Security analysis of an RSA key generation algorithm with a large private key

Authors:
Fanyu Kong;Jia Yu;Lei Wu
Affiliations:
Institute of Network Security, Shandong University and Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Jinan, China;College of Information Engineering, Qingdao University, Qingdao, China;School of Information Science and Engineering, Shandong Normal University, Jinan, China
Venue:
ISC'11 Proceedings of the 14th international conference on Information security
Year:
2011

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Abstract

In 2003, L. H. Encinas, J. M. Masqué and A. Q. Dios proposed an algorithm for generating the RSA modulus N with a large private key d, which was claimed secure. In this paper, we propose an attack on Encinas-Masqué-Dios algorithm and find its security flaw. Firstly, we prove that Encinas-Masqué-Dios algorithm is totally insecure when the public exponent e is larger than the sum of the two primes p and q. Secondly, we show that when e is larger than N1/4, Encinas-Masqué-Dios algorithm leaks sufficient secret information and then everyone can recover the factorization of the RSA modulus N in polynomial time.