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(**
Base field: 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1 = 115792089237316195423570985008687907853269984665640564039457584007908834671663 (255 bits - 32 bytes)
Scalar field: 115792089237316195423570985008687907852837564279074904382605163141518161494337 (255 bits - 32 bytes)
Base field multiplicative subgroup decomposition:
2 * 3 * 7 * 13441 * 205115282021455665897114700593932402728804164701536103180137503955397371
Prime field multiplication subgroup decomposition:
2^6 * 3 * 149 * 631 * 6414488540731361226607730496888035255996436684289152125202372832747357
*)
let two_z = Z.succ Z.one
module Fq = Ff.MakeFp (struct
let prime_order =
Z.(
(two_z ** 256) - (two_z ** 32) - (two_z ** 9) - (two_z ** 8)
- (two_z ** 7) - (two_z ** 6) - (two_z ** 4) - one)
end)
module Fp = Ff.MakeFp (struct
let prime_order =
Z.of_string
"115792089237316195423570985008687907852837564279074904382605163141518161494337"
end)
module Projective =
Ec.MakeProjectiveWeierstrass (Fq) (Fp)
(struct
let a = Fq.zero
let b = Fq.of_z (Z.of_int 7)
let cofactor = Z.one
let bytes_generator =
Bytes.concat
Bytes.empty
[
Fq.(
to_bytes
(of_string
"55066263022277343669578718895168534326250603453777594175500187360389116729240"));
Fq.(
to_bytes
(of_string
"32670510020758816978083085130507043184471273380659243275938904335757337482424"));
Fq.(to_bytes one);
]
end)
module Jacobian =
Ec.MakeJacobianWeierstrass (Fq) (Fp)
(struct
let a = Fq.zero
let b = Fq.of_z (Z.of_int 7)
let cofactor = Z.one
let bytes_generator =
Bytes.concat
Bytes.empty
[
Fq.(
to_bytes
(of_string
"55066263022277343669578718895168534326250603453777594175500187360389116729240"));
Fq.(
to_bytes
(of_string
"32670510020758816978083085130507043184471273380659243275938904335757337482424"));
Fq.(to_bytes one);
]
end)
module Affine =
Ec.MakeAffineWeierstrass (Fq) (Fp)
(struct
let a = Fq.zero
let b = Fq.of_z (Z.of_int 7)
let cofactor = Z.one
let bytes_generator =
Bytes.concat
Bytes.empty
[
Fq.(
to_bytes
(of_string
"55066263022277343669578718895168534326250603453777594175500187360389116729240"));
Fq.(
to_bytes
(of_string
"32670510020758816978083085130507043184471273380659243275938904335757337482424"));
]
end)
let from_affine_weierstrass_to_jacobian_weierstrass p =
Ec.from_affine_weierstrass_to_jacobian_weierstrass
(module Affine)
(module Jacobian)
p
let from_affine_weierstrass_to_projective_weierstrass p =
Ec.from_affine_weierstrass_to_projective_weierstrass
(module Affine)
(module Projective)
p
let from_jacobian_weierstrass_to_affine_weierstrass p =
Ec.from_jacobian_weierstrass_to_affine_weierstrass
(module Jacobian)
(module Affine)
p
let from_projective_weierstrass_to_affine_weierstrass p =
Ec.from_projective_weierstrass_to_affine_weierstrass
(module Projective)
(module Affine)
p