bb::Bn254Fq12Params Struct Reference

The twelfth degree extension of the base field of BN254. More...

#include <fq12.hpp>

Static Public Attributes
static constexpr fq2	frobenius_coefficients_1
static constexpr fq2	frobenius_coefficients_2
static constexpr fq2	frobenius_coefficients_3

Detailed Description

The twelfth degree extension of the base field of BN254.

Fq12 is defined as Fq6[w] / (w^2 - v), where v is the variable added to Fq2 to construct Fq6. We store in the struct the coefficients to compute the frobenius morphism (we need powers up to q^3 to compute the final exponentiation in the pairing calculation)

1. Power q

   \[ (a + bw)^q = a^q + b^q * w^q = a^q + b^q * \xi^{(q-1)/6} * v \]

2. Power q^2

   \[ (a + bw)^{q^2} = a^{q^2} + b^{q^2} * w^{q^2} = a + b * \xi^{(q^2-1)/6} * v \]

3. Power q^3

   \[ (a + bw)^{q^3} = a^{q^3} + b^{q^3} * w^{q^3} = a^q + b^q * \xi^{(q^3-1)/6} * v \]

Definition at line 36 of file fq12.hpp.

Member Data Documentation

frobenius_coefficients_1

constexpr fq2 bb::Bn254Fq12Params::frobenius_coefficients_1

staticconstexpr

Initial value:

{
        { 0xb75446af8a0c2399UL, 0xb5e243df8d8526c8UL, 0x7f6d66278fc2b89bUL, 0x2e05603062b5af58UL },
        { 0xaeefbf6e3bc6cc33UL, 0x7f50c04b4ed87762UL, 0x9a8b7572eb6a58d4UL, 0x9b83e6c410c870UL }
    }

Definition at line 54 of file fq12.hpp.

frobenius_coefficients_2

constexpr fq2 bb::Bn254Fq12Params::frobenius_coefficients_2

staticconstexpr

Initial value:

{
        { 0xd96ee8726e4983b2UL, 0xe9b7ed6a458f581eUL, 0x5361c2c89ea5d262UL, 0x24594fd198a79c6eUL },
        { 0UL, 0UL, 0UL, 0UL }
    }

Definition at line 59 of file fq12.hpp.

frobenius_coefficients_3

constexpr fq2 bb::Bn254Fq12Params::frobenius_coefficients_3

staticconstexpr

Initial value:

{
        { 0x9dc006978e6a3d3dUL, 0x695b3f038ef4bf24UL, 0x1a238968ba7a7ccdUL, 0x103828f20e49839cUL },
        { 0x5cbbb0bd4f4e6b31UL, 0xe83ce8be1b5b282bUL, 0x646d437ef03fbae3UL, 0x133cf9860031f0c0UL }
    }

Definition at line 64 of file fq12.hpp.

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The documentation for this struct was generated from the following file:

• src/barretenberg/ecc/curves/bn254/fq12.hpp