A multifactor RSA-like scheme with fast decryption based on R\'edei rational functions over the Pell hyperbola

TL;DR

This paper introduces a generalized RSA-like cryptosystem using R"edei rational functions over the Pell hyperbola, enabling faster decryption with multi-factor moduli while maintaining security and efficiency advantages over existing schemes.

Contribution

It presents a novel multi-factor modulus scheme based on R"edei functions, improving decryption speed and security compared to traditional RSA and elliptic curve schemes.

Findings

Decryption is quadratically faster with multiple primes.

The scheme offers better security at high levels.

It outperforms elliptic curve-based schemes in efficiency.

Abstract

We propose a generalization of an RSA-like scheme based on R\'edei rational functions over the Pell hyperbola. Instead of a modulus which is a product of two primes, we define the scheme on a multi-factor modulus, i.e. on a product of more than two primes. This results in a scheme with a decryption which is quadratically faster, in the number of primes factoring the modulus, than the original RSA, while preserving a better security. The scheme reaches its best efficiency advantage over RSA for high security levels, since in these cases the modulus can contain more primes. Compared to the analog schemes based on elliptic curves, as the KMOV cryptosystem, the proposed scheme is more efficient. Furthermore a variation of the scheme with larger ciphertext size does not suffer of impossible group operation attacks, as it happens for schemes based on elliptic curves.