# snarkvm-curves [](https://crates.io/crates/snarkvm-curves) [](https://aleo.org) [](./LICENSE.md) ## Overview Aleo uses a tailored set of pairing-friendly elliptic curves to perform efficient proof generation and verification. | | Edwards BLS12 | BLS12-377 | |:------------------- |:---------------:|:------------------:| | Curve Type | Twisted Edwards | Barreto-Lynn-Scott | | Scalar Field Size | 251 bits | 253 bits | | Base Field Size | 253 bits | 377 bits | | G1 Compressed Size* | 32 bytes | 48 bytes | | G2 Compressed Size* | N/A | 96 bytes | \* rounded to multiples of 8 bytes. ## Edwards BLS12 ### Scalar Field #### Modulus ##### Integer Representation ```ignore 2111115437357092606062206234695386632838870926408408195193685246394721360383 ``` ##### Hexadecimal Representation ```ignore 04aad957a68b2955982d1347970dec005293a3afc43c8afeb95aee9ac33fd9ff ``` ##### U64 Representation (Little-Endian) ```ignore [13356249993388743167, 5950279507993463550, 10965441865914903552, 336320092672043349] ``` #### Root of Unity ##### Integer Representation ```ignore 319259817323897909850357899558356952867916286821886696195104543796545181129 ``` ##### Hexadecimal Representation ```ignore 00b4b1d4c7e5e163b1af246173fdb411bdb82ac32901dcb9d289433ff2b7d5c9 ``` ##### U64 Representation (Little-Endian) ```ignore [15170730761708361161, 13670723686578117817, 12803492266614043665, 50861023252832611] ``` ### Base Field #### Modulus ##### Integer Representation ```ignore 8444461749428370424248824938781546531375899335154063827935233455917409239041 ``` ##### Hexadecimal Representation ```ignore 12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000001 ``` ##### U64 Representation (Little-Endian) ```ignore [725501752471715841, 6461107452199829505, 6968279316240510977, 1345280370688173398] ``` #### Root of Unity ##### Integer Representation ```ignore 5928890464389279575069867463136436689218492512582288454256978381122364252082 ``` ##### Hexadecimal Representation ```ignore 0d1ba211c5cc349cd7aacc7c597248269a14cda3ec99772b3c3d3ca739381fb2 ``` ##### U64 Representation (Little-Endian) ```ignore [4340692304772210610, 11102725085307959083, 15540458298643990566, 944526744080888988] ``` ## BLS12-377 ### Scalar Field #### Modulus ##### Integer Representation ```ignore 8444461749428370424248824938781546531375899335154063827935233455917409239041 ``` ##### Hexadecimal Representation ```ignore 12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000001 ``` ##### U64 Representation (Little-Endian) ```ignore [725501752471715841, 6461107452199829505, 6968279316240510977, 1345280370688173398] ``` #### Root of Unity ##### Integer Representation ```ignore 5928890464389279575069867463136436689218492512582288454256978381122364252082 ``` ##### Hexadecimal Representation ```ignore 0d1ba211c5cc349cd7aacc7c597248269a14cda3ec99772b3c3d3ca739381fb2 ``` ##### U64 Representation (Little-Endian) ```ignore [4340692304772210610, 11102725085307959083, 15540458298643990566, 944526744080888988] ``` ### Base Field #### Modulus ##### Integer Representation ```ignore 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177 ``` ##### Hexadecimal Representation ```ignore 01ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001 ``` ##### U64 Representation (Little-Endian) ```ignore [9586122913090633729, 1660523435060625408, 2230234197602682880, 1883307231910630287, 14284016967150029115, 121098312706494698] ``` #### Root of Unity ##### Integer Representation ```ignore 146552004846884389553264564610149105174701957497228680529098805315416492923550540437026734404078567406251254115855 ``` ##### Hexadecimal Representation ```ignore 00f3c1414ef58c54f95564f4cbc1b61fee086c1fe367c33776da78169a7f3950f1bd15c3898dd1af1c104955744e6e0f ``` ##### U64 Representation (Little-Endian) ```ignore [2022196864061697551, 17419102863309525423, 8564289679875062096, 17152078065055548215, 17966377291017729567, 68610905582439508] ``` ## Contributing ### How to Update this README This README is auto-generated during continuous integration. To update this README, submit a pull request updating the appropriate Markdown file in [documentation](./documentation) and the [configuration file](./documentation/config.json).