RSA cryptosystem for rings with commuting ideals
Marat Nasrutdinov, Serge Tronin (Lobachevskii Institute of Mathematics, and Mechanics, Kazan (Volga Region) Federal University)
TL;DR
This paper generalizes the RSA cryptosystem to rings with commuting ideals by defining analogues of Euler's function and RSA-ideals, enabling cryptographic schemes in this algebraic setting.
Contribution
It introduces a novel generalization of RSA for rings with commuting ideals, including new definitions and conditions for RSA-ideals.
Findings
Defined an analogue of Euler's function for ideals
Formulated an RSA-like cryptosystem for rings with commuting ideals
Characterized RSA-ideals suitable for this cryptosystem
Abstract
This article presents a generalization of the RSA cryptosystem for rings with commuting ideals. An analogue of the Euler function for ideals and the concept of an RSA-ideal are defined. An analog of a cryptosystem for the ring with commuting ideals is formulated and a description of the RSA-ideals for which this is possible is obtained.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Coding theory and cryptography · Chaos-based Image/Signal Encryption