Catalogo dei prodotti della ricerca

Integer Sequences in Cryptography: A New Generalized Family and its Application

RASO, MARIO

15/01/2025

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Abstract

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. As a result, our initial emphasis was on the thorough investigation and conceptualisation of a novel integer sequence generation model. This model holds the potential to be remarkably unique, capable of unifying and encompassing both existing integer sequences and those yet to be discovered into a cohesive and comprehensive framework. Following this foundational work, our attention shifted to analysing the prospective applications of this model, particularly within the field of cryptography. Here, we honed in on the intricate concept of randomness, delving into a detailed analysis of its potential significance and the various implications it may hold for advancing cryptographic techniques and security protocols. 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. Therefore, our model has been instrumental in the design of a PRNG which has exhibited statistically significant capabilities, as well as satisfactory performance metrics, to corroborate its inherent randomness properties. In summary, this study emphasises the considerable potential that exists for the ongoing exploration and development of novel applications involving integer sequences within the domain of cryptography. The findings suggest that these sequences could play a pivotal role in enhancing and advancing cryptographic methodologies, opening avenues for new innovations and improvements.