Post-Quantum Cryptography (PQC) Archivi

UOV and its Variants: Digital Signatures Based on Multivariate Systems

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,...

The mathematics behind PQC: the codes

03 Nov

Introduction In addition to lattices, the foundation of lattice-based cryptography, another mathematical structure used to construct post-quantum cryptography schemes is error-correcting codes, more briefly codes. The codes originated in the...

The Math Behind PQC: Learning With Errors

27 Mar

Introduction Some of the winning cryptographic schemes in the NIST standardization process belonging to the latex-based cryptography family are constructed from a problem called Learning With Errors (LWE). Given a...

The mathematics behind PQC: lattices

15 Feb

Introduction A large number of post-quantum cryptography schemes are built on a mathematical structure called “lattice“, on which hard-to-solve problems can be defined even for a quantum computer. Cryptosystems belonging...

Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC)

14 Nov

Today the quantum attacks threat is a real danger. The protection of data and communications is linked to technologies that give future-proof answers, capable of thwarting threats with still partially...