Construction of RSA Cryptosystem over the Algebraic Field Using Ideal Theory and Investigation of Its Security

Tsuyoshi Takagi, Shozo Naito

Research output: Contribution to journalArticle

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.

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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