NDLI: Approximate Integer Common Divisor Problem Relates to Implicit Factorization

Content Provider	IEEE Xplore Digital Library
Author	Sarkar, S. Maitra, S.
Copyright Year	1963
Abstract	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.
Sponsorship	IEEE Information Theory Society
Starting Page	4002
Ending Page	4013
Page Count	12
File Size	351815
File Format	PDF
ISSN	00189448
Volume Number	57
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation methods Polynomials Lattices Upper bound Approximation algorithms Vectors Complexity theory Lenstra–Lenstra–Lovász (LLL) Factorization greatest common divisor implicit factorization integer approximations lattice
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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Approximate integer common divisor problem relates to implicit factorization.

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