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Paper Abstract and Keywords
Presentation 2010-05-21 17:10
Applying Numerical Analysis Technique To Prime Factorization
Masaaki Shirase (FUN) ISEC2010-9
Abstract (in Japanese) (See Japanese page) 
(in English) It is important to analyze the hardness of prime factorization
which the security of RSA cryptosystems is based on.
There are some methods for solving prime factorization such as
the $\rho$ method, the $p-1$ method, the elliptic curve method, the quadratic sieve,
and the number field method.
The number field sieve is the current fastest algorithm for solving
prime factorization, and is a semi-exponential time algorithm whose cost is $O(\exp ((64/9)^{1/3}) (\ln n)^{1/3} (\ln \ln n)^{2/3})$. As sieves for solving discrete logarithm problem have improved, the number field sieve may be improved, however, the author thinks it is impossible that the number field sieve becomes a polynomial time algorithm. This report considers the possibility of further speed-up of prime factorization by constructing a \lq\lq finding divisor function'' ${\cal F}(n,x)$ whose zeros are divisors of $n$ and by applying a numerical analysis technique to the function.
Keyword (in Japanese) (See Japanese page) 
(in English) prime factorization / RSA cryptosystem / numerical analysis / / / / /  
Reference Info. IEICE Tech. Rep., vol. 110, no. 44, ISEC2010-9, pp. 57-62, May 2010.
Paper # ISEC2010-9 
Date of Issue 2010-05-14 (ISEC) 
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 ISEC2010-9

Conference Information
Committee ISEC  
Conference Date 2010-05-21 - 2010-05-21 
Place (in Japanese) (See Japanese page) 
Place (in English) Kikai-Shinko-Kaikan Bldg. 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To ISEC 
Conference Code 2010-05-ISEC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Applying Numerical Analysis Technique To Prime Factorization 
Sub Title (in English)  
Keyword(1) prime factorization  
Keyword(2) RSA cryptosystem  
Keyword(3) numerical analysis  
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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 2010-05-21 17:10:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # ISEC2010-9 
Volume (vol) vol.110 
Number (no) no.44 
Page pp.57-62 
#Pages 6 
Date of Issue 2010-05-14 (ISEC) 

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