Deterministic Polynomial Time Equivalence between Factoring and Key-Recovery Attack on Takagi's RSA

Noboru KUNIHIRO  Kaoru KUROSAWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.9   pp.2356-2364
Publication Date: 2008/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.9.2356
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
RSA,  factoring,  LLL algorithm,  

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Summary: 
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.