PQC Archivi - Telsy

HQC: key encapsulation based on codes

Introduction In 2022, the third round conclusion of the NIST standardization process on post-quantum cryptography selected a key encapsulation mechanism (CRYSTALS-Kyber/ML-KEM), three digital signature schemes (CRYSTALS-Dilithium/ML-DSA, Falcon/FN-DSA and SPHINCS+/SLH-DSA) and opened a fourth round devoted to evaluating an additional...

SQIsign: the isogeny-based digital signature proposed to NIST

08 Sep

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...

The Mathematics behind PQC: Isogenies of Elliptic Curves

19 May

Elliptic curves cryptography After presenting the main PQC algorithms based on lattices, error correcting codes, hash functions, and multivariate systems, this article is focused on the topic of isogenies of...

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...

Classic McEliece: key encapsulation based on codes

26 Feb

Introduction At the end of the third round of the NIST standardization process, the CRYSTALS-Kyber key encapsulation method aimed at replacing the current ECDH scheme was selected. NIST then defined...

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...

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...