An Adaptation of the NICE Cryptosystem to Real Quadratic Orders

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.

• Type: Conference
• Year: 2008
• Where: AFRICACRYPT
• Authors: Michael J. Jacobson Jr., Renate Scheidler, Daniel Weimer
• Keywords: AFRICACRYPT 2008, Cryptology, Imaginary Quadratic Number, Public Key Cryptosystem, Real Quadratic fields