &z3 + &z3; // 31. Z3 = Z3 + Z3
let mut x3: FpElt;
let mut y3: FpElt;
let mut z3: FpElt;

let mut t0: FpElt;
let mut t1: FpElt;
let mut t2: FpElt;
let mut t3: FpElt;
t0 = x * x; // 1. t0 = X * X
t1 = y * y; // 2. t1 = Y * Y
t2 = z * z; // 3. t2 = Z * Z
t3 = x * y; // 4. t3 = X * Y
t3 = t3.add_nomod(&t3); // 5. t3 = t3 + t3
z3 = x * z; // 6. Z3 = X * Z
z3 = z3.add_nomod(&z3); // 7. Z3 = Z3 + Z3
x3 = a * &z3; // 8. X3 = a * Z3
y3 = b3 * &t2; // 9. Y3 = b3 * t2
y3.add_nomod_inplace(&x3); // 10. Y3 = X3 + Y3
x3 = t1.sub_nomod(&y3); // 11. X3 = t1 - Y3
y3.add_nomod_inplace(&t1); // 12. Y3 = t1 + Y3
y3 = &x3 * &y3; // 13. Y3 = X3 * Y3
x3 = &t3 * &x3; // 14. X3 = t3 * X3
z3 = b3 * &z3; // 15. Z3 = b3 * Z3
t2 = a * &t2; // 16. t2 = a * t2
t3 = t0.sub_nomod(&t2); // 17. t3 = t0 - t2
t3 = a * &t3; // 18. t3 = a * t3
t3.add_nomod_inplace(&z3); // 19. t3 = t3 + Z3
z3 = t0.add_nomod(&t0); // 20. Z3 = t0 + t0
t0.add_nomod_inplace(&z3); // 21. t0 = Z3 + t0
t0.add_nomod_inplace(&t2); // 22. t0 = t0 + t2
t0 = &t0 * &t3; // 23. t0 = t0 * t3
y3.add_nomod_inplace(&t0); // 24. Y3 = Y3 + t0
t2 = y * z; // 25. t2 = Y * Z
t2 = t2.add_nomod(&t2); // 26. t2 = t2 + t2
t0 = &t2 * &t3; // 27. t2 = t2 * t3
x3.sub_nomod_inplace(&t0); // 28. X3 = X3 - t0
z3 = &t2 * &t1; // 29. Z3 = t2 * t1
z3 = z3.add_nomod(&z3); // 30. Z3 = Z3 + Z3
z3 = z3.add_nomod(&z3); // 31. Z3 = Z3 + Z3
self.e.new_proy_point(ProyCoordinates {
x: x3,
y: y3,
Expand Down