Barretenberg
The ZK-SNARK library at the core of Aztec
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Static Public Attributes | List of all members
bb::secp256k1::FqParams Struct Reference

Parameters defining the base field of the secp256k1 curve. More...

#include <secp256k1.hpp>

Static Public Attributes

static constexpr uint64_t modulus_0 = 0xFFFFFFFEFFFFFC2FULL
 
static constexpr uint64_t modulus_1 = 0xFFFFFFFFFFFFFFFFULL
 
static constexpr uint64_t modulus_2 = 0xFFFFFFFFFFFFFFFFULL
 
static constexpr uint64_t modulus_3 = 0xFFFFFFFFFFFFFFFFULL
 
static constexpr uint64_t r_squared_0 = 8392367050913ULL
 
static constexpr uint64_t r_squared_1 = 1
 
static constexpr uint64_t r_squared_2 = 0
 
static constexpr uint64_t r_squared_3 = 0
 
static constexpr uint64_t r_inv = 15580212934572586289ULL
 
static constexpr uint64_t r_inv_0 = 0xffffffff27c7f3a9UL
 
static constexpr uint64_t r_inv_1 = 0xffffffffffffffffUL
 
static constexpr uint64_t r_inv_2 = 0xffffffffffffffffUL
 
static constexpr uint64_t r_inv_3 = 0xd838091dd2253530UL
 
static constexpr uint64_t cube_root_0 = 0x58a4361c8e81894eULL
 
static constexpr uint64_t cube_root_1 = 0x03fde1631c4b80afULL
 
static constexpr uint64_t cube_root_2 = 0xf8e98978d02e3905ULL
 
static constexpr uint64_t cube_root_3 = 0x7a4a36aebcbb3d53ULL
 
static constexpr uint64_t primitive_root_0 = 0UL
 
static constexpr uint64_t primitive_root_1 = 0UL
 
static constexpr uint64_t primitive_root_2 = 0UL
 
static constexpr uint64_t primitive_root_3 = 0UL
 
static constexpr uint64_t coset_generator_0 = 0x300000b73ULL
 
static constexpr uint64_t coset_generator_1 = 0
 
static constexpr uint64_t coset_generator_2 = 0
 
static constexpr uint64_t coset_generator_3 = 0
 
static constexpr uint64_t modulus_wasm_0 = 0x1ffffc2f
 
static constexpr uint64_t modulus_wasm_1 = 0x1ffffff7
 
static constexpr uint64_t modulus_wasm_2 = 0x1fffffff
 
static constexpr uint64_t modulus_wasm_3 = 0x1fffffff
 
static constexpr uint64_t modulus_wasm_4 = 0x1fffffff
 
static constexpr uint64_t modulus_wasm_5 = 0x1fffffff
 
static constexpr uint64_t modulus_wasm_6 = 0x1fffffff
 
static constexpr uint64_t modulus_wasm_7 = 0x1fffffff
 
static constexpr uint64_t modulus_wasm_8 = 0xffffff
 
static constexpr uint64_t r_squared_wasm_0 = 0x001e88003a428400UL
 
static constexpr uint64_t r_squared_wasm_1 = 0x0000000000000400UL
 
static constexpr uint64_t r_squared_wasm_2 = 0x0000000000000000UL
 
static constexpr uint64_t r_squared_wasm_3 = 0x0000000000000000UL
 
static constexpr uint64_t r_inv_wasm_0 = 0xed6544e
 
static constexpr uint64_t r_inv_wasm_1 = 0x1ffffffb
 
static constexpr uint64_t r_inv_wasm_2 = 0x1fffffff
 
static constexpr uint64_t r_inv_wasm_3 = 0x1fffffff
 
static constexpr uint64_t r_inv_wasm_4 = 0x1fffffff
 
static constexpr uint64_t r_inv_wasm_5 = 0x1fffffff
 
static constexpr uint64_t r_inv_wasm_6 = 0x1fffffff
 
static constexpr uint64_t r_inv_wasm_7 = 0x10ffffff
 
static constexpr uint64_t r_inv_wasm_8 = 0x9129a9
 
static constexpr uint64_t cube_root_wasm_0 = 0x1486c3a0d03162ffUL
 
static constexpr uint64_t cube_root_wasm_1 = 0x7fbc2c63897015ebUL
 
static constexpr uint64_t cube_root_wasm_2 = 0x1d312f1a05c720a0UL
 
static constexpr uint64_t cube_root_wasm_3 = 0x4946d5d79767aa7fUL
 
static constexpr uint64_t primitive_root_wasm_0 = 0x0000000000000000UL
 
static constexpr uint64_t primitive_root_wasm_1 = 0x0000000000000000UL
 
static constexpr uint64_t primitive_root_wasm_2 = 0x0000000000000000UL
 
static constexpr uint64_t primitive_root_wasm_3 = 0x0000000000000000UL
 
static constexpr uint64_t coset_generator_wasm_0 = 0x0000006000016e60ULL
 
static constexpr uint64_t coset_generator_wasm_1 = 0
 
static constexpr uint64_t coset_generator_wasm_2 = 0
 
static constexpr uint64_t coset_generator_wasm_3 = 0
 
static constexpr size_t PUBLIC_INPUTS_SIZE = BIGFIELD_PUBLIC_INPUTS_SIZE
 
static constexpr char schema_name [] = "secp256k1_fq"
 

Detailed Description

Parameters defining the base field of the secp256k1 curve.

When split into 4 64-bit words, the parameters are represented in little-endian, i.e. the least significant bit comes first. For example, to recover the modulus from the 64-bit words we concatenate its limbs to obtain: 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f

Note
These parameters can be extracted by running the script parameter_helper.py in ecc/fields

Definition at line 26 of file secp256k1.hpp.

Member Data Documentation

◆ coset_generator_0

constexpr uint64_t bb::secp256k1::FqParams::coset_generator_0 = 0x300000b73ULL
staticconstexpr

Definition at line 71 of file secp256k1.hpp.

◆ coset_generator_1

constexpr uint64_t bb::secp256k1::FqParams::coset_generator_1 = 0
staticconstexpr

Definition at line 72 of file secp256k1.hpp.

◆ coset_generator_2

constexpr uint64_t bb::secp256k1::FqParams::coset_generator_2 = 0
staticconstexpr

Definition at line 73 of file secp256k1.hpp.

◆ coset_generator_3

constexpr uint64_t bb::secp256k1::FqParams::coset_generator_3 = 0
staticconstexpr

Definition at line 74 of file secp256k1.hpp.

◆ coset_generator_wasm_0

constexpr uint64_t bb::secp256k1::FqParams::coset_generator_wasm_0 = 0x0000006000016e60ULL
staticconstexpr

Definition at line 124 of file secp256k1.hpp.

◆ coset_generator_wasm_1

constexpr uint64_t bb::secp256k1::FqParams::coset_generator_wasm_1 = 0
staticconstexpr

Definition at line 125 of file secp256k1.hpp.

◆ coset_generator_wasm_2

constexpr uint64_t bb::secp256k1::FqParams::coset_generator_wasm_2 = 0
staticconstexpr

Definition at line 126 of file secp256k1.hpp.

◆ coset_generator_wasm_3

constexpr uint64_t bb::secp256k1::FqParams::coset_generator_wasm_3 = 0
staticconstexpr

Definition at line 127 of file secp256k1.hpp.

◆ cube_root_0

constexpr uint64_t bb::secp256k1::FqParams::cube_root_0 = 0x58a4361c8e81894eULL
staticconstexpr

Definition at line 59 of file secp256k1.hpp.

◆ cube_root_1

constexpr uint64_t bb::secp256k1::FqParams::cube_root_1 = 0x03fde1631c4b80afULL
staticconstexpr

Definition at line 60 of file secp256k1.hpp.

◆ cube_root_2

constexpr uint64_t bb::secp256k1::FqParams::cube_root_2 = 0xf8e98978d02e3905ULL
staticconstexpr

Definition at line 61 of file secp256k1.hpp.

◆ cube_root_3

constexpr uint64_t bb::secp256k1::FqParams::cube_root_3 = 0x7a4a36aebcbb3d53ULL
staticconstexpr

Definition at line 62 of file secp256k1.hpp.

◆ cube_root_wasm_0

constexpr uint64_t bb::secp256k1::FqParams::cube_root_wasm_0 = 0x1486c3a0d03162ffUL
staticconstexpr

Definition at line 111 of file secp256k1.hpp.

◆ cube_root_wasm_1

constexpr uint64_t bb::secp256k1::FqParams::cube_root_wasm_1 = 0x7fbc2c63897015ebUL
staticconstexpr

Definition at line 112 of file secp256k1.hpp.

◆ cube_root_wasm_2

constexpr uint64_t bb::secp256k1::FqParams::cube_root_wasm_2 = 0x1d312f1a05c720a0UL
staticconstexpr

Definition at line 113 of file secp256k1.hpp.

◆ cube_root_wasm_3

constexpr uint64_t bb::secp256k1::FqParams::cube_root_wasm_3 = 0x4946d5d79767aa7fUL
staticconstexpr

Definition at line 114 of file secp256k1.hpp.

◆ modulus_0

constexpr uint64_t bb::secp256k1::FqParams::modulus_0 = 0xFFFFFFFEFFFFFC2FULL
staticconstexpr

Definition at line 31 of file secp256k1.hpp.

◆ modulus_1

constexpr uint64_t bb::secp256k1::FqParams::modulus_1 = 0xFFFFFFFFFFFFFFFFULL
staticconstexpr

Definition at line 32 of file secp256k1.hpp.

◆ modulus_2

constexpr uint64_t bb::secp256k1::FqParams::modulus_2 = 0xFFFFFFFFFFFFFFFFULL
staticconstexpr

Definition at line 33 of file secp256k1.hpp.

◆ modulus_3

constexpr uint64_t bb::secp256k1::FqParams::modulus_3 = 0xFFFFFFFFFFFFFFFFULL
staticconstexpr

Definition at line 34 of file secp256k1.hpp.

◆ modulus_wasm_0

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_0 = 0x1ffffc2f
staticconstexpr

Definition at line 78 of file secp256k1.hpp.

◆ modulus_wasm_1

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_1 = 0x1ffffff7
staticconstexpr

Definition at line 79 of file secp256k1.hpp.

◆ modulus_wasm_2

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_2 = 0x1fffffff
staticconstexpr

Definition at line 80 of file secp256k1.hpp.

◆ modulus_wasm_3

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_3 = 0x1fffffff
staticconstexpr

Definition at line 81 of file secp256k1.hpp.

◆ modulus_wasm_4

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_4 = 0x1fffffff
staticconstexpr

Definition at line 82 of file secp256k1.hpp.

◆ modulus_wasm_5

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_5 = 0x1fffffff
staticconstexpr

Definition at line 83 of file secp256k1.hpp.

◆ modulus_wasm_6

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_6 = 0x1fffffff
staticconstexpr

Definition at line 84 of file secp256k1.hpp.

◆ modulus_wasm_7

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_7 = 0x1fffffff
staticconstexpr

Definition at line 85 of file secp256k1.hpp.

◆ modulus_wasm_8

constexpr uint64_t bb::secp256k1::FqParams::modulus_wasm_8 = 0xffffff
staticconstexpr

Definition at line 86 of file secp256k1.hpp.

◆ primitive_root_0

constexpr uint64_t bb::secp256k1::FqParams::primitive_root_0 = 0UL
staticconstexpr

Definition at line 65 of file secp256k1.hpp.

◆ primitive_root_1

constexpr uint64_t bb::secp256k1::FqParams::primitive_root_1 = 0UL
staticconstexpr

Definition at line 66 of file secp256k1.hpp.

◆ primitive_root_2

constexpr uint64_t bb::secp256k1::FqParams::primitive_root_2 = 0UL
staticconstexpr

Definition at line 67 of file secp256k1.hpp.

◆ primitive_root_3

constexpr uint64_t bb::secp256k1::FqParams::primitive_root_3 = 0UL
staticconstexpr

Definition at line 68 of file secp256k1.hpp.

◆ primitive_root_wasm_0

constexpr uint64_t bb::secp256k1::FqParams::primitive_root_wasm_0 = 0x0000000000000000UL
staticconstexpr

Definition at line 117 of file secp256k1.hpp.

◆ primitive_root_wasm_1

constexpr uint64_t bb::secp256k1::FqParams::primitive_root_wasm_1 = 0x0000000000000000UL
staticconstexpr

Definition at line 118 of file secp256k1.hpp.

◆ primitive_root_wasm_2

constexpr uint64_t bb::secp256k1::FqParams::primitive_root_wasm_2 = 0x0000000000000000UL
staticconstexpr

Definition at line 119 of file secp256k1.hpp.

◆ primitive_root_wasm_3

constexpr uint64_t bb::secp256k1::FqParams::primitive_root_wasm_3 = 0x0000000000000000UL
staticconstexpr

Definition at line 120 of file secp256k1.hpp.

◆ PUBLIC_INPUTS_SIZE

constexpr size_t bb::secp256k1::FqParams::PUBLIC_INPUTS_SIZE = BIGFIELD_PUBLIC_INPUTS_SIZE
staticconstexpr

Definition at line 131 of file secp256k1.hpp.

◆ r_inv

constexpr uint64_t bb::secp256k1::FqParams::r_inv = 15580212934572586289ULL
staticconstexpr

Definition at line 47 of file secp256k1.hpp.

◆ r_inv_0

constexpr uint64_t bb::secp256k1::FqParams::r_inv_0 = 0xffffffff27c7f3a9UL
staticconstexpr

Definition at line 53 of file secp256k1.hpp.

◆ r_inv_1

constexpr uint64_t bb::secp256k1::FqParams::r_inv_1 = 0xffffffffffffffffUL
staticconstexpr

Definition at line 54 of file secp256k1.hpp.

◆ r_inv_2

constexpr uint64_t bb::secp256k1::FqParams::r_inv_2 = 0xffffffffffffffffUL
staticconstexpr

Definition at line 55 of file secp256k1.hpp.

◆ r_inv_3

constexpr uint64_t bb::secp256k1::FqParams::r_inv_3 = 0xd838091dd2253530UL
staticconstexpr

Definition at line 56 of file secp256k1.hpp.

◆ r_inv_wasm_0

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_0 = 0xed6544e
staticconstexpr

Definition at line 99 of file secp256k1.hpp.

◆ r_inv_wasm_1

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_1 = 0x1ffffffb
staticconstexpr

Definition at line 100 of file secp256k1.hpp.

◆ r_inv_wasm_2

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_2 = 0x1fffffff
staticconstexpr

Definition at line 101 of file secp256k1.hpp.

◆ r_inv_wasm_3

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_3 = 0x1fffffff
staticconstexpr

Definition at line 102 of file secp256k1.hpp.

◆ r_inv_wasm_4

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_4 = 0x1fffffff
staticconstexpr

Definition at line 103 of file secp256k1.hpp.

◆ r_inv_wasm_5

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_5 = 0x1fffffff
staticconstexpr

Definition at line 104 of file secp256k1.hpp.

◆ r_inv_wasm_6

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_6 = 0x1fffffff
staticconstexpr

Definition at line 105 of file secp256k1.hpp.

◆ r_inv_wasm_7

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_7 = 0x10ffffff
staticconstexpr

Definition at line 106 of file secp256k1.hpp.

◆ r_inv_wasm_8

constexpr uint64_t bb::secp256k1::FqParams::r_inv_wasm_8 = 0x9129a9
staticconstexpr

Definition at line 107 of file secp256k1.hpp.

◆ r_squared_0

constexpr uint64_t bb::secp256k1::FqParams::r_squared_0 = 8392367050913ULL
staticconstexpr

Definition at line 37 of file secp256k1.hpp.

◆ r_squared_1

constexpr uint64_t bb::secp256k1::FqParams::r_squared_1 = 1
staticconstexpr

Definition at line 38 of file secp256k1.hpp.

◆ r_squared_2

constexpr uint64_t bb::secp256k1::FqParams::r_squared_2 = 0
staticconstexpr

Definition at line 39 of file secp256k1.hpp.

◆ r_squared_3

constexpr uint64_t bb::secp256k1::FqParams::r_squared_3 = 0
staticconstexpr

Definition at line 40 of file secp256k1.hpp.

◆ r_squared_wasm_0

constexpr uint64_t bb::secp256k1::FqParams::r_squared_wasm_0 = 0x001e88003a428400UL
staticconstexpr

Definition at line 90 of file secp256k1.hpp.

◆ r_squared_wasm_1

constexpr uint64_t bb::secp256k1::FqParams::r_squared_wasm_1 = 0x0000000000000400UL
staticconstexpr

Definition at line 91 of file secp256k1.hpp.

◆ r_squared_wasm_2

constexpr uint64_t bb::secp256k1::FqParams::r_squared_wasm_2 = 0x0000000000000000UL
staticconstexpr

Definition at line 92 of file secp256k1.hpp.

◆ r_squared_wasm_3

constexpr uint64_t bb::secp256k1::FqParams::r_squared_wasm_3 = 0x0000000000000000UL
staticconstexpr

Definition at line 93 of file secp256k1.hpp.

◆ schema_name

constexpr char bb::secp256k1::FqParams::schema_name[] = "secp256k1_fq"
staticconstexpr

Definition at line 133 of file secp256k1.hpp.

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