The Rabin cryptosystem over number fields

TL;DR

This paper generalizes Rabin's cryptosystem to arbitrary number fields, demonstrating its security based on the difficulty of integer factorization and analyzing its performance relative to classical and Gaussian integer variants.

Contribution

It introduces a new Rabin cryptosystem over general number fields and assesses its security and efficiency compared to existing schemes.

Findings

Decryption remains as hard as integer factorization with proper modulus selection

Performance analysis shows competitive efficiency with classical Rabin and Gaussian integer schemes

The scheme extends Rabin's cryptosystem to a broader mathematical setting

Abstract

We extend Rabin's cryptosystem to general number fields. We show that decryption of a random plaintext is as hard as the integer factorisation problem, provided the modulus in our scheme has been chosen carefully. We investigate the performance of our new cryptosystem in comparison with the classical Rabin scheme and a more recent version over the Gaussian integers.