Security Analysis of an RSA Key Generation Algorithm with a Large Private Key
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 \(N^{\frac{1}{4}}\), Encinas-Masqué-Dios algorithm leaks sufficient secret information and then everyone can recover the factorization of the RSA modulus N in polynomial time.
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