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  central to Ethereum 2.0, zero-knowledge arguments central to Zcash and Filecoin , 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
In October 2020, Supranational, Protocol Labs and the Ethereum Foundation engaged NCC Group’s Cryptography Services team to conduct a cryptographic implementation review of the BLST library. This library implements support for the draft IETF specifications on Hashing to Elliptic Curves and BLS Signatures. The latter specification uses advanced cryptographic-pairing operations to feature aggregation properties for … Continue reading Public Report – BLST Cryptographic Implementation Review
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 , and support for a related pairing configuration in precompiled contracts is already in operation [2, 3]. The first post  covered modular arithmetic, finite fields, the embedding degree, and … Continue reading Pairing over BLS12-381, Part 3: Pairing!
This is the second of three code-centric blog posts on pairing based cryptography. The first post  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
Ethereum, a popular cryptocurrency, utilizes a P2P flood network overlay protocol in order to propagate new transactions and state around the network. As has been shown in previous works[^1][^2], observing the propagation of transactions through the peer-to-peer network layer is often enough to deanonymize users of cryptocurrency networks....