TY - GEN

T1 - A simple and improved algorithm for integer factorization with implicit hints

AU - Nuida, Koji

AU - Itakura, Naoto

AU - Kurosawa, Kaoru

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - Given two integers N1 = p1q1 and N2 = p2q2 with α-bit primes q1, q2, suppose that the t least significant bits of p1 and p2 are equal. May and Ritzenhofen (PKC 2009) developed a factoring algorithm for N1,N2 when t ≥ 2α+3; Kurosawa and Ueda (IWSEC 2013) improved the bound to t ≥ 2α + 1. In this paper, we propose a polynomial-time algorithm in a parameter κ, with an improved bound t = 2α−O(log κ); it is the first non-constant improvement of the bound. Both the construction and the proof of our algorithm are very simple; the worst-case complexity of our algorithm is evaluated by an easy argument. We also give some computer experimental results showing the efficiency of our algorithm for concrete parameters, and discuss potential applications of our result to security evaluations of existing factoring-based primitives.

AB - Given two integers N1 = p1q1 and N2 = p2q2 with α-bit primes q1, q2, suppose that the t least significant bits of p1 and p2 are equal. May and Ritzenhofen (PKC 2009) developed a factoring algorithm for N1,N2 when t ≥ 2α+3; Kurosawa and Ueda (IWSEC 2013) improved the bound to t ≥ 2α + 1. In this paper, we propose a polynomial-time algorithm in a parameter κ, with an improved bound t = 2α−O(log κ); it is the first non-constant improvement of the bound. Both the construction and the proof of our algorithm are very simple; the worst-case complexity of our algorithm is evaluated by an easy argument. We also give some computer experimental results showing the efficiency of our algorithm for concrete parameters, and discuss potential applications of our result to security evaluations of existing factoring-based primitives.

UR - http://www.scopus.com/inward/record.url?scp=84930466967&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84930466967&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-16715-2_14

DO - 10.1007/978-3-319-16715-2_14

M3 - Conference contribution

AN - SCOPUS:84930466967

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 258

EP - 269

BT - Topics in Cryptology - CT-RSA 2015 - The Cryptographers’ Track at the RSA Conference 2015, Proceedings

A2 - Nyberg, Kaisa

PB - Springer Verlag

T2 - RSA Conference Cryptographers’ Track, CT-RSA 2015

Y2 - 21 April 2015 through 24 April 2015

ER -