An efficient and secure RSA--like cryptosystem exploiting R\'edei rational functions over conics

摘要

We define an isomorphism between the group of points of a conic and the setof integers modulo a prime equipped with a non-standard product. This productcan be efficiently evaluated through the use of R\'edei rational functions. Wethen exploit the isomorphism to construct a novel RSA-like scheme. We compareour scheme with classic RSA and with RSA-like schemes based on the cubic orconic equation. The decryption operation of the proposed scheme turns to be twotimes faster than RSA, and involves the lowest number of modular inversionswith respect to other RSA-like schemes based on curves. Our solution offers thesame security as RSA in a one-to-one communication and more security inbroadcast applications.