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Module 0x2::bls12381

Group operations of BLS12-381.

use 0x2::group_ops;

Struct Scalar​

structScalar
Fields
dummy_field: bool

Struct G1​

structG1
Fields
dummy_field: bool

Struct G2​

structG2
Fields
dummy_field: bool

Struct GT​

structGT
Fields
dummy_field: bool

Constants​

const G1_GENERATOR_BYTES: vector<u8> = [151, 241, 211, 167, 49, 151, 215, 148, 38, 149, 99, 140, 79, 169, 172, 15, 195, 104, 140, 79, 151, 116, 185, 5, 161, 78, 58, 63, 23, 27, 172, 88, 108, 85, 232, 63, 249, 122, 26, 239, 251, 58, 240, 10, 219, 34, 198, 187];
const G1_IDENTITY_BYTES: vector<u8> = [192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
const G1_TYPE: u8 = 1;
const G2_GENERATOR_BYTES: vector<u8> = [147, 224, 43, 96, 82, 113, 159, 96, 125, 172, 211, 160, 136, 39, 79, 101, 89, 107, 208, 208, 153, 32, 182, 26, 181, 218, 97, 187, 220, 127, 80, 73, 51, 76, 241, 18, 19, 148, 93, 87, 229, 172, 125, 5, 93, 4, 43, 126, 2, 74, 162, 178, 240, 143, 10, 145, 38, 8, 5, 39, 45, 197, 16, 81, 198, 228, 122, 212, 250, 64, 59, 2, 180, 81, 11, 100, 122, 227, 209, 119, 11, 172, 3, 38, 168, 5, 187, 239, 212, 128, 86, 200, 193, 33, 189, 184];
const G2_IDENTITY_BYTES: vector<u8> = [192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
const G2_TYPE: u8 = 2;
const GT_GENERATOR_BYTES: vector<u8> = [18, 80, 235, 216, 113, 252, 10, 146, 167, 178, 216, 49, 104, 208, 215, 39, 39, 45, 68, 27, 239, 161, 92, 80, 61, 216, 233, 12, 233, 141, 179, 231, 182, 209, 148, 246, 8, 57, 197, 8, 168, 67, 5, 170, 202, 23, 137, 182, 8, 154, 28, 91, 70, 229, 17, 11, 134, 117, 14, 198, 165, 50, 52, 136, 104, 168, 64, 69, 72, 60, 146, 183, 175, 90, 246, 137, 69, 46, 175, 171, 241, 168, 148, 62, 80, 67, 159, 29, 89, 136, 42, 152, 234, 160, 23, 15, 25, 242, 99, 55, 210, 5, 251, 70, 156, 214, 189, 21, 195, 213, 160, 77, 200, 135, 132, 251, 179, 208, 178, 219, 222, 165, 77, 67, 178, 183, 63, 44, 187, 18, 213, 131, 134, 168, 112, 62, 15, 148, 130, 38, 228, 126, 232, 157, 6, 251, 162, 62, 183, 197, 175, 13, 159, 128, 148, 12, 167, 113, 182, 255, 213, 133, 123, 170, 242, 34, 235, 149, 167, 210, 128, 157, 97, 191, 224, 46, 27, 253, 27, 104, 255, 2, 240, 184, 16, 42, 225, 194, 213, 213, 171, 26, 19, 104, 187, 68, 92, 124, 45, 32, 151, 3, 242, 57, 104, 156, 227, 76, 3, 120, 166, 142, 114, 166, 179, 178, 22, 218, 14, 34, 165, 3, 27, 84, 221, 255, 87, 48, 147, 150, 179, 140, 136, 28, 76, 132, 158, 194, 62, 135, 25, 53, 2, 184, 110, 219, 136, 87, 194, 115, 250, 7, 90, 80, 81, 41, 55, 224, 121, 78, 30, 101, 167, 97, 124, 144, 216, 189, 102, 6, 91, 31, 255, 229, 29, 122, 87, 153, 115, 177, 49, 80, 33, 236, 60, 25, 147, 79, 17, 184, 180, 36, 205, 72, 191, 56, 252, 239, 104, 8, 59, 11, 14, 197, 200, 26, 147, 179, 48, 238, 26, 103, 125, 13, 21, 255, 123, 152, 78, 137, 120, 239, 72, 136, 30, 50, 250, 201, 27, 147, 180, 115, 51, 226, 186, 87, 3, 53, 15, 85, 167, 174, 252, 211, 195, 27, 79, 203, 108, 229, 119, 28, 198, 160, 233, 120, 106, 181, 151, 51, 32, 200, 6, 173, 54, 8, 41, 16, 123, 168, 16, 197, 160, 159, 253, 217, 190, 34, 145, 160, 194, 90, 153, 162, 1, 178, 245, 34, 71, 61, 23, 19, 145, 18, 91, 168, 77, 196, 0, 124, 251, 242, 248, 218, 117, 47, 124, 116, 24, 82, 3, 252, 202, 88, 154, 199, 25, 195, 77, 255, 187, 170, 216, 67, 29, 173, 28, 31, 181, 151, 170, 165, 1, 129, 7, 21, 79, 37, 167, 100, 189, 60, 121, 147, 122, 69, 184, 69, 70, 218, 99, 75, 143, 107, 225, 74, 128, 97, 229, 92, 206, 186, 71, 139, 35, 247, 218, 202, 163, 92, 140, 167, 139, 234, 233, 98, 64, 69, 180, 182, 4, 197, 129, 35, 77, 8, 106, 153, 2, 36, 155, 100, 114, 143, 253, 33, 161, 137, 232, 121, 53, 169, 84, 5, 28, 124, 219, 167, 179, 135, 38, 41, 164, 250, 252, 5, 6, 98, 69, 203, 145, 8, 240, 36, 45, 15, 227, 239, 15, 65, 229, 134, 99, 191, 8, 207, 6, 134, 114, 203, 208, 26, 126, 199, 59, 172, 164, 215, 44, 169, 53, 68, 222, 255, 104, 107, 253, 109, 245, 67, 212, 142, 170, 36, 175, 228, 126, 30, 253, 228, 73, 56, 59, 103, 102, 49];
const GT_IDENTITY_BYTES: vector<u8> = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
const GT_TYPE: u8 = 3;
const SCALAR_ONE_BYTES: vector<u8> = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1];
const SCALAR_TYPE: u8 = 0;
const SCALAR_ZERO_BYTES: vector<u8> = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

Function bls12381_min_sig_verify​

@param signature: A 48-bytes signature that is a point on the G1 subgroup. @param public_key: A 96-bytes public key that is a point on the G2 subgroup. @param msg: The message that we test the signature against.

If the signature is a valid signature of the message and public key according to BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_, return true. Otherwise, return false.

public fun bls12381_min_sig_verify(signature: &vector<u8>, public_key: &vector<u8>, msg: &vector<u8>): bool
Implementation
public native fun bls12381_min_sig_verify(signature: &vector<u8>, public_key: &vector<u8>, msg: &vector<u8>): bool;

Function bls12381_min_pk_verify​

@param signature: A 96-bytes signature that is a point on the G2 subgroup. @param public_key: A 48-bytes public key that is a point on the G1 subgroup. @param msg: The message that we test the signature against.

If the signature is a valid signature of the message and public key according to BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_, return true. Otherwise, return false.

public fun bls12381_min_pk_verify(signature: &vector<u8>, public_key: &vector<u8>, msg: &vector<u8>): bool
Implementation
public native fun bls12381_min_pk_verify(signature: &vector<u8>, public_key: &vector<u8>, msg: &vector<u8>): bool;

Function scalar_from_bytes​

public fun scalar_from_bytes(bytes: &vector<u8>): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_from_bytes(bytes: &vector<u8>): Element<Scalar> {
group_ops::from_bytes(SCALAR_TYPE, bytes, false)
}

Function scalar_from_u64​

public fun scalar_from_u64(x: u64): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_from_u64(x: u64): Element<Scalar> {
let mut bytes = SCALAR_ZERO_BYTES;
group_ops::set_as_prefix(x, true, &mut bytes);
group_ops::from_bytes(SCALAR_TYPE, &bytes, true)
}

Function scalar_zero​

public fun scalar_zero(): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_zero(): Element<Scalar> {
let zero = SCALAR_ZERO_BYTES;
group_ops::from_bytes(SCALAR_TYPE, &zero, true)
}

Function scalar_one​

public fun scalar_one(): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_one(): Element<Scalar> {
let one = SCALAR_ONE_BYTES;
group_ops::from_bytes(SCALAR_TYPE, &one, true)
}

Function scalar_add​

public fun scalar_add(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::Scalar>): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_add(e1: &Element<Scalar>, e2: &Element<Scalar>): Element<Scalar> {
group_ops::add(SCALAR_TYPE, e1, e2)
}

Function scalar_sub​

public fun scalar_sub(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::Scalar>): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_sub(e1: &Element<Scalar>, e2: &Element<Scalar>): Element<Scalar> {
group_ops::sub(SCALAR_TYPE, e1, e2)
}

Function scalar_mul​

public fun scalar_mul(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::Scalar>): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_mul(e1: &Element<Scalar>, e2: &Element<Scalar>): Element<Scalar> {
group_ops::mul(SCALAR_TYPE, e1, e2)
}

Function scalar_div​

Returns e2/e1, fails if a is zero.

public fun scalar_div(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::Scalar>): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_div(e1: &Element<Scalar>, e2: &Element<Scalar>): Element<Scalar> {
group_ops::div(SCALAR_TYPE, e1, e2)
}

Function scalar_neg​

public fun scalar_neg(e: &group_ops::Element<bls12381::Scalar>): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_neg(e: &Element<Scalar>): Element<Scalar> {
scalar_sub(&scalar_zero(), e)
}

Function scalar_inv​

public fun scalar_inv(e: &group_ops::Element<bls12381::Scalar>): group_ops::Element<bls12381::Scalar>
Implementation
public fun scalar_inv(e: &Element<Scalar>): Element<Scalar> {
scalar_div(e, &scalar_one())
}

Function g1_from_bytes​

public fun g1_from_bytes(bytes: &vector<u8>): group_ops::Element<bls12381::G1>
Implementation
public fun g1_from_bytes(bytes: &vector<u8>): Element<G1> {
group_ops::from_bytes(G1_TYPE, bytes, false)
}

Function g1_identity​

public fun g1_identity(): group_ops::Element<bls12381::G1>
Implementation
public fun g1_identity(): Element<G1> {
let identity = G1_IDENTITY_BYTES;
group_ops::from_bytes(G1_TYPE, &identity, true)
}

Function g1_generator​

public fun g1_generator(): group_ops::Element<bls12381::G1>
Implementation
public fun g1_generator(): Element<G1> {
let generator = G1_GENERATOR_BYTES;
group_ops::from_bytes(G1_TYPE, &generator, true)
}

Function g1_add​

public fun g1_add(e1: &group_ops::Element<bls12381::G1>, e2: &group_ops::Element<bls12381::G1>): group_ops::Element<bls12381::G1>
Implementation
public fun g1_add(e1: &Element<G1>, e2: &Element<G1>): Element<G1> {
group_ops::add(G1_TYPE, e1, e2)
}

Function g1_sub​

public fun g1_sub(e1: &group_ops::Element<bls12381::G1>, e2: &group_ops::Element<bls12381::G1>): group_ops::Element<bls12381::G1>
Implementation
public fun g1_sub(e1: &Element<G1>, e2: &Element<G1>): Element<G1> {
group_ops::sub(G1_TYPE, e1, e2)
}

Function g1_mul​

public fun g1_mul(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::G1>): group_ops::Element<bls12381::G1>
Implementation
public fun g1_mul(e1: &Element<Scalar>, e2: &Element<G1>): Element<G1> {
group_ops::mul(G1_TYPE, e1, e2)
}

Function g1_div​

Returns e2 / e1, fails if scalar is zero.

public fun g1_div(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::G1>): group_ops::Element<bls12381::G1>
Implementation
public fun g1_div(e1: &Element<Scalar>, e2: &Element<G1>): Element<G1> {
group_ops::div(G1_TYPE, e1, e2)
}

Function g1_neg​

public fun g1_neg(e: &group_ops::Element<bls12381::G1>): group_ops::Element<bls12381::G1>
Implementation
public fun g1_neg(e: &Element<G1>): Element<G1> {
g1_sub(&g1_identity(), e)
}

Function hash_to_g1​

Hash using DST = BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_

public fun hash_to_g1(m: &vector<u8>): group_ops::Element<bls12381::G1>
Implementation
public fun hash_to_g1(m: &vector<u8>): Element<G1> {
group_ops::hash_to(G1_TYPE, m)
}

Function g1_multi_scalar_multiplication​

Let 'scalars' be the vector [s1, s2, ..., sn] and 'elements' be the vector [e1, e2, ..., en]. Returns s1e1 + s2e2 + ... + sn*en. Aborts with EInputTooLong if the vectors are larger than 32 (may increase in the future).

public fun g1_multi_scalar_multiplication(scalars: &vector<group_ops::Element<bls12381::Scalar>>, elements: &vector<group_ops::Element<bls12381::G1>>): group_ops::Element<bls12381::G1>
Implementation
public fun g1_multi_scalar_multiplication(scalars: &vector<Element<Scalar>>, elements: &vector<Element<G1>>): Element<G1> {
group_ops::multi_scalar_multiplication(G1_TYPE, scalars, elements)
}

Function g2_from_bytes​

public fun g2_from_bytes(bytes: &vector<u8>): group_ops::Element<bls12381::G2>
Implementation
public fun g2_from_bytes(bytes: &vector<u8>): Element<G2> {
group_ops::from_bytes(G2_TYPE, bytes, false)
}

Function g2_identity​

public fun g2_identity(): group_ops::Element<bls12381::G2>
Implementation
public fun g2_identity(): Element<G2> {
let identity = G2_IDENTITY_BYTES;
group_ops::from_bytes(G2_TYPE, &identity, true)
}

Function g2_generator​

public fun g2_generator(): group_ops::Element<bls12381::G2>
Implementation
public fun g2_generator(): Element<G2> {
let generator = G2_GENERATOR_BYTES;
group_ops::from_bytes(G2_TYPE, &generator, true)
}

Function g2_add​

public fun g2_add(e1: &group_ops::Element<bls12381::G2>, e2: &group_ops::Element<bls12381::G2>): group_ops::Element<bls12381::G2>
Implementation
public fun g2_add(e1: &Element<G2>, e2: &Element<G2>): Element<G2> {
group_ops::add(G2_TYPE, e1, e2)
}

Function g2_sub​

public fun g2_sub(e1: &group_ops::Element<bls12381::G2>, e2: &group_ops::Element<bls12381::G2>): group_ops::Element<bls12381::G2>
Implementation
public fun g2_sub(e1: &Element<G2>, e2: &Element<G2>): Element<G2> {
group_ops::sub(G2_TYPE, e1, e2)
}

Function g2_mul​

public fun g2_mul(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::G2>): group_ops::Element<bls12381::G2>
Implementation
public fun g2_mul(e1: &Element<Scalar>, e2: &Element<G2>): Element<G2> {
group_ops::mul(G2_TYPE, e1, e2)
}

Function g2_div​

Returns e2 / e1, fails if scalar is zero.

public fun g2_div(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::G2>): group_ops::Element<bls12381::G2>
Implementation
public fun g2_div(e1: &Element<Scalar>, e2: &Element<G2>): Element<G2> {
group_ops::div(G2_TYPE, e1, e2)
}

Function g2_neg​

public fun g2_neg(e: &group_ops::Element<bls12381::G2>): group_ops::Element<bls12381::G2>
Implementation
public fun g2_neg(e: &Element<G2>): Element<G2> {
g2_sub(&g2_identity(), e)
}

Function hash_to_g2​

Hash using DST = BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_

public fun hash_to_g2(m: &vector<u8>): group_ops::Element<bls12381::G2>
Implementation
public fun hash_to_g2(m: &vector<u8>): Element<G2> {
group_ops::hash_to(G2_TYPE, m)
}

Function g2_multi_scalar_multiplication​

Let 'scalars' be the vector [s1, s2, ..., sn] and 'elements' be the vector [e1, e2, ..., en]. Returns s1e1 + s2e2 + ... + sn*en. Aborts with EInputTooLong if the vectors are larger than 32 (may increase in the future).

public fun g2_multi_scalar_multiplication(scalars: &vector<group_ops::Element<bls12381::Scalar>>, elements: &vector<group_ops::Element<bls12381::G2>>): group_ops::Element<bls12381::G2>
Implementation
public fun g2_multi_scalar_multiplication(scalars: &vector<Element<Scalar>>, elements: &vector<Element<G2>>): Element<G2> {
group_ops::multi_scalar_multiplication(G2_TYPE, scalars, elements)
}

Function gt_identity​

public fun gt_identity(): group_ops::Element<bls12381::GT>
Implementation
public fun gt_identity(): Element<GT> {
let identity = GT_IDENTITY_BYTES;
group_ops::from_bytes(GT_TYPE, &identity, true)
}

Function gt_generator​

public fun gt_generator(): group_ops::Element<bls12381::GT>
Implementation
public fun gt_generator(): Element<GT> {
let generator = GT_GENERATOR_BYTES;
group_ops::from_bytes(GT_TYPE, &generator, true)
}

Function gt_add​

public fun gt_add(e1: &group_ops::Element<bls12381::GT>, e2: &group_ops::Element<bls12381::GT>): group_ops::Element<bls12381::GT>
Implementation
public fun gt_add(e1: &Element<GT>, e2: &Element<GT>): Element<GT> {
group_ops::add(GT_TYPE, e1, e2)
}

Function gt_sub​

public fun gt_sub(e1: &group_ops::Element<bls12381::GT>, e2: &group_ops::Element<bls12381::GT>): group_ops::Element<bls12381::GT>
Implementation
public fun gt_sub(e1: &Element<GT>, e2: &Element<GT>): Element<GT> {
group_ops::sub(GT_TYPE, e1, e2)
}

Function gt_mul​

public fun gt_mul(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::GT>): group_ops::Element<bls12381::GT>
Implementation
public fun gt_mul(e1: &Element<Scalar>, e2: &Element<GT>): Element<GT> {
group_ops::mul(GT_TYPE, e1, e2)
}

Function gt_div​

Returns e2 / e1, fails if scalar is zero.

public fun gt_div(e1: &group_ops::Element<bls12381::Scalar>, e2: &group_ops::Element<bls12381::GT>): group_ops::Element<bls12381::GT>
Implementation
public fun gt_div(e1: &Element<Scalar>, e2: &Element<GT>): Element<GT> {
group_ops::div(GT_TYPE, e1, e2)
}

Function gt_neg​

public fun gt_neg(e: &group_ops::Element<bls12381::GT>): group_ops::Element<bls12381::GT>
Implementation
public fun gt_neg(e: &Element<GT>): Element<GT> {
gt_sub(&gt_identity(), e)
}

Function pairing​

public fun pairing(e1: &group_ops::Element<bls12381::G1>, e2: &group_ops::Element<bls12381::G2>): group_ops::Element<bls12381::GT>
Implementation
public fun pairing(e1: &Element<G1>, e2: &Element<G2>): Element<GT> {
group_ops::pairing(G1_TYPE, e1, e2)
}