From cdcfd9a3a3e9ded1a650b3e1aa1bec2a3563acd3 Mon Sep 17 00:00:00 2001 From: Adam Wick Date: Tue, 8 Jan 2019 09:45:02 -0800 Subject: [PATCH] Basic point math, with tests. Distressingly slow. --- src/ecdsa/point.rs | 401 ++- test-generator/ECDSATesting.hs | 6 +- testdata/ecc/add/P224.test | 6006 ++++++++++++++++++++++++++++++++ testdata/ecc/add/P256.test | 6006 ++++++++++++++++++++++++++++++++ testdata/ecc/add/P384.test | 6006 ++++++++++++++++++++++++++++++++ testdata/ecc/add/P521.test | 6006 ++++++++++++++++++++++++++++++++ testdata/ecc/double/P224.test | 4004 +++++++++++++++++++++ testdata/ecc/double/P256.test | 4004 +++++++++++++++++++++ testdata/ecc/double/P384.test | 4004 +++++++++++++++++++++ testdata/ecc/double/P521.test | 4004 +++++++++++++++++++++ testdata/ecc/negate/P224.test | 4004 +++++++++++++++++++++ testdata/ecc/negate/P256.test | 4004 +++++++++++++++++++++ testdata/ecc/negate/P384.test | 4004 +++++++++++++++++++++ testdata/ecc/negate/P521.test | 4004 +++++++++++++++++++++ testdata/ecc/scale/P224.test | 5005 ++++++++++++++++++++++++++ testdata/ecc/scale/P256.test | 5005 ++++++++++++++++++++++++++ testdata/ecc/scale/P384.test | 5005 ++++++++++++++++++++++++++ testdata/ecc/scale/P521.test | 5005 ++++++++++++++++++++++++++ 18 files changed, 76294 insertions(+), 189 deletions(-) create mode 100644 testdata/ecc/add/P224.test create mode 100644 testdata/ecc/add/P256.test create mode 100644 testdata/ecc/add/P384.test create mode 100644 testdata/ecc/add/P521.test create mode 100644 testdata/ecc/double/P224.test create mode 100644 testdata/ecc/double/P256.test create mode 100644 testdata/ecc/double/P384.test create mode 100644 testdata/ecc/double/P521.test create mode 100644 testdata/ecc/negate/P224.test create mode 100644 testdata/ecc/negate/P256.test create mode 100644 testdata/ecc/negate/P384.test create mode 100644 testdata/ecc/negate/P521.test create mode 100644 testdata/ecc/scale/P224.test create mode 100644 testdata/ecc/scale/P256.test create mode 100644 testdata/ecc/scale/P384.test create mode 100644 testdata/ecc/scale/P521.test diff --git a/src/ecdsa/point.rs b/src/ecdsa/point.rs index 4ec00a6..899737a 100644 --- a/src/ecdsa/point.rs +++ b/src/ecdsa/point.rs @@ -19,202 +19,227 @@ pub struct Point pub y: T::Signed } -impl Clone for Point { - fn clone(&self) -> Point { - Point { - x: self.x.clone(), - y: self.y.clone() - } - } -} - -impl ECCPoint for Point { - type Curve = P192; - type Scale = I192; - - fn default() -> Point - { - Point { - x: P192::Gx(), - y: P192::Gy() - } - } - - fn negate(&self) -> Point - { - let mut newy = I192::new(false, P192::p()); - newy -= &self.y; - Point{ x: self.x.clone(), y: newy } - } - - fn double(&self) -> Point - { - let ua = P192::a(); - let up = P192::p(); - let bigp = I384::new(false, U384::from(&up)); - // lambda = (3 * xp ^ 2 + a) / 2 yp - let mut lambda_top = I384::from(3i64) * (&self.x * &self.x); - lambda_top += I768::new(false, U768::from(ua)); - let mut lambda_bot = I768::from(&self.y); - lambda_bot <<= 1; - let lambda = I192::from(lambda_top.moddiv(&lambda_bot, &I768::from(&bigp))); - // xr = lambda^2 - 2 xp - let mut xr = &lambda * λ - let mut xr_right = I384::from(&self.x); - xr_right <<= 1; - xr -= xr_right; - xr %= &bigp; - let x = I192::from(xr); - // yr = lambda (xp - xr) - yp - let xdiff = I192::from(&self.x - &x); - let mut yr = &lambda * &xdiff; - yr -= I384::from(&self.y); - let y = I192::from(&yr % &bigp); - // - Point{ x, y } - } - - fn add(&self, other: &Point) -> Point - { - let xdiff: I256 = &self.x - &other.x; - let ydiff: I256 = &self.y - &other.y; - let signedp = I256::from(U256::from(P192::p())); - let s = ydiff.moddiv(&xdiff, &signedp); - let mut xr = &s * &s; - xr -= I512::from(&self.x); - xr -= I512::from(&other.x); - let bigsignedp = I512::from(&signedp); - xr %= &bigsignedp; - let mut yr = I512::from(&self.x); - yr -= &xr; - yr *= I512::from(&s); - yr -= I512::from(&self.y); - yr %= &bigsignedp; - Point{ x: I192::from(xr), y: I192::from(yr) } - } - - fn scale(&self, d: &I192) -> Point - { - assert!(!d.is_zero()); - #[allow(non_snake_case)] - let mut Q: Point = self.clone(); - let mut bit = 191; - - // Skip down until we hit a set bit - while !d.testbit(bit as usize) { - bit -= 1; - } - // drop one - bit -= 1; - // do the double and add algorithm - while bit >= 0 { - Q = Q.double(); - - let test = d.testbit(bit as usize); - if test { - Q = Q.add(&self); +macro_rules! point_impl +{ + ($curve: ident, $base: ident, + $s2: ident, $u2: ident, + $s2p1: ident, $u2p1: ident) => + { + impl Clone for Point<$curve> { + fn clone(&self) -> Point<$curve> { + Point { + x: self.x.clone(), + y: self.y.clone() + } } - - bit -= 1; } - if d.is_negative() { - Q.negate() - } else { - Q + impl ECCPoint for Point<$curve> { + type Curve = $curve; + type Scale = $base; + + fn default() -> Point<$curve> + { + Point { + x: $curve::Gx(), + y: $curve::Gy() + } + } + + fn negate(&self) -> Point<$curve> + { + let mut newy = $base::new(false, $curve::p()); + newy -= &self.y; + Point{ x: self.x.clone(), y: newy } + } + + fn double(&self) -> Point<$curve> + { + let up = $curve::p(); + let bigp = $s2::new(false, $u2::from(&up)); + // lambda = (3 * xp ^ 2 + a) / 2 yp + let xsquared = self.x.square(); + let mut lambda_top = &xsquared * 3u64; + lambda_top += $s2p1::new(false, $u2p1::from($curve::a())); + let mut lambda_bot = $s2p1::from(&self.y); + lambda_bot <<= 1; + let lambda = $base::from(lambda_top.moddiv(&lambda_bot, &$s2p1::from(&bigp))); + // xr = lambda^2 - 2 xp + let mut xr = lambda.square(); + let mut xr_right = $s2::from(&self.x); + xr_right <<= 1; + xr -= xr_right; + xr %= &bigp; + let x = $base::from(xr); + // yr = lambda (xp - xr) - yp + let xdiff = $base::from(&self.x - &x); + let mut yr = &lambda * &xdiff; + yr -= $s2::from(&self.y); + let y = $base::from(&yr % &bigp); + // + Point{ x, y } + } + + fn add(&self, other: &Point<$curve>) -> Point<$curve> + { + let mut xdiff = self.x.clone(); xdiff -= &other.x; + let mut ydiff = self.y.clone(); ydiff -= &other.y; + let signedp = $base::new(false, $curve::p()); + let s = ydiff.moddiv(&xdiff, &signedp); + let mut xr = &s * &s; + xr -= $s2::from(&self.x); + xr -= $s2::from(&other.x); + let bigsignedp = $s2::from(&signedp); + xr %= &bigsignedp; + let mut yr = $s2::from(&self.x); + yr -= &xr; + yr *= $s2::from(&s); + yr -= $s2::from(&self.y); + yr %= &bigsignedp; + Point{ x: $base::from(xr), y: $base::from(yr) } + } + + fn scale(&self, d: &$base) -> Point<$curve> + { + assert!(!d.is_zero()); + #[allow(non_snake_case)] + let mut Q: Point<$curve> = self.clone(); + let mut bit = ($base::bit_length() - 1) as isize; + + // Skip down until we hit a set bit + while !d.testbit(bit as usize) { + bit -= 1; + } + // drop one + bit -= 1; + // do the double and add algorithm + while bit >= 0 { + Q = Q.double(); + + let test = d.testbit(bit as usize); + if test { + Q = Q.add(&self); + } + + bit -= 1; + } + + if d.is_negative() { + Q.negate() + } else { + Q + } + } } } } -#[cfg(test)] -mod tests { - use super::*; - use testing::*; +point_impl!(P192, I192, I384, U384, I448, U448); +point_impl!(P224, I256, I512, U512, I576, U576); +point_impl!(P256, I256, I512, U512, I576, U576); +point_impl!(P384, I384, I768, U768, I832, U832); +point_impl!(P521, I576, I1152, U1152, I1216, U1216); - #[test] - fn p192_negate() { - let fname = build_test_path("ecc/negate","P192"); - run_test(fname.to_string(), 4, |case| { - let (negx, xbytes) = case.get("x").unwrap(); - let (negy, ybytes) = case.get("y").unwrap(); - let (nega, abytes) = case.get("a").unwrap(); - let (negb, bbytes) = case.get("b").unwrap(); +macro_rules! point_tests +{ + ($curve: ident, $lcurve: ident, $stype: ident, $utype: ident) => { + #[cfg(test)] + mod $lcurve { + use super::*; + use testing::*; - let x = I192::new(*negx, U192::from_bytes(xbytes)); - let y = I192::new(*negy, U192::from_bytes(ybytes)); - let a = I192::new(*nega, U192::from_bytes(abytes)); - let b = I192::new(*negb, U192::from_bytes(bbytes)); - let point = Point{ x, y }; - let dbl = point.negate(); - assert_eq!(a, dbl.x, "x equivalence"); - assert_eq!(b, dbl.y, "y equivalence"); - }); + #[test] + fn negate() { + let fname = build_test_path("ecc/negate",stringify!($curve)); + run_test(fname.to_string(), 4, |case| { + let (negx, xbytes) = case.get("x").unwrap(); + let (negy, ybytes) = case.get("y").unwrap(); + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + let x = $stype::new(*negx, $utype::from_bytes(xbytes)); + let y = $stype::new(*negy, $utype::from_bytes(ybytes)); + let a = $stype::new(*nega, $utype::from_bytes(abytes)); + let b = $stype::new(*negb, $utype::from_bytes(bbytes)); + let point = Point::<$curve>{ x, y }; + let dbl = point.negate(); + assert_eq!(a, dbl.x, "x equivalence"); + assert_eq!(b, dbl.y, "y equivalence"); + }); + } + + #[test] + fn double() { + let fname = build_test_path("ecc/double",stringify!($curve)); + run_test(fname.to_string(), 4, |case| { + let (negx, xbytes) = case.get("x").unwrap(); + let (negy, ybytes) = case.get("y").unwrap(); + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + let x = $stype::new(*negx, $utype::from_bytes(xbytes)); + let y = $stype::new(*negy, $utype::from_bytes(ybytes)); + let a = $stype::new(*nega, $utype::from_bytes(abytes)); + let b = $stype::new(*negb, $utype::from_bytes(bbytes)); + let point = Point::<$curve>{ x, y }; + let dbl = point.double(); + assert_eq!(a, dbl.x, "x equivalence"); + assert_eq!(b, dbl.y, "y equivalence"); + }); + } + + #[test] + fn add() { + let fname = build_test_path("ecc/add",stringify!($curve)); + run_test(fname.to_string(), 6, move |case| { + let (negx, xbytes) = case.get("x").unwrap(); + let (negy, ybytes) = case.get("y").unwrap(); + let (negu, ubytes) = case.get("u").unwrap(); + let (negv, vbytes) = case.get("v").unwrap(); + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + let x = $stype::new(*negx, $utype::from_bytes(xbytes)); + let y = $stype::new(*negy, $utype::from_bytes(ybytes)); + let u = $stype::new(*negu, $utype::from_bytes(ubytes)); + let v = $stype::new(*negv, $utype::from_bytes(vbytes)); + let a = $stype::new(*nega, $utype::from_bytes(abytes)); + let b = $stype::new(*negb, $utype::from_bytes(bbytes)); + let point1 = Point::<$curve>{ x: x, y: y }; + let point2 = Point::<$curve>{ x: u, y: v }; + let res = point1.add(&point2); + assert_eq!(a, res.x, "x equivalence"); + assert_eq!(b, res.y, "y equivalence"); + }); + } + + #[test] + fn scale() { + let fname = build_test_path("ecc/scale",stringify!($curve)); + run_test(fname.to_string(), 5, |case| { + let (negx, xbytes) = case.get("x").unwrap(); + let (negy, ybytes) = case.get("y").unwrap(); + let (negk, kbytes) = case.get("k").unwrap(); + let (nega, abytes) = case.get("a").unwrap(); + let (negb, bbytes) = case.get("b").unwrap(); + + let x = $stype::new(*negx, $utype::from_bytes(xbytes)); + let y = $stype::new(*negy, $utype::from_bytes(ybytes)); + let k = $stype::new(*negk, $utype::from_bytes(kbytes)); + let a = $stype::new(*nega, $utype::from_bytes(abytes)); + let b = $stype::new(*negb, $utype::from_bytes(bbytes)); + let point = Point::<$curve>{ x: x, y: y }; + let res = point.scale(&k); + assert_eq!(a, res.x, "x equivalence"); + assert_eq!(b, res.y, "y equivalence"); + }); + } + } } +} - #[test] - fn p192_double() { - let fname = build_test_path("ecc/double","P192"); - run_test(fname.to_string(), 4, |case| { - let (negx, xbytes) = case.get("x").unwrap(); - let (negy, ybytes) = case.get("y").unwrap(); - let (nega, abytes) = case.get("a").unwrap(); - let (negb, bbytes) = case.get("b").unwrap(); - - let x = I192::new(*negx, U192::from_bytes(xbytes)); - let y = I192::new(*negy, U192::from_bytes(ybytes)); - let a = I192::new(*nega, U192::from_bytes(abytes)); - let b = I192::new(*negb, U192::from_bytes(bbytes)); - let point = Point{ x, y }; - let dbl = point.double(); - assert_eq!(a, dbl.x, "x equivalence"); - assert_eq!(b, dbl.y, "y equivalence"); - }); - } - - #[test] - fn p192_add() { - let fname = build_test_path("ecc/add","P192"); - run_test(fname.to_string(), 6, move |case| { - let (negx, xbytes) = case.get("x").unwrap(); - let (negy, ybytes) = case.get("y").unwrap(); - let (negu, ubytes) = case.get("u").unwrap(); - let (negv, vbytes) = case.get("v").unwrap(); - let (nega, abytes) = case.get("a").unwrap(); - let (negb, bbytes) = case.get("b").unwrap(); - - let x = I192::new(*negx, U192::from_bytes(xbytes)); - let y = I192::new(*negy, U192::from_bytes(ybytes)); - let u = I192::new(*negu, U192::from_bytes(ubytes)); - let v = I192::new(*negv, U192::from_bytes(vbytes)); - let a = I192::new(*nega, U192::from_bytes(abytes)); - let b = I192::new(*negb, U192::from_bytes(bbytes)); - let point1 = Point{ x: x, y: y }; - let point2 = Point{ x: u, y: v }; - let res = point1.add(&point2); - assert_eq!(a, res.x, "x equivalence"); - assert_eq!(b, res.y, "y equivalence"); - }); - } - - #[test] - fn p192_scale() { - let fname = build_test_path("ecc/scale","P192"); - run_test(fname.to_string(), 5, |case| { - let (negx, xbytes) = case.get("x").unwrap(); - let (negy, ybytes) = case.get("y").unwrap(); - let (negk, kbytes) = case.get("k").unwrap(); - let (nega, abytes) = case.get("a").unwrap(); - let (negb, bbytes) = case.get("b").unwrap(); - - let x = I192::new(*negx, U192::from_bytes(xbytes)); - let y = I192::new(*negy, U192::from_bytes(ybytes)); - let k = I192::new(*negk, U192::from_bytes(kbytes)); - let a = I192::new(*nega, U192::from_bytes(abytes)); - let b = I192::new(*negb, U192::from_bytes(bbytes)); - let point = Point{ x: x, y: y }; - let res = point.scale(&k); - assert_eq!(a, res.x, "x equivalence"); - assert_eq!(b, res.y, "y equivalence"); - }); - } -} \ No newline at end of file +point_tests!(P192, p192, I192, U192); +point_tests!(P224, p224, I256, U256); +point_tests!(P256, p256, I256, U256); +point_tests!(P384, p384, I384, U384); +point_tests!(P521, p521, I576, U576); \ No newline at end of file diff --git a/test-generator/ECDSATesting.hs b/test-generator/ECDSATesting.hs index 5cbe644..4e32675 100644 --- a/test-generator/ECDSATesting.hs +++ b/test-generator/ECDSATesting.hs @@ -12,7 +12,11 @@ import Math(showX) import Task(Task(..)) curves :: [(String, Curve)] -curves = [("P192", getCurveByName SEC_p192r1)] +curves = [("P192", getCurveByName SEC_p192r1), + ("P224", getCurveByName SEC_p224r1), + ("P256", getCurveByName SEC_p256r1), + ("P384", getCurveByName SEC_p384r1), + ("P521", getCurveByName SEC_p521r1)] negateTest :: String -> Curve -> Task negateTest name curve = Task { diff --git a/testdata/ecc/add/P224.test b/testdata/ecc/add/P224.test new file mode 100644 index 0000000..7ef6ed9 --- /dev/null +++ b/testdata/ecc/add/P224.test @@ -0,0 +1,6006 @@ +a: 4c792cbea3fb8f622e81dd2f5b7e6072cc02ac5e73173c6316e867d +b: b4ca974f91dcff4da390a50e664e443e3b9e47c44c03049dd06efe0d +u: 39037da32fd54c291686bf8ae37f06179504db47efd9ad951c2b0b24 +v: f548b6c95108092300ea3027c58227b18375644407b0a8eb80d9b154 +x: 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