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 = pr q 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.

• Type: Conference
• Year: 2007
• Where: PKC
• Authors: Noboru Kunihiro, Kaoru Kurosawa
• Keywords: Cryptography, Deterministic Polynomial Time, PKC 2007, Polynomial Time Equivalence, Standard Rsa