Extension of Rabin Cryptosystem to Eisenstein and Gauss Fields

Tsuyoshi TAKAGI  Shozo NAITO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.4   pp.753-760
Publication Date: 1997/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Security
Rabin cryptosystem,  quadratic field,  Eisenstein field,  Gauss field,  factoring ,  low exponent attack,  

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We extend the Rabin cryptosystem to the Eisenstein and Gauss fields. Methods for constructing the complete representation class and modulo operation of the ideal are presented. Based on these, we describe the methods of encryption and decryption. This proposed cryptosystem is shown to be as intractable as factorization, and recently presented low exponent attacks do not work against it.