An efficient and secure RSA--like cryptosystem exploiting Rédei rational functions over conics
This work addresses the need for more efficient and secure public-key cryptosystems, particularly in broadcast applications, though it appears incremental as it builds on existing RSA-like methods.
The authors tackled the problem of improving RSA-like cryptosystems by constructing a novel scheme using Rédei rational functions over conics, resulting in decryption that is two times faster than RSA and involves the lowest number of modular inversions compared to other curve-based schemes.
We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of Rédei rational functions. We then exploit the isomorphism to construct a novel RSA-like scheme. We compare our scheme with classic RSA and with RSA-like schemes based on the cubic or conic equation. The decryption operation of the proposed scheme turns to be two times faster than RSA, and involves the lowest number of modular inversions with respect to other RSA-like schemes based on curves. Our solution offers the same security as RSA in a one-to-one communication and more security in broadcast applications.