Construction of RSA cryptosystem over the algebraic field using ideal theory and investigation of its security

Abstract

The RSA cryptosystem is extended to the algebraic field by using ideal theory. In this paper, we describe the generation algorithm of prime ideals, how to select a representative class using an ideal as modulus, and the algorithm to compute a representative element, for cyclotomic fields and quadratic fields. From here, an RSA cryptosystem can be constructed on cyclotomic fields and quadratic fields. To break completely the proposed cryptosystem, when the public key is a product of inert prime numbers, is the same as for the conventional RSA cryptosystem and its security is better against the Håstad attacks. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(8): 19–29, 2000