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

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.