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 Paper Abstract and Keywords Presentation 2012-07-20 14:20 An Improved Algorithm for Approximate GCD ProblemsAtsushi Takayasu, Noboru Kunihiro (UT) ISEC2012-35 SITE2012-31 ICSS2012-37 EMM2012-27 Abstract (in Japanese) (See Japanese page) (in English) In this paper, we analyze multivariate approximate common divisor problem(ACDP), given approximate multiples of the integer and we recover the integer. So far, via lattice based Coppersmith's theorem, the polynomial time ACDP algorithms have been proposed. In 2001, Howgrave-Graham proposed the polynomial time algorithms for ACDP as long as the tolerated errors are sufficiently small, when given two approximate multiples. In 2011, Cohn and Heninger gave the multivariate generalization of Howgrave-Graham's algorithm, when given plural approximate multiples. In this paper, we analyze only partially approximate common divisor problem(PACDP) when given one exact multiple of the integer. We propose the improved polynomial time algorithm by Cohn and Heninger when given plural approximate multiples. Cohn and Heninger revealed that PACDP can be solved when $(\alpha _1+\cdots+\alpha _n)/n<\beta^{(n+1)/n}$. We change the lattice construction by Cohn and Heninger's algorithm and improve the condition $\sqrt[n]{\alpha _1 \cdots \alpha _n}<\beta^{(n+1)/n}$. In the left hand side of the inequality, where is the arithmetic mean of $\alpha _1,\ldots,\alpha _n$ in Cohn and Heninger's condition become the geometric mean of $\alpha _1,\ldots,\alpha _n$ in our condition. Our algorithm can be applied to broader context. Moreover, considering the multivariate generalization of Howgrave-Graham's algorithm, our condition is more natural than Cohn and Heninger's condition. Keyword (in Japanese) (See Japanese page) (in English) approximate-GCD / lattice / Coppersmith's theorem / / / / / Reference Info. IEICE Tech. Rep., vol. 112, no. 126, ISEC2012-35, pp. 189-194, July 2012. Paper # ISEC2012-35 Date of Issue 2012-07-12 (ISEC, SITE, ICSS, EMM) ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380 Copyrightandreproduction All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (No. 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) Download PDF ISEC2012-35 SITE2012-31 ICSS2012-37 EMM2012-27

 Conference Information Committee EMM ISEC SITE ICSS IPSJ-CSEC IPSJ-SPT Conference Date 2012-07-19 - 2012-07-20 Place (in Japanese) (See Japanese page) Place (in English) Topics (in Japanese) (See Japanese page) Topics (in English) Security Paper Information Registration To ISEC Conference Code 2012-07-EMM-ISEC-SITE-ICSS-CSEC-SPT Language Japanese Title (in Japanese) (See Japanese page) Sub Title (in Japanese) (See Japanese page) Title (in English) An Improved Algorithm for Approximate GCD Problems Sub Title (in English) Keyword(1) approximate-GCD Keyword(2) lattice Keyword(3) Coppersmith's theorem Keyword(4) Keyword(5) Keyword(6) Keyword(7) Keyword(8) 1st Author's Name Atsushi Takayasu 1st Author's Affiliation The University of Tokyo (UT) 2nd Author's Name Noboru Kunihiro 2nd Author's Affiliation The University of Tokyo (UT) 3rd Author's Name 3rd Author's Affiliation () 4th Author's Name 4th Author's Affiliation () 5th Author's Name 5th Author's Affiliation () 6th Author's Name 6th Author's Affiliation () 7th Author's Name 7th Author's Affiliation () 8th Author's Name 8th Author's Affiliation () 9th Author's Name 9th Author's Affiliation () 10th Author's Name 10th Author's Affiliation () 11th Author's Name 11th Author's Affiliation () 12th Author's Name 12th Author's Affiliation () 13th Author's Name 13th Author's Affiliation () 14th Author's Name 14th Author's Affiliation () 15th Author's Name 15th Author's Affiliation () 16th Author's Name 16th Author's Affiliation () 17th Author's Name 17th Author's Affiliation () 18th Author's Name 18th Author's Affiliation () Speaker 1 Date Time 2012-07-20 14:20:00 Presentation Time 25 Registration for ISEC Paper # IEICE-ISEC2012-35,IEICE-SITE2012-31,IEICE-ICSS2012-37,IEICE-EMM2012-27 Volume (vol) IEICE-112 Number (no) no.126(ISEC), no.127(SITE), no.128(ICSS), no.129(EMM) Page pp.189-194 #Pages IEICE-6 Date of Issue IEICE-ISEC-2012-07-12,IEICE-SITE-2012-07-12,IEICE-ICSS-2012-07-12,IEICE-EMM-2012-07-12