Math
In questa sezione vorrei tenere un backup di qualche lavoro passato.
Tendenzialmente mi interesso a crittografia post-quantum. Nel dettaglio lavoro molto con
schemi di firma code-based, tuttavia mi piace studiare a tempo perso anche gli altri rami del settore,
ovvero reticoli, multivariate, isogenie e hash.
Number Theory
- The Bombieri-Vinogradov Theorem (Slide) - Description of the Bombieri-Vinogradov theorem, a result about the error term in the prime number theorem in arithmetic progression.
Algebra
- Corrispondenza di Galois per estensioni di grado infinito (Notes, Slide) - Descrizione di come estendere i risultati standard ottenuti da Galois al caso di estensioni di campo infinito dimensionale.
Cryptography
- Complexity Theory and Zero-Knowledge Protocols (Slide) - Description of the basic concepts of complexity theory, and how cryptography relates to them.
Post-Quantum Cryptography
- Code-Based Digital Signature Schemes: Construction, Cryptanalysis and Theoretical Foundations (Thesis) - My thesis as a PhD student in Trento.
- Notes on Isogeny-Based Crypto (Notes, Slide) - A gentle introduction on isogeny based cryptography.
- Proposal of Hash&Sign Code-Based DSA (Slide) - We built a code-based post quantum signature scheme, which takes advantage of quasi-cyclic codes to obtain compact keys, and LDPC codes to have good execution performance.
- An Improvement on Ajtai-GGH Hash Function (Slide) - Description a family of hash functions proposed in the early 2000s, based on lattices, which generalize and improve the hash functions of Ajtai-GGH.
- Latest Developments in Rainbow Cryptanalysis (Slide) - Description of the state of the art of Rainbow cryptanalysis, with particular reference to the works of Beullens published in 2022.
- Notes on Lyubashevsky Rejection Sampling (Slide) - A gentle introduction on rejection sapling with lattices.