In 2000, Boneh-Durfee extended the bound for low private exponent from 0.25 (provided by wiener) to 0.292 with public exponent size is same as modulus size. They have used powerful lattice reduction algorithm (LLL) with coppersmith's theory of polynomials. In this paper we generalize their attack to arbitrary public exponent.

Lattice basis reduction algorithms have contributed a lot to cryptanalysis of RSA crypto system. With coppersmith's theory of polynomials, these algorithms are searching for the weak instances of Number-theoretic cryptography, mainly RSA. In this paper we present several lattice based attacks on low private exponent of RSA.