extern crate num;
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extern crate num_bigint;
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extern crate num_traits;
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use num_bigint::BigInt;
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use num_traits::{One, Zero};
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mod utils;
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#[derive(Clone, Debug)]
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pub struct Point {
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pub x: BigInt,
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pub y: BigInt,
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}
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pub struct Babyjubjub {
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d: BigInt,
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a: BigInt,
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q: BigInt,
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}
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impl Babyjubjub {
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pub fn new() -> Babyjubjub {
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let d: BigInt = BigInt::parse_bytes(b"168696", 10).unwrap();
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let a: BigInt = BigInt::parse_bytes(b"168700", 10).unwrap();
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let q: BigInt = BigInt::parse_bytes(
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b"21888242871839275222246405745257275088548364400416034343698204186575808495617",
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10,
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)
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.unwrap();
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Babyjubjub { d: d, a: a, q: q }
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}
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pub fn add(&self, p: &Point, q: &Point) -> Point {
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// x = (x1*y2+y1*x2)/(c*(1+d*x1*x2*y1*y2))
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// y = (y1*y2-x1*x2)/(c*(1-d*x1*x2*y1*y2))
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// x = (x1 * y2 + y1 * x2) / (1 + d * x1 * y1 * y2)
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let one: BigInt = One::one();
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let x_num: BigInt = &p.x * &q.y + &p.y * &q.x;
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let x_den: BigInt = &one + &self.d * &p.x * &q.x * &p.y * &q.y;
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let x_den_inv = utils::mod_inverse0(&x_den, &self.q);
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// let x_den_inv = utils::mod_inverse1(x_den, self.q.clone());
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// let x_den_inv = utils::mod_inverse2(x_den, self.q.clone());
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let x: BigInt = utils::modulus(&(&x_num * &x_den_inv), &self.q);
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// y = (y1 * y2 - a * x1 * x2) / (1 - d * x1 * x2 * y1 * y2)
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let y_num = &p.y * &q.y - &self.a * &p.x * &q.x;
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let y_den = utils::modulus(&(&one - &self.d * &p.x * &q.x * &p.y * &q.y), &self.q);
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let y_den_inv = utils::mod_inverse0(&y_den, &self.q);
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// let y_den_inv = utils::mod_inverse1(y_den, self.q.clone());
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// let y_den_inv = utils::mod_inverse2(y_den, self.q.clone());
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let y: BigInt = utils::modulus(&(&y_num * &y_den_inv), &self.q);
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Point { x: x, y: y }
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}
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pub fn mul_scalar(&self, p: Point, n: BigInt) -> Point {
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// TODO use & in p and n to avoid clones on function call
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let mut r: Point = Point {
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x: Zero::zero(),
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y: One::one(),
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};
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let mut rem: BigInt = n;
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let mut exp: Point = p;
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let zero: BigInt = Zero::zero();
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let one: BigInt = One::one();
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while rem != zero {
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let is_odd = &rem & &one == one;
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if is_odd == true {
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r = self.add(&r, &exp);
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}
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exp = self.add(&exp, &exp);
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rem = rem >> 1;
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}
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r
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use num_bigint::ToBigInt;
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#[test]
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fn test_add_same_point() {
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let p: Point = Point {
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x: BigInt::parse_bytes(
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b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
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10,
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)
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.unwrap(),
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y: BigInt::parse_bytes(
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b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
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10,
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)
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.unwrap(),
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};
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let q: Point = Point {
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x: BigInt::parse_bytes(
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b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
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10,
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)
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.unwrap(),
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y: BigInt::parse_bytes(
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b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
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10,
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)
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.unwrap(),
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};
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let bbj = Babyjubjub::new();
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let res = bbj.add(&p, &q);
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assert_eq!(
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res.x.to_string(),
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"6890855772600357754907169075114257697580319025794532037257385534741338397365"
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);
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assert_eq!(
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res.y.to_string(),
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"4338620300185947561074059802482547481416142213883829469920100239455078257889"
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);
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}
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#[test]
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fn test_add_different_points() {
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let p: Point = Point {
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x: BigInt::parse_bytes(
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b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
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10,
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)
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.unwrap(),
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y: BigInt::parse_bytes(
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b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
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10,
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)
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.unwrap(),
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};
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let q: Point = Point {
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x: BigInt::parse_bytes(
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b"16540640123574156134436876038791482806971768689494387082833631921987005038935",
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10,
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)
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.unwrap(),
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y: BigInt::parse_bytes(
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b"20819045374670962167435360035096875258406992893633759881276124905556507972311",
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10,
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)
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.unwrap(),
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};
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let bbj = Babyjubjub::new();
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let res = bbj.add(&p, &q);
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assert_eq!(
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res.x.to_string(),
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"7916061937171219682591368294088513039687205273691143098332585753343424131937"
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);
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assert_eq!(
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res.y.to_string(),
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"14035240266687799601661095864649209771790948434046947201833777492504781204499"
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);
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}
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#[test]
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fn test_mul_scalar() {
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let p: Point = Point {
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x: BigInt::parse_bytes(
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b"17777552123799933955779906779655732241715742912184938656739573121738514868268",
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10,
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)
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.unwrap(),
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y: BigInt::parse_bytes(
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b"2626589144620713026669568689430873010625803728049924121243784502389097019475",
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10,
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)
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.unwrap(),
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};
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let bbj = Babyjubjub::new();
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let res_m = bbj.mul_scalar(p.clone(), 3.to_bigint().unwrap());
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let res_a = bbj.add(&p, &p);
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let res_a = bbj.add(&res_a, &p);
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assert_eq!(res_m.x, res_a.x);
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assert_eq!(
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res_m.x.to_string(),
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"19372461775513343691590086534037741906533799473648040012278229434133483800898"
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);
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assert_eq!(
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res_m.y.to_string(),
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"9458658722007214007257525444427903161243386465067105737478306991484593958249"
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);
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let n = BigInt::parse_bytes(
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b"14035240266687799601661095864649209771790948434046947201833777492504781204499",
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10,
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)
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.unwrap();
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let res2 = bbj.mul_scalar(p.clone(), n);
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assert_eq!(
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res2.x.to_string(),
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"17070357974431721403481313912716834497662307308519659060910483826664480189605"
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);
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assert_eq!(
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res2.y.to_string(),
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"4014745322800118607127020275658861516666525056516280575712425373174125159339"
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);
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}
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}
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