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Paper Abstract and Keywords
Presentation 2007-12-19 14:15
Efficiency Analysis of Multi-Scalar Multiplications using Direct Computation Methods
Hisashi Yamada, Tsuyoshi Takagi (FUN), Kouichi Sakurai (Kyushu Univ.) ISEC2007-121
Abstract (in Japanese) (See Japanese page) 
(in English) The most time consuming operation to verify a signature
with the elliptic curve digital signature algorithm (ECDSA)
is a multi-scalar multiplication with two scalars.
The Interleave method with NAF (IL-NAF)
and the Interleave method with MOF (IL-MOF) are efficient methods for
the multi-scalar multiplications without any pre-computations.
We have to the estimate the length of the consecutive zero digits (zero-run) for efficiency analysis of multi-scalar multiplications
using the IL-NAF/MOF.
In this paper, we consider the appearance probability of the zero-runs
and their average zero-run length using the markov chain.
We present asymptotic length of the consecutive zero digits (zero-run length)
of IL-NAF/MOF for randomly chosen $n$ bit two scalars.
Indeed, the average zero-run length of the IL-NAF and IL-MOF is
asymptotically 3 and 256/85, respectively.
Moreover, we apply the appearance probability of zero-runs
to the speed estimation of
multi-scalar multiplications using the direct computation method.
We prove that the IL-NAF/MOF using direct computation method can achieve $4.7\sim 4.8\%$ faster computation than the standard IL-NAF/MOF with iterated doubling.
Keyword (in Japanese) (See Japanese page) 
(in English) multi-scalar multiplication / interleave method / IL-NAF / IL-MOF / / / /  
Reference Info. IEICE Tech. Rep., vol. 107, no. 397, ISEC2007-121, pp. 59-66, Dec. 2007.
Paper # ISEC2007-121 
Date of Issue 2007-12-12 (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 ISEC2007-121

Conference Information
Committee ISEC  
Conference Date 2007-12-19 - 2007-12-19 
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 2007-12-ISEC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Efficiency Analysis of Multi-Scalar Multiplications using Direct Computation Methods 
Sub Title (in English)  
Keyword(1) multi-scalar multiplication  
Keyword(2) interleave method  
Keyword(3) IL-NAF  
Keyword(4) IL-MOF  
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Keyword(8)  
1st Author's Name Hisashi Yamada  
1st Author's Affiliation Future University-Hakodate (FUN)
2nd Author's Name Tsuyoshi Takagi  
2nd Author's Affiliation Future University-Hakodate (FUN)
3rd Author's Name Kouichi Sakurai  
3rd Author's Affiliation Kyushu University (Kyushu Univ.)
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Speaker Author-1 
Date Time 2007-12-19 14:15:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # ISEC2007-121 
Volume (vol) vol.107 
Number (no) no.397 
Page pp.59-66 
#Pages 8 
Date of Issue 2007-12-12 (ISEC) 

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