By Topic

Approximate Integer Common Divisor Problem Relates to Implicit Factorization

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Santanu Sarkar ; Applied Statistics Unit, Indian Statistical Institute, Calcutta, India ; Subhamoy Maitra

In this paper, we analyze how to calculate the GCD of k ( ≥ 2) many large integers, given their approximations. This problem is known as the approximate integer common divisor problem in literature. Two versions of the problem, presented by Howgrave-Graham in CaLC 2001, turn out to be special cases of our analysis when k = 2. We relate the approximate common divisor problem to the implicit factorization problem as well. The later was introduced by May and Ritzenhofen in PKC 2009 and studied under the assumption that some of Least Significant Bits (LSBs) of certain primes are the same. Our strategy can be applied to the implicit factorization problem in a general framework considering the equality of (i) most significant bits (MSBs), (ii) least significant bits (LSBs), and (iii) MSBs and LSBs together. We present new and improved theoretical as well as experimental results in comparison with the state of the art work in this area.

Published in:

IEEE Transactions on Information Theory  (Volume:57 ,  Issue: 6 )