Rabin and RSA analogues based on non-maximal imaginary quadratic orders

Abstract. In 14] and 21] there are proposed ElGamal-type cryptosystems based on non-maximal imaginary quadratic orders with fast trapdoor decryption. The trapdoor information is the factorization of the non-fundamental discriminant q = q2 . We will extend the ideas given there to set up Rabin and RSA analogues based on non-maximal imaginary quadratic orders. To implement the Rabin analogue we will introduce a new algorithm, which reduces the computation of square roots in Cl( q) to the computation of square roots in Cl( ). This is more e cient than the classical Gaussian algorithm. If the class number h( ) for = ;p, p 3 mod4 prime, is known, it is possible to extract square roots by a simple exponentiantion. In this case it is easy to set up RSA analogues as well. It will be shown, that breaking the Rabin analogue is as hard as factoring, just like the original scheme in (ZZ=nZZ ). The major advantage of our schemes compared to the original Rabin and RSA schemes is that they are immune...

• Type: Conference
• Year: 1998
• Where: ICISC
• Authors: Detlef Hühnlein, Andreas Meyer, Tsuyoshi Takagi
• Keywords: ICISC 1998, ICISC 2007, Imaginary Quadratic Orders, Rabin Analogue, Square Roots