Research

  ONGOING RESEARCH PROJECTS

• REPORT ON BITCOIN MINING ( Bitcoin Observatory )
• CRYPTANALYSIS OF POST-QUANTUM DIGITAL SIGNATURES CANDIDATES AND AUTOMATED CRYPTANALYSIS OF SYMMETRIC PRIMITIVES - TII (Technology Innovation Institute) - https://tii.ae
• SCHEMI DI FIRMA DIGITALE POST-QUANTISTICA CANDIDATI AL PROCESSO DI STANDARDARDIZZAZIONE DEL NIST - Banca Intesa Sanpaolo S.p.A. - https://www.intesasanpaolo.com/
• QUBIP (Quantum-oriented Update to Browsers and Infrastructure for the PQ Transition) - Horizon Europe Framework Programme (HORIZON)
• STRIDE (Secure and TRaceable Identities in Distributed Environments) -  Partenariato Esteso PNRR - Spoke 5 del progetto Cybersecurity, nuove tecnologie e tutela dei diritti Security and Rights in the CyberSpace (SERICS) - https://serics.eu
• PROGETTO PRIN 2022: Algebraic Methods in Cryptanalysis (Politecnico di Torino, Università di Trento, Università di Milano, Università dell'Aquila e Università di Bari)
• MODELLAZIONE DI FLUSSI IN AMBITO BLOCKCHAIN - Meltatech - https://meltatech.com/

  COMPLETED RESEARCH PROJECTS

• Applicazioni della tecnologia blockchain in ambito industriale - TurinTech - http://www.turintech.it/
• Potenza di calcolo applicata alla Blockchain - PING-S - https://ping-s.it/
• La blockchain e le sue applicazioni - INWIT S.p.A. - https://www.inwit.it
• Design and cryptanalysis of post-quantum signature schemes and Automatic methods for key recovery attacks in symmetric ciphers - TII (Technology Innovation Institute) - https://tii.ae
• Mining di criptomonete - PING-S - https://ping-s.it/
• Design di piattaforme decentralizzate user-rewarding - SEA Soluzioni Eco Ambientali s.r.l. - https://www.seaeco.it
• Cryptanalysis of multivariate-based cryptosystems and Machine learning applied to cryptanalysis - TII (Technology Innovation Institute) - https://tii.ae
• Cryptanalysis of ARX ciphers - DarkMatter - https://www.darkmatter.ae
• Crittografia Post-Quantum per applicazioni cloud - Telsy SpA (TIM Group) - https://www.telsy.com/

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  RESEARCH TOPICS

CRYPTOGRAPHY AND BLOCKCHAIN 

The activities of the research group in Cryptography include:

• Public-key cryptography. RSA-like schemes based on the Pell conic. RSA schemes with multifactor and/or multiprime moduli. Discrete logarithm problem over the Pell conic.
• Post-quantum cryptography. Shor's algorithmo and Hidden Subgroup Problem. Lattice-based cryptography. Code-based cryptography. Supersingular isogeny-based cryptography. Multivariate cryptography. Design and cryptanalysis of post-quantum signature schemes.
• Cryptanalysis. Cryptanalysis of ARX ciphers. Machine learning applied to cryptanalysis. Automatic methods for key recovery attacks in symmetric ciphers.
• Pseudorandom number generators. Pseudorandom number generators and tests for the evaluation of the distribution of the generated sequences.
• Blockchain and applications. Consensus protocols. Cryptocurrency mining and staking. Traceability and supply chain. Design of decentralized user-rewarding platforms. Online dispute resolution for blockchain smart contracts. Blockchain applied to cybersecurity. Decentralized exchanges. Analysis of protocols of various cryptocurrencies. De-anonymization of ledger information with machine learning algorithms. Zero-knowledge proof algorithms applied to blockchain.

NUMBER THEORY

The activity of the research group in Number Theory is focused on the following topics, with a special attention to the possible applications in cryptography and coding theory:

• Distribution of prime numbers. Study of the distribution of prime numbers and other numbers satisfying specific arithmetic properties. Additive problems with prime numbers. Distribution of arithmetic functions and study of exceptional sets of the most known conjectures of the number theory. Primality tests and factorization algorithms.
• Linear recurrences. Study of the arithmetic properties of terms of linear recurrences of integers and other classical sequences of integers, with a special focus on prime factors and divisibility properties.
• Continued fractions and generalizations. Study of approximations and periodic representations of algebraic irrationalities by means of continued fractions and their generalizations.
• Diophantine geometry. Problems of unlikely intersections in families of abelian varieties. Integral points on algebraic varieties over number fields and function fields. Solvability of Diophantine equations in integers and polynomials.