Welcome to the resource topic for 2013/249
Title:
How to Factor N_1 and N_2 When p_1=p_2 mod 2^t
Authors: Kaoru Kurosawa, Takuma Ueda
Abstract:Let N_1=p_1q_1 and N_2=p_2q_2 be two different RSA moduli. Suppose that p_1=p_2 \bmod 2^t for some t, and q_1 and q_2 are \alpha bit primes. Then May and Ritzenhofen showed that N_1 and N_2 can be factored in quadratic time if [ t \geq 2\alpha+3. ] In this paper, we improve this lower bound on t. Namely we prove that N_1 and N_2 can be factored in quadratic time if [ t \geq 2\alpha+1. ] Further our simulation result shows that our bound is tight.
ePrint: https://eprint.iacr.org/2013/249
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