Deterministic polynomial time equivalence between factoring and key-recovery attack on Takagi's RSA

Abstract

For RSA, May showed a deterministic polynomial time equivalence of computing d to factoring N(= pq). On the other hand, Takagi showed a variant of RSA such that the decryption algorithm is faster than the standard RSA, where N = prq while ed = 1 mod (p- 1)(q -1). In this paper, we show that a deterministic polynomial time equivalence also holds in this variant. The coefficient matrix T to which LLL algorithm is applied is no longer lower triangular, and hence we develop a new technique to overcome this problem. © International Association for Cryptologic Research 2007.