Abstract. In 2000, Paulus and Takagi introduced a public key cryptosystem called NICE that exploits the relationship between maximal and non-maximal orders in imaginary quadratic number fields. Relying on the intractability of integer factorization, NICE provides a similar level of security as RSA, but has faster decryption. This paper presents REAL-NICE, an adaptation of NICE to orders in real quadratic fields. REAL-NICE supports smaller public keys than NICE, and while preliminary computations suggest that it is somewhat slower than NICE, it still significantly outperforms RSA in decryption.
Michael J. Jacobson Jr., Renate Scheidler, Daniel