On integer sequences in cryptography

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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. In conclusion, this research underscores the potential for further discovery and innovative applications of integer sequences in the cryptographic field.