CryptoDB
Deterministic Polynomial-Time Equivalence of Computing the CRT-RSA Secret Keys and Factoring
Authors: | |
---|---|
Download: | |
Abstract: | Let $N = pq$ be the product of two large primes. Consider CRT-RSA with the public encryption exponent $e$ and private decryption exponents $d_p, d_q$. It is well known that given any one of $d_p$ or $d_q$ (or both) one can factorize $N$ in probabilistic poly$(\log N)$ time with success probability almost equal to 1. Though this serves all the practical purposes, from theoretical point of view, this is not a deterministic polynomial time algorithm. In this paper, we present a lattice based deterministic poly$(\log N)$ time algorithm that uses both $d_p, d_q$ (in addition to the public information $e, N$) to factorize $N$. |
BibTeX
@misc{eprint-2009-18254, title={Deterministic Polynomial-Time Equivalence of Computing the CRT-RSA Secret Keys and Factoring}, booktitle={IACR Eprint archive}, keywords={public-key cryptography / CRT-RSA, Cryptanalysis, Factorization, LLL Algorithm, RSA.}, url={http://eprint.iacr.org/2009/062}, note={ subho@isical.ac.in 14286 received 6 Feb 2009, last revised 10 Feb 2009}, author={Subhamoy Maitra and Santanu Sarkar}, year=2009 }