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**/*.rs.bk
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Copyrights in the "bls12_381" library are retained by their contributors. No
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The "bls12_381" library is licensed under either of
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* Apache License, Version 2.0, (see ./LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
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* MIT license (see ./LICENSE-MIT or http://opensource.org/licenses/MIT)
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@ -0,0 +1,24 @@
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[package]
|
||||||
|
authors = ["Sean Bowe <ewillbefull@gmail.com>"]
|
||||||
|
description = "Implementation of the BLS12-381 pairing-friendly elliptic curve construction"
|
||||||
|
documentation = "https://docs.rs/bls12_381/"
|
||||||
|
homepage = "https://github.com/zkcrypto/bls12_381"
|
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|
license = "MIT/Apache-2.0"
|
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|
name = "bls12_381"
|
||||||
|
repository = "https://github.com/zkcrypto/bls12_381"
|
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|
version = "0.0.0"
|
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|
edition = "2018"
|
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|
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|
[dependencies.subtle]
|
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|
version = "2.1"
|
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|
default-features = false
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[dependencies.byteorder]
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[features]
|
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|
default = ["groups", "pairings"]
|
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|
groups = []
|
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|
pairings = []
|
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|
nightly = ["subtle/nightly"]
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# bls12_381 [![Crates.io](https://img.shields.io/crates/v/bls12_381.svg)](https://crates.io/crates/bls12_381) #
|
||||||
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|
||||||
|
This crate provides an implementation of the BLS12-381 pairing-friendly elliptic curve construction.
|
||||||
|
|
||||||
|
* **This implementation has not been reviewed or audited. Use at your own risk.**
|
||||||
|
* This implementation targets Rust `1.36` or later.
|
||||||
|
* This implementation does not require the Rust standard library.
|
||||||
|
* All operations are constant time unless explicitly noted.
|
||||||
|
|
||||||
|
## Features
|
||||||
|
|
||||||
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* `groups` (on by default): Enables APIs for performing group arithmetic with G1, G2, and GT.
|
||||||
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* `pairings` (on by default): Enables APIs for performing pairings. This depends on the `alloc` crate.
|
||||||
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* `nightly`: Enables `subtle/nightly` which prevents compiler optimizations that could jeopardize constant time operations.
|
||||||
|
|
||||||
|
## [Documentation](https://docs.rs/bls12_381)
|
||||||
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|
||||||
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## Curve Description
|
||||||
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|
||||||
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BLS12-381 is a pairing-friendly elliptic curve construction from the [BLS family](https://eprint.iacr.org/2002/088), with embedding degree 12. It is built over a 381-bit prime field `GF(p)` with...
|
||||||
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||||||
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* z = `-0xd201000000010000`
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||||||
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* p = (z - 1)<sup>2</sup> ((z<sup>4</sup> - z<sup>2</sup> + 1) / 3) + z
|
||||||
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* = `0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab`
|
||||||
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* q = z<sup>4</sup> - z<sup>2</sup> + 1
|
||||||
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* = `0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001`
|
||||||
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|
||||||
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... yielding two **source groups** G<sub>1</sub> and G<sub>2</sub>, each of 255-bit prime order `q`, such that an efficiently computable non-degenerate bilinear pairing function `e` exists into a third **target group** G<sub>T</sub>. Specifically, G<sub>1</sub> is the `q`-order subgroup of E(F<sub>p</sub>) : y^2 = x^3 + 4 and G<sub>2</sub> is the `q`-order subgroup of E'(F<sub>p<sup>2</sup></sub>) : y<sup>2</sup> = x<sup>3</sup> + 4(u + 1) where the extention field F<sub>p<sup>2</sup></sub> is defined as F<sub>p</sub>(u) / (u<sup>2</sup> + 1).
|
||||||
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|
||||||
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BLS12-381 is chosen so that `z` has small Hamming weight (to improve pairing performance) and also so that `GF(q)` has a large 2<sup>32</sup> primitive root of unity for performing radix-2 fast Fourier transforms for efficient multi-point evaluation and interpolation. It is also chosen so that it exists in a particularly efficient and rigid subfamily of BLS12 curves.
|
||||||
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|
||||||
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### Curve Security
|
||||||
|
|
||||||
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Pairing-friendly elliptic curve constructions are (necessarily) less secure than conventional elliptic curves due to their small "embedding degree". Given a small enough embedding degree, the pairing function itself would allow for a break in DLP hardness if it projected into a weak target group, as weaknesses in this target group are immediately translated into weaknesses in the source group.
|
||||||
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|
||||||
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In order to achieve reasonable security without an unreasonably expensive pairing function, a careful choice of embedding degree, base field characteristic and prime subgroup order must be made. BLS12-381 uses an embedding degree of 12 to ensure fast pairing performance but a choice of a 381-bit base field characteristic to yeild a 255-bit subgroup order (for protection against [Pollard's rho algorithm](https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm)) while reaching close to a 128-bit security level.
|
||||||
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|
||||||
|
There are [known optimizations](https://ellipticnews.wordpress.com/2016/05/02/kim-barbulescu-variant-of-the-number-field-sieve-to-compute-discrete-logarithms-in-finite-fields/) of the [Number Field Sieve algorithm](https://en.wikipedia.org/wiki/General_number_field_sieve) which could be used to weaken DLP security in the target group by taking advantage of its structure, as it is a multiplicative subgroup of a low-degree extension field. However, these attacks require an (as of yet unknown) efficient algorithm for scanning a large space of polynomials. Even if the attack were practical it would only reduce security to roughly 117 to 120 bits. (This contrasts with 254-bit BN curves which usually have less than 100 bits of security in the same situation.)
|
||||||
|
|
||||||
|
### Alternative Curves
|
||||||
|
|
||||||
|
Applications may wish to exchange pairing performance and/or G<sub>2</sub> performance by using BLS24 or KSS16 curves which conservatively target 128-bit security. In applications that need cycles of elliptic curves for e.g. arbitrary proof composition, MNT6/MNT4 curve cycles are known that target the 128-bit security level. In applications that only need fixed-depth proof composition, curves of this form have been constructed as part of ZEXE.
|
||||||
|
|
||||||
|
## Acknowledgements
|
||||||
|
|
||||||
|
Please see `Cargo.toml` for a list of primary authors of this codebase.
|
||||||
|
|
||||||
|
## License
|
||||||
|
|
||||||
|
Licensed under either of
|
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|
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|
* Apache License, Version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
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|
* MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
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at your option.
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### Contribution
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|
|
||||||
|
Unless you explicitly state otherwise, any contribution intentionally
|
||||||
|
submitted for inclusion in the work by you, as defined in the Apache-2.0
|
||||||
|
license, shall be dual licensed as above, without any additional terms or
|
||||||
|
conditions.
|
|
@ -0,0 +1 @@
|
||||||
|
1.36.0
|
|
@ -0,0 +1,20 @@
|
||||||
|
//! # `bls12_381`
|
||||||
|
//!
|
||||||
|
//! This crate provides an implementation of the BLS12-381 pairing-friendly elliptic
|
||||||
|
//! curve construction.
|
||||||
|
//!
|
||||||
|
//! * **This implementation has not been reviewed or audited. Use at your own risk.**
|
||||||
|
//! * This implementation targets Rust `1.36` or later.
|
||||||
|
//! * This implementation does not require the Rust standard library.
|
||||||
|
//! * All operations are constant time unless explicitly noted.
|
||||||
|
|
||||||
|
#![no_std]
|
||||||
|
#![deny(missing_debug_implementations)]
|
||||||
|
#![deny(missing_docs)]
|
||||||
|
#![deny(unsafe_code)]
|
||||||
|
|
||||||
|
#[cfg(feature = "pairings")]
|
||||||
|
extern crate alloc;
|
||||||
|
|
||||||
|
#[cfg(test)]
|
||||||
|
extern crate std;
|
Loading…
Reference in New Issue