Extending Wiener's Extension to RSA-Like Cryptosystems over Elliptic Curves

Abstract

The studies on Wiener's attack on RSA with small deciphering exponents led to the refinement of attack bounds on the deciphering exponent in the paper \Revisiting Wiener's Attack - New Weak Keys in RSA" by Subhamoy Maitra and Santanu Sarkar. Further in the paper \ Extending The Wiener's Attack to RSA-Type Cryptosystem" by R. G. E. Pinch, it is proved that Wiener's attack on RSA Cryptosystem with small deciphering exponent may be extended to RSA-like Cryptosystems on elliptic curves. Now in this paper we show that the Wiener's extension on RSA that refines the attack bound on deciphering exponent can also be extended to RSA-like Cryptosystems on elliptic curves.