Factoring RSA modulo N with high bits of p known revisited

The factorization problem with knowledge of some bits of prime factor p of RSA modulo N is one of the earliest partial key exposure attacks on RSA. The result proposed by Coppersmith is still the best, i.e., when some of p´s higher bits is known as ptilde, assume the unknown part of p and q is p₀ and q₀, respectively (say, p = ptilde + p₀, q = + qtilde + q₀), if the upper bounds of them, say X and Y separately, satisfy XY les N^0.5, then N can be factored in polynomial time. Our method shows improved bounds that when RSA private key d < N^0.483, knowing a smaller fraction of p is sufficient in yielding the factorization of N in polynomial time.