use cryptonum::signed::{I192,I256,I384,I576};
use cryptonum::unsigned::{Decoder};
use cryptonum::unsigned::{U192,U256,U384,U576};
use ecdsa::point::Point;
use std::fmt::Debug;

/// Elliptic curves must implement this trait in order to work with the rest
/// of the ECDSA system. I've included instances for the core NIST curves
/// used in most systems, but this could be extended without issues.
/// (Eventually the curves defined here should actually be extended in
/// interesting ways to make the math faster, but we haven't gotten there
/// yet.)
#[allow(non_snake_case)]
pub trait EllipticCurve {
    /// The unsigned numeric type that fits constants for this curve.
    type Unsigned : Clone;
    /// The signed numeric type that fits constants for this curve.
    type Signed : Clone + Debug + PartialEq;
    /// The type of a point on the curve
    type Point;

    /// The size of the curve in bits.
    fn size() -> usize;
    /// The `p` value for the curve.
    fn p() -> Self::Unsigned;
    /// The `p` value for the curve.
    fn n() -> Self::Unsigned;
    /// The seed value for the curve.
    fn SEED() -> Self::Unsigned;
    /// The `c` value for the curve.
    fn c() -> Self::Unsigned;
    /// The `a` value for the curve.
    fn a() -> Self::Unsigned;
    /// The `b` value for the curve.
    fn b() -> Self::Unsigned;
    /// The `x` coordinate of the base point for the curve.
    fn Gx() -> Self::Signed;
    /// The `y` coordinate of the base point for the curve.
    fn Gy() -> Self::Signed;
    /// Generate a point for the curve given the provided values.
    fn new_point(x: Self::Unsigned, y: Self::Unsigned) -> Self::Point;
}

/// NIST curve P-192 (FIPS 186-4, page 101-102), a.k.a. secp192r1 from RFC5480
#[derive(Debug,PartialEq)]
pub struct P192 {}

impl EllipticCurve for P192 {
    type Unsigned = U192;
    type Signed = I192;
    type Point = Point<P192>;

    fn size() -> usize {
        192
    }

    fn p() -> U192 {
        U192::from([0xffffffffffffffff, 0xfffffffffffffffe, 0xffffffffffffffff])
    }

    fn n() -> U192 {
        U192::from([0x146bc9b1b4d22831, 0xffffffff99def836, 0xffffffffffffffff])
    }

    fn SEED() -> U192 {
        U192::from([0xd38020eae12196d5, 0xc8422f64ed579528, 0x3045ae6f])
    }

    fn c() -> U192 {
        U192::from([0x5f3d6fe2c745de65, 0x542dcd5fb078b6ef, 0x3099d2bbbfcb2538])
    }

    fn a() -> U192 {
        U192::from([0xfffffffffffffffc, 0xfffffffffffffffe, 0xffffffffffffffff])
    }

    fn b() -> U192 {
        U192::from([0xfeb8deecc146b9b1, 0x0fa7e9ab72243049, 0x64210519e59c80e7])
    }

    fn Gx() -> I192 {
        I192::from(U192::from([0xf4ff0afd82ff1012, 0x7cbf20eb43a18800, 0x188da80eb03090f6]))
    }

    fn Gy() -> I192 {
        I192::from(U192::from([0x73f977a11e794811, 0x631011ed6b24cdd5, 0x07192b95ffc8da78]))
    }

    fn new_point(x: Self::Unsigned, y: Self::Unsigned) -> Self::Point {
        Point::<P192>{ x: I192::from(x), y: I192::from(y) }
    }
}

/// NIST curve P-224 (FIPS 186-4, page 102), a.k.a. secp224r1 from RFC5480
#[derive(Debug,PartialEq)]
pub struct P224 {}

impl EllipticCurve for P224 {
    type Unsigned = U256;
    type Signed = I256;
    type Point = Point<P224>;

    fn size() -> usize {
        224
    }

    fn p() -> U256 {
        U256::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x01
        ])
    }

    fn n() -> U256 {
        U256::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
                0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
                0x5c, 0x5c, 0x2a, 0x3d
        ])
    }
    
    fn SEED() -> U256 {
        U256::from_bytes(&[
                0xbd, 0x71, 0x34, 0x47, 0x99, 0xd5, 0xc7, 0xfc,
                0xdc, 0x45, 0xb5, 0x9f, 0xa3, 0xb9, 0xab, 0x8f,
                0x6a, 0x94, 0x8b, 0xc5
        ])
    }

    fn c() -> U256 {
        U256::from_bytes(&[
                0x5b, 0x05, 0x6c, 0x7e, 0x11, 0xdd, 0x68, 0xf4,
                0x04, 0x69, 0xee, 0x7f, 0x3c, 0x7a, 0x7d, 0x74,
                0xf7, 0xd1, 0x21, 0x11, 0x65, 0x06, 0xd0, 0x31,
                0x21, 0x82, 0x91, 0xfb
        ])
    }
    
    fn a() -> U256 {
        U256::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xfe
        ])
    }
    
    fn b() -> U256 {
        U256::from_bytes(&[
                0xb4, 0x05, 0x0a, 0x85, 0x0c, 0x04, 0xb3, 0xab,
                0xf5, 0x41, 0x32, 0x56, 0x50, 0x44, 0xb0, 0xb7,
                0xd7, 0xbf, 0xd8, 0xba, 0x27, 0x0b, 0x39, 0x43,
                0x23, 0x55, 0xff, 0xb4
        ])
    }
    
    fn Gx() -> I256 {
        I256::from(U256::from_bytes(&[
                0xb7, 0x0e, 0x0c, 0xbd, 0x6b, 0xb4, 0xbf, 0x7f,
                0x32, 0x13, 0x90, 0xb9, 0x4a, 0x03, 0xc1, 0xd3,
                0x56, 0xc2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xd6,
                0x11, 0x5c, 0x1d, 0x21
        ]))
    }
    
    fn Gy() -> I256 {
        I256::from(U256::from_bytes(&[
                0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb,
                0x4c, 0x22, 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0,
                0x5a, 0x07, 0x47, 0x64, 0x44, 0xd5, 0x81, 0x99,
                0x85, 0x00, 0x7e, 0x34
        ]))
    }

    fn new_point(x: Self::Unsigned, y: Self::Unsigned) -> Self::Point {
        Point::<P224>{ x: I256::from(x), y: I256::from(y) }
    }
}

/// NIST curve P-256 (FIPS 186-4, page 102-103), a.k.a. secp256r1 from RFC5480
#[derive(Debug,PartialEq)]
pub struct P256 {}

impl EllipticCurve for P256 {
    type Signed = I256;
    type Unsigned = U256;
    type Point = Point<P256>;

    fn size() -> usize {
        256
    }

    fn p() -> U256 {
        U256::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff
        ])
    }
    
    fn n() -> U256 {
        U256::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xbc, 0xe6, 0xfa, 0xad, 0xa7, 0x17, 0x9e, 0x84,
                0xf3, 0xb9, 0xca, 0xc2, 0xfc, 0x63, 0x25, 0x51
        ])
    }
    
    fn SEED() -> U256 {
        U256::from_bytes(&[
                0xc4, 0x9d, 0x36, 0x08, 0x86, 0xe7, 0x04, 0x93,
                0x6a, 0x66, 0x78, 0xe1, 0x13, 0x9d, 0x26, 0xb7,
                0x81, 0x9f, 0x7e, 0x90
        ])
    }
    

    fn c() -> U256 {
        U256::from_bytes(&[
                0x7e, 0xfb, 0xa1, 0x66, 0x29, 0x85, 0xbe, 0x94,
                0x03, 0xcb, 0x05, 0x5c, 0x75, 0xd4, 0xf7, 0xe0,
                0xce, 0x8d, 0x84, 0xa9, 0xc5, 0x11, 0x4a, 0xbc,
                0xaf, 0x31, 0x77, 0x68, 0x01, 0x04, 0xfa, 0x0d
        ])
    }
    
    fn a() -> U256 {
        U256::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc
        ])
    }
    
    fn b() -> U256 {
        U256::from_bytes(&[
                0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7,
                0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc,
                0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6,
                0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b
        ])
    }
    
    fn Gx() -> I256 {
        I256::from(U256::from_bytes(&[
                0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47,
                0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2,
                0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0,
                0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96
        ]))
    }
    
    fn Gy() -> I256 {
        I256::from(U256::from_bytes(&[
                0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b,
                0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16,
                0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce,
                0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5
        ]))
    }

    fn new_point(x: Self::Unsigned, y: Self::Unsigned) -> Self::Point {
        Point::<P256>{ x: I256::from(x), y: I256::from(y) }
    }
}

/// NIST curve P-384 (FIPS 186-4, page 103-104), a.k.a. secp384r1 from RFC5480
#[derive(Debug,PartialEq)]
pub struct P384 {}

impl EllipticCurve for P384 {
    type Signed = I384;
    type Unsigned = U384;
    type Point = Point<P384>;

    fn size() -> usize {
        384
    }

    fn p() -> U384 {
        U384::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
                0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff
        ])
    }

    fn n() -> U384 {
        U384::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xc7, 0x63, 0x4d, 0x81, 0xf4, 0x37, 0x2d, 0xdf,
                0x58, 0x1a, 0x0d, 0xb2, 0x48, 0xb0, 0xa7, 0x7a,
                0xec, 0xec, 0x19, 0x6a, 0xcc, 0xc5, 0x29, 0x73
        ])
    }
    
    fn SEED() -> U384 {
        U384::from_bytes(&[
                0xa3, 0x35, 0x92, 0x6a, 0xa3, 0x19, 0xa2, 0x7a,
                0x1d, 0x00, 0x89, 0x6a, 0x67, 0x73, 0xa4, 0x82,
                0x7a, 0xcd, 0xac, 0x73
        ])
    }
    
    fn c() -> U384 {
        U384::from_bytes(&[
                0x79, 0xd1, 0xe6, 0x55, 0xf8, 0x68, 0xf0, 0x2f,
                0xff, 0x48, 0xdc, 0xde, 0xe1, 0x41, 0x51, 0xdd,
                0xb8, 0x06, 0x43, 0xc1, 0x40, 0x6d, 0x0c, 0xa1,
                0x0d, 0xfe, 0x6f, 0xc5, 0x20, 0x09, 0x54, 0x0a,
                0x49, 0x5e, 0x80, 0x42, 0xea, 0x5f, 0x74, 0x4f,
                0x6e, 0x18, 0x46, 0x67, 0xcc, 0x72, 0x24, 0x83
        ])
    }
    
    fn a() -> U384 {
        U384::from_bytes(&[
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
                0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xfc
        ])
    }
    
    fn b() -> U384 {
        U384::from_bytes(&[
                0xb3, 0x31, 0x2f, 0xa7, 0xe2, 0x3e, 0xe7, 0xe4,
                0x98, 0x8e, 0x05, 0x6b, 0xe3, 0xf8, 0x2d, 0x19,
                0x18, 0x1d, 0x9c, 0x6e, 0xfe, 0x81, 0x41, 0x12,
                0x03, 0x14, 0x08, 0x8f, 0x50, 0x13, 0x87, 0x5a,
                0xc6, 0x56, 0x39, 0x8d, 0x8a, 0x2e, 0xd1, 0x9d,
                0x2a, 0x85, 0xc8, 0xed, 0xd3, 0xec, 0x2a, 0xef
        ])
    }
    
    fn Gx() -> I384 {
        I384::from(U384::from_bytes(&[
                0xaa, 0x87, 0xca, 0x22, 0xbe, 0x8b, 0x05, 0x37,
                0x8e, 0xb1, 0xc7, 0x1e, 0xf3, 0x20, 0xad, 0x74,
                0x6e, 0x1d, 0x3b, 0x62, 0x8b, 0xa7, 0x9b, 0x98,
                0x59, 0xf7, 0x41, 0xe0, 0x82, 0x54, 0x2a, 0x38,
                0x55, 0x02, 0xf2, 0x5d, 0xbf, 0x55, 0x29, 0x6c,
                0x3a, 0x54, 0x5e, 0x38, 0x72, 0x76, 0x0a, 0xb7
        ]))
    }
    
    fn Gy() -> I384 {
        I384::from(U384::from_bytes(&[
                0x36, 0x17, 0xde, 0x4a, 0x96, 0x26, 0x2c, 0x6f,
                0x5d, 0x9e, 0x98, 0xbf, 0x92, 0x92, 0xdc, 0x29,
                0xf8, 0xf4, 0x1d, 0xbd, 0x28, 0x9a, 0x14, 0x7c,
                0xe9, 0xda, 0x31, 0x13, 0xb5, 0xf0, 0xb8, 0xc0,
                0x0a, 0x60, 0xb1, 0xce, 0x1d, 0x7e, 0x81, 0x9d,
                0x7a, 0x43, 0x1d, 0x7c, 0x90, 0xea, 0x0e, 0x5f
        ]))
    }

    fn new_point(x: Self::Unsigned, y: Self::Unsigned) -> Self::Point {
        Point::<P384>{ x: I384::from(x), y: I384::from(y) }
    }
}

/// NIST curve P-521 (FIPS 186-4, page 104), a.k.a. secp521r1 from RFC5480
#[derive(Debug,PartialEq)]
pub struct P521 {}

impl EllipticCurve for P521 {
    type Signed = I576;
    type Unsigned = U576;
    type Point = Point<P521>;

    fn size() -> usize {
        521
    }

    fn p() -> U576 {
        U576::from_bytes(&[
                0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff
        ])
    }

    fn n() -> U576 {
        U576::from_bytes(&[
                0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xfa, 0x51, 0x86, 0x87, 0x83, 0xbf, 0x2f,
                0x96, 0x6b, 0x7f, 0xcc, 0x01, 0x48, 0xf7, 0x09,
                0xa5, 0xd0, 0x3b, 0xb5, 0xc9, 0xb8, 0x89, 0x9c,
                0x47, 0xae, 0xbb, 0x6f, 0xb7, 0x1e, 0x91, 0x38,
                0x64, 0x09
        ])
    }
    
    fn SEED() -> U576 {
        U576::from_bytes(&[
                0xd0, 0x9e, 0x88, 0x00, 0x29, 0x1c, 0xb8, 0x53,
                0x96, 0xcc, 0x67, 0x17, 0x39, 0x32, 0x84, 0xaa,
                0xa0, 0xda, 0x64, 0xba
        ])
    }
        
    fn c() -> U576 {
        U576::from_bytes(&[
                0xb4, 0x8b, 0xfa, 0x5f, 0x42, 0x0a, 0x34, 0x94,
                0x95, 0x39, 0xd2, 0xbd, 0xfc, 0x26, 0x4e, 0xee,
                0xeb, 0x07, 0x76, 0x88, 0xe4, 0x4f, 0xbf, 0x0a,
                0xd8, 0xf6, 0xd0, 0xed, 0xb3, 0x7b, 0xd6, 0xb5,
                0x33, 0x28, 0x10, 0x00, 0x51, 0x8e, 0x19, 0xf1,
                0xb9, 0xff, 0xbe, 0x0f, 0xe9, 0xed, 0x8a, 0x3c,
                0x22, 0x00, 0xb8, 0xf8, 0x75, 0xe5, 0x23, 0x86,
                0x8c, 0x70, 0xc1, 0xe5, 0xbf, 0x55, 0xba, 0xd6,
                0x37
        ])
    }
    
    fn a() -> U576 {
        U576::from_bytes(&[
                0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xfc
        ])
    }
    
    fn b() -> U576 {
        U576::from_bytes(&[
                0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, 0x9a,
                0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, 0x40,
                0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3, 0x15,
                0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, 0x09,
                0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, 0x93,
                0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1, 0xbf,
                0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, 0x34,
                0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, 0x3f,
                0x00
        ])
    }
    
    fn Gx() -> I576 {
        I576::from(U576::from_bytes(&[
                0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04,
                0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95,
                0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f,
                0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d,
                0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7,
                0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff,
                0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a,
                0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5,
                0xbd, 0x66
        ]))
    }
    
    fn Gy() -> I576 {
        I576::from(U576::from_bytes(&[
                0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b,
                0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d,
                0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b,
                0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e,
                0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4,
                0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad,
                0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72,
                0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1,
                0x66, 0x50
        ]))
    }

    fn new_point(x: Self::Unsigned, y: Self::Unsigned) -> Self::Point {
        Point::<P521>{ x: I576::from(x), y: I576::from(y) }
    }
}