package octez-libs
A package that contains multiple base libraries used by the Octez suite
Install
Dune Dependency
Authors
Maintainers
Sources
tezos-18.1.tar.gz
sha256=aa2f5bc99cc4ca2217c52a1af2a2cdfd3b383208cb859ca2e79ca0903396ca1d
sha512=d68bb3eb615e3dcccc845fddfc9901c95b3c6dc8e105e39522ce97637b1308a7fa7aa1d271351d5933febd7476b2819e1694f31198f1f0919681f1f9cc97cb3a
doc/src/octez-libs.mec/bls12_381_ref.ml.html
Source file bls12_381_ref.ml
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225(** The equation of G1 is x^3 + 4 = y^2 *) module Fq = Ff.MakeFp (struct let prime_order = (* 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787 in decimal *) Z.of_string "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab" end) module Fp = Ff.MakeFp (struct let prime_order = Z.of_string "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001" end) module G1 = struct module Projective = Ec.MakeProjectiveWeierstrass (Fq) (Fp) (struct let a = Fq.zero let b = Fq.of_string "4" (* See https://github.com/zkcrypto/bls12_381/blob/main/src/notes/design.rs The value has been obtained by running the following code in SAGE ``` def g1_h(x): return ((x-1)**2) // 3 param = -0xd201000000010000 g1_h(param) ``` *) let cofactor = Z.of_string "76329603384216526031706109802092473003" (* https://github.com/zkcrypto/bls12_381/blob/main/src/g1.rs#L572 ``` x: Fp::from_raw_unchecked([ 0x5cb3_8790_fd53_0c16, 0x7817_fc67_9976_fff5, 0x154f_95c7_143b_a1c1, 0xf0ae_6acd_f3d0_e747, 0xedce_6ecc_21db_f440, 0x1201_7741_9e0b_fb75, ]), y: Fp::from_raw_unchecked([ 0xbaac_93d5_0ce7_2271, 0x8c22_631a_7918_fd8e, 0xdd59_5f13_5707_25ce, 0x51ac_5829_5040_5194, 0x0e1c_8c3f_ad00_59c0, 0x0bbc_3efc_5008_a26a, ]), z: Fp::one(), ``` Using decimal representation, computed using ``` Z.(to_string (of_string "0x...")) ``` *) let bytes_generator = Bytes.concat Bytes.empty [ Fq.( to_bytes (of_string "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507")); Fq.( to_bytes (of_string "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569")); Fq.(to_bytes one); ] end) module Affine = Ec.MakeAffineWeierstrass (Fq) (Fp) (struct let a = Fq.zero let b = Fq.of_string "4" (* See https://github.com/zkcrypto/bls12_381/blob/main/src/notes/design.rs The value has been obtained by running the following code in SAGE ``` def g1_h(x): return ((x-1)**2) // 3 param = -0xd201000000010000 g1_h(param) ``` *) let cofactor = Z.of_string "76329603384216526031706109802092473003" (* https://github.com/zkcrypto/bls12_381/blob/main/src/g1.rs#L572 ``` x: Fp::from_raw_unchecked([ 0x5cb3_8790_fd53_0c16, 0x7817_fc67_9976_fff5, 0x154f_95c7_143b_a1c1, 0xf0ae_6acd_f3d0_e747, 0xedce_6ecc_21db_f440, 0x1201_7741_9e0b_fb75, ]), y: Fp::from_raw_unchecked([ 0xbaac_93d5_0ce7_2271, 0x8c22_631a_7918_fd8e, 0xdd59_5f13_5707_25ce, 0x51ac_5829_5040_5194, 0x0e1c_8c3f_ad00_59c0, 0x0bbc_3efc_5008_a26a, ]), ``` Using decimal representation, computed using ``` Z.(to_string (of_string "0x...")) ``` *) let bytes_generator = Bytes.concat Bytes.empty [ Fq.( to_bytes (of_string "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507")); Fq.( to_bytes (of_string "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569")); ] end) end module Fq2 = Ff.MakeFp2 (Fq) (struct let nsr = Fq.of_string "4" end) (* TODO: require to implement sqrt_opt for Fq2. Not yet available in ocaml-ff *) (* module G2 = struct * module Projective = * Ec.MakeProjectiveWeierstrass (Fq2) (Fp) * (struct * let a = Fq2.zero * * let b = Fq2.of_string "4" * * let cofactor = * Z.of_string_base * 16 * "5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5" * * (\* * https://github.com/zkcrypto/bls12_381/blob/main/src/g1.rs#L572 * ``` * x: Fp::from_raw_unchecked([ * 0x5cb3_8790_fd53_0c16, * 0x7817_fc67_9976_fff5, * 0x154f_95c7_143b_a1c1, * 0xf0ae_6acd_f3d0_e747, * 0xedce_6ecc_21db_f440, * 0x1201_7741_9e0b_fb75, * ]), * y: Fp::from_raw_unchecked([ * 0xbaac_93d5_0ce7_2271, * 0x8c22_631a_7918_fd8e, * 0xdd59_5f13_5707_25ce, * 0x51ac_5829_5040_5194, * 0x0e1c_8c3f_ad00_59c0, * 0x0bbc_3efc_5008_a26a, * ]), * z: Fp::one(), * ``` * Using decimal representation, computed using * ``` * Z.(to_string (of_string "0x...")) * ``` * *\) * let bytes_generator = * Bytes.concat * Bytes.empty * [ Fq.( * to_bytes * (of_string * "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507")); * Fq.( * to_bytes * (of_string * "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569")); * Fq.(to_bytes one) ] * end) * * module Affine = * Ec.MakeAffineWeierstrass (Fq2) (Fp) * (struct * let a = Fq2.zero * * let b = Fq2.of_string "4" * * let cofactor = * Z.of_string_base * 16 * "5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5" * * let bytes_generator = * Bytes.concat * Bytes.empty * [ Fq.( * to_bytes * (of_string * "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507")); * Fq.( * to_bytes * (of_string * "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569")) * ] * end) * end *)