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Paper Abstract and Keywords
Presentation 2015-12-18 15:45
[Invited Talk] Higher Order Differntial Attack and Integral Attack
Toshinobu Kaneko (TUS) ISEC2015-58
Abstract (in Japanese) (See Japanese page) 
(in English) Higher order differential (HOD) attack and Integral attack are one of the general purpose attacks to common key block ciphers. The former uses the concept of recursive application of differential of discrete functions, and the latter uses the XOR sum property of discrete functions.
As HOD can be also expressed as XOR-sum formula, they are very similar, but Integral attack has a wider concept.
Todo introduced the Division property as the method to find good integral characteristic.
This article uses the Division property as a link of HOD and Integral, and shows the followings.
The best Integral attack derived by Division property is equal to the HOD attack. The data complexity is the same; both needs $2^{d+1}$ texts for non-linear function $f(Vec{x})$ of degree $d$.
The number of different characteristics is the same for both attacks.
It is $2^{m-d-1}prod ^d_{i=0}frac{2^{m-i}-1}{2^{d-i}-1}$, where $m$ is a input width of $f(Vec{x})$.
These results are derived from the minimum distance and weight distribution of RM codes.
Keyword (in Japanese) (See Japanese page) 
(in English) Higer order differential attack / Integral attack / Division property / common key block cipher / / / /  
Reference Info. IEICE Tech. Rep., vol. 115, no. 376, ISEC2015-58, pp. 23-29, Dec. 2015.
Paper # ISEC2015-58 
Date of Issue 2015-12-11 (ISEC) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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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)
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Conference Information
Committee ISEC  
Conference Date 2015-12-18 - 2015-12-18 
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 2015-12-ISEC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Higher Order Differntial Attack and Integral Attack 
Sub Title (in English)  
Keyword(1) Higer order differential attack  
Keyword(2) Integral attack  
Keyword(3) Division property  
Keyword(4) common key block cipher  
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1st Author's Name Toshinobu Kaneko  
1st Author's Affiliation Tokyou University of Science (TUS)
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Speaker Author-1 
Date Time 2015-12-18 15:45:00 
Presentation Time 30 minutes 
Registration for ISEC 
Paper # ISEC2015-58 
Volume (vol) vol.115 
Number (no) no.376 
Page pp.23-29 
#Pages
Date of Issue 2015-12-11 (ISEC) 


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