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During the Autumn of 2023, Google engaged NCC Group to conduct a security assessment of the white paper entitled “RSA Blind Signatures with Public Metadata”, along with the corresponding IETF draft for “Partially Blind RSA Signatures”. The work is inspired by the growing importance of anonymous tokens for the privacy of real-world applications. In particular, […]

This post is about a rather technical coding strategy choice that arises when implementing cryptographic algorithms on some elliptic curves, namely how to represent elements of the base field. We will be discussing Curve25519 implementations, in particular as part of Ed25519 signatures, as specified in RFC 8032. The most widely used Rust implementation of these […]

First things first: there is now a specification for the jq255e and jq255s elliptic curves; it is published on the C2SP initiative and is formally in (draft) version 0.0.1: https://github.com/C2SP/C2SP/blob/main/jq255.md The jq255e and jq255s groups are prime-order groups appropriate for building cryptographic protocols, and based on elliptic curves. These curves are from the large class […]

Last week, NIST announced some algorithms selected for standardization as part of their Post-Quantum Cryptography project. This is a good opportunity to recall the history of this process, observe its current state, and comment on the selected algorithms. It is important to remember that the process is not finished: round 4 has started, and should […]

In this post we present a newly published key encapsulation mechanism (KEM) called BAT. It is a post-quantum algorithm, using NTRU lattices, and its main advantages are that it is both small and fast. The paper was accepted by TCHES (it should appear in volume 2022, issue 2) and is also available on ePrint: https://eprint.iacr.org/2022/031 […]

We present here a new construction which has no real immediate usefulness, but is a good illustration of a fundamental concept of cryptography, namely that there is a great difference between knowing that some mathematical object exists, and being able to build it in practice. Thus, this construction can be thought of as having some […]

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 […]

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 […]

This post is about elliptic curves as they are used in cryptography, in particular for signatures. There are many ways to define specific elliptic curves that strive to offer a good balance between security and performance; here, I am talking about specific contributions of mine: a new curve definition, and some algorithmic improvements that target […]

I have been asked about the usefulness of security monitoring of entropy levels in the Linux kernel. This calls for some explanation of how random generation works in Linux systems. So, randomness and the Linux kernel. This is an area where there is longstanding confusion, notably among some Linux kernel developers, including Linus Torvalds himself. […]