Cryptanalysis of large RSA exponent by using the LLL algorithm

The study of paper “Cryptanalysis of RSA with Private Key d less than N0.292' [IEEE Trans. Information Theory, 46 (2000) 1339], which Boneh and Durfee published in IEEE Transactions on Information Theory in July 2000, supported that when d < N0.292, the RSA system can be cracked by using the LLL algorithm. In this paper, we find ways to utilize the LLL algorithm to break the RSA system even when the value of d is large. According to the proposed cryptanalysis, if d satisfies ∣λ − d∣ < N0.25, the RSA system will be possible to be resolved computationally.