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.
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