On the Use of Pedersen Commitments for Confidential Payments

The increased adoption of financial blockchains has fueled a lot of cryptography research in recent years. One area of high interest is transaction confidentiality which requires hiding investors' account balances and transaction amounts, while enforcing compliance rules and performing validity checks on all activities. This blog post will look at the Zether [2] protocol, which … Continue reading On the Use of Pedersen Commitments for Confidential Payments

Optimizing Pairing-Based Cryptography: Montgomery Arithmetic in Rust

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

Public Report – Protocol Labs Groth16 Proof Aggregation: Cryptography and Implementation Review

During April 2021, Protocol Labs engaged NCC Group’s Cryptography Services team to conduct a cryptography and implementation review of the Groth16 proof aggregation functionality in the bellperson and two other related GitHub repositories. This code utilizes inner product arguments to efficiently aggregate existing Groth16 proofs while re-using existing powers of tau ceremony transcripts. Full source … Continue reading Public Report – Protocol Labs Groth16 Proof Aggregation: Cryptography and Implementation Review

Cryptopals: Exploiting CBC Padding Oracles

This is a write-up of the classic padding oracle attack on CBC-mode block ciphers. If you've done the Cryptopals cryptography challenges, you'll remember it as challenge 17. This is a famous and elegant attack. With it, we will see how even a small data leak (in this case, the presence of a "padding oracle" - … Continue reading Cryptopals: Exploiting CBC Padding Oracles

Software Verification and Analysis Using Z3

We provide a technical introduction on how to leverage the Z3 Theorem Prover to reason about the correctness of cryptographic software, protocols and otherwise, and to identify potential security vulnerabilities. We cover two distinct use cases: modeling and analysis of an algorithm documented in an old version of the QUIC Transport protocol IETF draft; modeling of specific finite field arithmetic operations for elliptic curve cryptography, with integers represented using a uniform saturated limb schedule, to prove equivalence with arbitrary-precision arithmetic, and for test cases generation.

Real World Cryptography Conference 2021: A Virtual Experience

Earlier this month, our Cryptography Services team got together and attended (virtually) the IACR's annual Real World Cryptography (RWC) conference. RWC is a fantastic venue for the latest results in real world cryptography from industry and academia. Holding this conference virtually inevitably introduced some changes: to accommodate as many time zones as possible, the daily … Continue reading Real World Cryptography Conference 2021: A Virtual Experience

Public Report – BLST Cryptographic Implementation Review

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

Double-odd Elliptic Curves

This post is about some new (or sort of new) elliptic curves for use in cryptographic protocols. They were made public in mid-December 2020, on a dedicated Web site: https://doubleodd.group/There is also a complete whitepaper, full of mathematical demonstrations, and several implementations. Oh noes, more curves! Will this never end? It is true that there … Continue reading Double-odd Elliptic Curves

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

Faster Modular Inversion and Legendre Symbol, and an X25519 Speed Record

Elliptic curves are commonly used to implement asymmetric cryptographic operations such as key exchange and signatures. These operations are used in many places, in particular to initiate secure network connections within protocols such as TLS and Noise. However, they are relatively expensive in terms of computing resources, especially for low-end embedded systems, which run on … Continue reading Faster Modular Inversion and Legendre Symbol, and an X25519 Speed Record