This is the first blog post in a new code-centric series about selected optimizations found in pairing-based cryptography. Pairing operations are foundational to the BLS Signatures [1] central to Ethereum 2.0, zero-knowledge arguments central to Zcash and Filecoin [2], and a wide variety of other emerging applications. A prior blog series implemented the entire pairing … Continue reading Optimizing Pairing-Based Cryptography: Montgomery Arithmetic in Rust
Tag: pairing based cryptography
Public Report – Filecoin Bellman and BLS Signatures Cryptographic Review
In May 2020, Protocol Labs engaged NCC Group's Cryptography Services team to conduct a cryptography review of multiple Filecoin code repositories. Filecoin is a decentralized storage and content distribution network developed by Protocol Labs. These repositories implement finite field and group arithmetic, cryptographic pairings, SHA2 via intrinsics, BLS signatures and zk-SNARK operations. Taken together, these … Continue reading Public Report – Filecoin Bellman and BLS Signatures Cryptographic Review
Pairing over BLS12-381, Part 3: Pairing!
This is the last of three code-centric blog posts on pairing based cryptography. Support for these operations in an Ethereum precompiled contract has been proposed [1], and support for a related pairing configuration in precompiled contracts is already in operation [2, 3]. The first post [4] covered modular arithmetic, finite fields, the embedding degree, and … Continue reading Pairing over BLS12-381, Part 3: Pairing!
Pairing over BLS12-381, Part 2: Curves
This is the second of three code-centric blog posts on pairing based cryptography. The first post [1] covered modular arithmetic, finite fields, the embedding degree, and presented an implementation of a 12-degree prime extension field tower. The series will ultimately conclude with a detailed review of the popular BLS12-381 pairing operations found in a variety … Continue reading Pairing over BLS12-381, Part 2: Curves
Pairing over BLS12-381, Part 1: Fields
This is the first of three code-centric blog posts on pairing based cryptography. The series will ultimately conclude with a detailed review of the popular BLS12-381 pairing operations found in a variety of applications such as BLS signatures [1]. Support for these operations in an Ethereum precompiled contract has been proposed [2], and support for … Continue reading Pairing over BLS12-381, Part 1: Fields