Dottorato in INFORMATICA

Titolo della tesi: Integer Sequences in Cryptography: A New Generalized Family and its Application.

Integer sequences play a pivotal role in cryptography, acting as foundational elements for numerous cryptographic algorithms. This comprehensive investigation examines integer sequences that have significantly impacted the sector in domains such as key generation, hash function design, and encryption protocol development, including their specific implementations. We conduct an unprecedented systematic review of existing literature, analysing fundamental properties of these sequences and detailing their contributions to well-established cryptographic areas. In addition, the research emphasises the various strengths and limitations associated with these sequences, as well as their practical applications in the realm of digital information security. This is accomplished by developing a categorisation framework that facilitates mapping of their contributions. Furthermore, this framework can be used as a reference point for future analyses in this field. Randomness is a key ingredient in every area of cryptography and producing it should not be left to chance. Unfortunately, it is very difficult to produce true randomness, and consuming applications often call for large, high quality amounts on boot or in quick succession. To meet this requirement, we make use of Pseudo-Random Number Generators (PRNGs) which we initialise with a small amount of randomness to produce what we hope to be high quality pseudo-random. output. In the thesis work, we have determined a new sequence generation model that is largely novel and capable of aggregating existing sequences into a single family. This model was then used for the development of a PRNG on which statistics have been performed to validate its randomness. In conclusion, this research underscores the potential for further discovery and innovative applications of integer sequences in the cryptographic field.