ML-DSA: standardizirana post-kvantna podpisna shema

Jozić, Katarina (author), Žitnik, Arjana (mentor)

Podpisna shema ML-DSA je eden izmed prvih post-kvantnih kriptografskih algoritmov, standardiziranih s strani ameriškega instituta NIST. Gre za podpisno shemo, ki temelji na problemih na rešetkah. V tem diplomskem delu najprej predstavimo zgoščevalne funkcije in njihovo vlogo v podpisnih shemah. Nato definiramo digitalni podpis oziroma podpisno shemo, opišemo potek uporabe podpisne sheme in definiramo, kaj pomeni, da je podpis varen. Predstavimo probleme na rešetkah, na katerih sloni varnosti podpisne sheme ML-DSA in sicer problem učenja z napakami na modulu, problem iskanja kratkih celoštevilskih rešitev na modulu in problem SelfTargetMSIS. Opišemo tudi interaktivni protokol, iz katerega izhaja sama ideja digitalnega podpisa ML-DSA in vse tri glavne algoritme, ki so vključeni v shemo. Na koncu obravnavamo še varnost podpisne sheme ML-DSA in naredimo pregled vseh različic podpisne sheme, ki so vključene v standard FIPS 204.

• Language: Slovenian
• Keywords: digitalni podpis, postkvantna kriptografija, problemi na rešetkah
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2025
• PID: 20.500.12556/RUL-170523
• COBISS.SI-ID: 243152387
• Publication date in RUL: 08.07.2025

Secondary language

• Language: English
• Title: ML-DSA: a post-quantum cryptography digital signature standard

Abstract

The ML-DSA signature sheme is one of the first post-quantum cryptographic algorithms standardized by NIST. It is a signature scheme based on lattice problems. In this thesis we first introduce hash functions and their role in signature schemes. Next, we define digital signatures, describe how a signature scheme is used, and define what it means for a signature to be secure. We present the lattice problems on which the security of the ML-DSA signature scheme is based: the Module learning with errors problem, the Module short integer solution problem and the SelfTargetMSIS problem. We describe the interactive protocol, from which the idea of the ML-DSA originates, along with all three main algorithms involved in the signature scheme. At the end, we discuss the security of the ML-DSA signature scheme and provide an overview of all of its variants included in the FIPS 204 standard.

• Keywords: digital signature, post-quantum cryptography, lattice problem