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Paper Abstract and Keywords
Presentation 2016-11-07 14:55
Factorization of Composite Numbers having a Prime of Special Form with Elliptic Curve Method
Masaaki Shirase (FUN) ISEC2016-54 SITE2016-44 LOIS2016-32
Abstract (in Japanese) (See Japanese page) 
(in English) A previous work cite{Shirase16}
considered when the elliptic curve method (ECM) successes with a scalar value $N$
for a composite number $N$ one would like to factor,
and showed that
if a special form of prime $p=(DV^2+1)/4 (V in Z，Din {3,11,19,43,67,163})$ divided $N$
and we could take $P in E(ZN)$ for an elliptic curve $E$ having a designated $j$-invariant
then a polynomial time algorithm in the length of $N$
like the ECM could find a non-trivial divisor of $N$ with probability from $1/6$ to $1/2$.
However, although taking $P in E$ is easy for $D=3$,
it is not for other $D$'s.
This paper considers $E$ as on a residue ring of a polynomial ring $(Z/NZ)[X]$
to easily take $P in E$,
and improves the algorithm so that it can be repeatedly used
until a non-trivial divisor of $N$ is found for $Din {11,19,43,67,163}$.
Keyword (in Japanese) (See Japanese page) 
(in English) Elliptic curve method / Prime factorizetion / Anomalous curve / Residue ring / / / /  
Reference Info. IEICE Tech. Rep., vol. 116, no. 289, ISEC2016-54, pp. 19-26, Nov. 2016.
Paper # ISEC2016-54 
Date of Issue 2016-10-31 (ISEC, SITE, LOIS) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 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. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF ISEC2016-54 SITE2016-44 LOIS2016-32

Conference Information
Committee ISEC LOIS SITE  
Conference Date 2016-11-07 - 2016-11-08 
Place (in Japanese) (See Japanese page) 
Place (in English) Community Hall & AOSSA Mall, Fukui 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To ISEC 
Conference Code 2016-11-ISEC-LOIS-SITE 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Factorization of Composite Numbers having a Prime of Special Form with Elliptic Curve Method 
Sub Title (in English)  
Keyword(1) Elliptic curve method  
Keyword(2) Prime factorizetion  
Keyword(3) Anomalous curve  
Keyword(4) Residue ring  
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1st Author's Name Masaaki Shirase  
1st Author's Affiliation Future University Hakodate (FUN)
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Speaker Author-1 
Date Time 2016-11-07 14:55:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # ISEC2016-54, SITE2016-44, LOIS2016-32 
Volume (vol) vol.116 
Number (no) no.289(ISEC), no.290(SITE), no.291(LOIS) 
Page pp.19-26 
#Pages 8 
Date of Issue 2016-10-31 (ISEC, SITE, LOIS) 

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