Post-Quantum Cryptography (PQC) Archivi

SQIsign: the isogeny-based digital signature proposed to NIST

Introduction Among the digital signatures submitted in 2023 to the NIST call in the post-quantum standardization process, the only proposal based on isogenies is SQIsign (Short Quaternion Isogeny Signature). Unique...

The applications of isogenies in Post Quantum Cryptography

14 Jul

After introducing the theory of elliptic curves and defining the necessary tools, we present some classical schemes in isogeny-based cryptography. As mentioned in the previous article, this part of Post...

Post-Quantum Cryptography for Embedded Systems: Challenges and Accelerator Integration over RISC-V Architecture

28 Apr

Introduction Information security has taken an increasingly crucial and pervasive role, particularly for embedded systems, which are low-power, resource-constrained devices involved in critical applications such as automotive, IoT and industrial...

Multivariate signatures based on identification schemes

15 Feb

Introduction The goal of an identification protocol is to enable the verification of someone’s identity. More specifically, a Prover must demonstrate to an interlocutor, called the Verifier, that they...

UOV and its Variants: Digital Signatures Based on Multivariate Systems

24 Nov

In the previous exploration of multivariate cryptography, we examined how systems of polynomial equations over finite fields can form the basis for cryptographic schemes resistant to quantum computing attacks. The...

The Mathematics behind PQC: Multivariate Polynomials

14 Oct

Introduction Multivariate cryptography, along with lattice-based, code-based and hash-based cryptosystems, is one of the primary classes of cryptographic schemes resistant to quantum attacks. These schemes are based on the difficulty...

SPHINCS+: stateless hash-based digital signature

26 Aug

Introduction The Forest Of Random Subset (FORS) scheme constitutes the last element needed in order to describe the complete structure of the SPHINCS+ digital signature algorithm, selected at the end...

XMSS: hash-based stateful digital signature

01 Jul

Introduction XMSS (eXtended Merkle Signature Scheme) represents a fundamental component of the SPHINCS+’s construction, which is a post-quantum hash-based digital signature selected in the NIST standardization process. As a standalone...

The Mathematics behind PQC: hash functions

06 May

Introduction After analyzing in detail the Post Quantum algorithms that base their security on mathematical problems defined over lattices (Kyber, Dilithium, Falcon) and on error correcting codes (Classic McEliece), we...

The math behind the PQC: Syndrome Decoding Problem

11 Dec

Introduction Cryptographic schemes starring in the NIST standardization process belonging to the code-based cryptography family are constructed from a problem called the Decoding Problem. Given a code and a vector,...