Attacks on Low Private Exponent RSA: An Experimental Study

RSA cryptosystem is the most popular public key cryptosystem which provides both secrecy and digital signatures. Due to RSA´s popularity, many attacks on it have been developed. In this paper, we consider experimentally attacks on low private exponent RSA and find that: (i) lattice attack using Gauss lattice reduction algorithm is more effective than Wiener attack, and (ii) it is not always to recover decryption exponent even if its bit-length is less than one-quarter bit-length of the modulus. The results also raise an open question on the conditions to recover the RSA private key from public key.