研究者詳細 - 野上　保之

How to Generate a Secure Composite Order Ordinary Pairing-friendly Curve of Embedding Degree 3

Y.Nogami, K.Nishii, Y.Sakemi, H.Kato, Y.Morikawa

ITC-CSCC2009 1474 - 1447 2009年

Thread Computing for Miller's algorithm of Pairing

Shoichi Takeuchi, Yumi Sakemi, Yasuyuki Nogami, Yoshitaka Morikawa

ISCE: 2009 IEEE 13TH INTERNATIONAL SYMPOSIUM ON CONSUMER ELECTRONICS, VOLS 1 AND 2 587 - 591 2009年

記述言語：英語出版者・発行元：IEEE

This paper shows an improvement of Miller's algorithm so as to be efficient for thread programming by using divisor theorem. Then, this paper implements a thread program of the improved Miller's algorithm by which it is shown that the proposed technique is more efficient than ordinary Miller's algorithm.

DOI： 10.1109/ISCE.2009.5156956

Web of Science

Cost Evaluation of The Improvement of Twisted Ate Pairing That Uses Integer Variable Chi of Small Hamming Weight

Y. Sakemi, H. Kato, Y. Nogami, Y. Morikawa

Memoirs of the Faculty of Engineering, Okayama University 43 ( 15 ) 113 - 116 2009年

記述言語：英語出版者・発行元：Faculty of Engineering, Okayama University

Barreto–Naehrig (BN) curve has been introduced as an efficient pairing-friendly elliptic curve over prime field F(p) whose embedding degree is 12. The characteristic and Frobenius trace are given as polynomials of integer variable X. The authors proposed an improvement of Miller's algorithm of twisted Ate pairing with BN curve by applying X of small hamming weight in ITC–CSCC2008; however, its cost evaluation has not been explicitly shown. This paper shows the detail of the cost evaluation.

A High-Speed Square Root Algorithm for Extension Fields --Especially for Fast Extension Fields--

Hidehiro Kato, Yasuyuki Nogami, Yoshitaka Morikawa

Memoirs of the Faculty of Engineering, Okayama University 43 99 - 107 2009年

記述言語：英語出版者・発行元：Faculty of Engineering, Okayama University

A square root (SQRT) algorithm in extension field F(p(m))(m = r(0)r(1)･･･r(n−1)･2(d), r(i) : odd prime, d : positive integer) is proposed in this paper. First, a conventional SQRT algorithm, the Tonelli-Shanks algorithm, is modified to compute the inverse SQRT in F(p(2d)), where most of the computations are performed in the corresponding subfields F(p(2i)) for 0 ≤ i ≤ d-1. Then the Frobenius mappings with addition chain are adopted for the proposed SQRT algorithm, in which a lot of computations in a given extension field F(p(m)) are also reduced to those in a proper subfield by the norm computations. Those reductions of the field degree increase efficiency in the SQRT implementation. The Tonelli-Shanks algorithm and the proposed algorithm in F(p(6)) and F(p(10)) were implemented on a Core2 (2.66 GHz) using the C++ programming language. The computer simulations showed that, on average, the proposed algorithm accelerated the SQRT computation by 6 times in F(p(6)), and by 10 times in F(p(10)), compared to the Tonelli-Shanks algorithm.

Cross Twisted Xate Pairing with Barreto-Naehrig Curve for Multi-pairing Technique

Inversion with Normal Bases in Tower Field F_{((2^{2})^{2})^2} for S-Box of AES

Y. Nogami, M. Hagio(Oki Network LSI, E. Yanagi, Y. Morikawa

ITC-CSCC2009 1337 - 1338 2009年

Y. Sakemi, Y. Nogami, H. Kato, and Y. Morikawa

ISIT 2009 2386 - 2390 2009年

Determining Basis Conversion Matrix without Gauss Period Normal Basis

Y.Nogami, E.Yanagi, M.Hagio, Oki Network LSI, Y.Morikawa

ITC-CSCC2009 1331 - 1332 2009年

Zero Correlation Distribution of ZCZ Sequences Obtained from a Perfect Sequence and a Unitary Matrix

Satoshi Uehara(The University of Kitakyushu), Shuichi JONO(NEC Communication Systems), Yasuyuki Nogami

IEICE Trans. fundamentals E91A ( 12 ) 3745 - 3748 2008年12月

Efficient Exponentiation in Extensions of Finite Fields without Fast Frobenius Mappings

Yasuyuki Nogami, Hidehiro Kato, Kenta Nekado, and Yoshitaka Morikawa

ETRI Journal 30 ( 6 ) 818 - 825 2008年12月

A Method for Constructing A Self-Dual Normal Basis in Odd Characteristic Extension Field

H.Nasu, *Y.Nogami, R.Namba, and Y.Morikawa

8th International Conference on Finite Fields and Applications 14 ( 4 ) 867 - 876 2008年11月

A method for constructing a self-dual normal basis in odd characteristic extension fields

Yasuyuki Nogami, Hiroaki Nasu, Yoshitaka Morikawa, Satoshi Uehara

FINITE FIELDS AND THEIR APPLICATIONS 14 ( 4 ) 867 - 876 2008年11月

記述言語：英語出版者・発行元：ACADEMIC PRESS INC ELSEVIER SCIENCE

This paper proposes a useful method for constructing a self-dual normal basis in an arbitrary extension field F-p(m) such that 4p does not divide m(p - 1) and m is odd. In detail, when the characteristic p and extension degree in satisfies the following conditions (1) and either (2a) or (2b); (1) 2km + 1 is a prime number, (2a) the order of p in F2km+ 1 is 2km, (2b) 2 dagger km and the order of p in F2km + 1 is km, we can consider a class of Gauss period normal bases. Using this Gauss period normal basis, this paper shows a method to construct a self-dual normal basis in the extension field F-p(m). (C) 2008 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.ffa.2008.04.001

Web of Science

Scopus

ペアリング暗号に効果的な拡大体上べき乗算に関する一考察

吉田知輝, 加藤英洋, 根角健太, 野上保之, 森川良孝

電子情報通信学会技術研究報告. ISEC, 情報セキュリティ 108 ( 162 ) 101 - 107 2008年7月

記述言語：日本語出版者・発行元：一般社団法人電子情報通信学会

近年,グループ署名やID-based暗号といった楕円曲線上の双線形写像(ペアリング)に基づく暗号方式が注目されている.これらの暗号方式は暗号化・復号・署名などの処理の際に,ペアリング計算後の拡大上の乗法群G_Tにおける演算(べき乗算)を必要とする.暗号に用いられるべき乗算は指数部が大きく計算に時間を要するため,本稿ではBarreto-Naehrig (BN)曲線とよばれる,埋め込み次数κ=12をもつ非超特異なペアリングフレンドリ曲線を用いた場合に組織的に与えられる整数χで指数部を展開することでべき乗算を高速化する手法を提案する.加えて,本稿ではこれまでに提案されているBinary法やNAF法,Window法,Avanzi法といった拡大体上のべき乗算アルゴリズムと提案法を組み合わせた実装および検証を行う.とくにNAF法との組み合わせによってべき乗する際の指数部のハミング重みに大きく依存せず高速に計算できることを示す.

ペアリング暗号に効果的な拡大体上べき乗算に関する一考察

吉田知輝, 加藤英洋, 根角健太, 野上保之, 森川良孝

情報処理学会研究報告コンピュータセキュリティ（CSEC） 2008 ( 71 ) 235 - 241 2008年7月

記述言語：日本語出版者・発行元：一般社団法人情報処理学会

近年，グループ署名 [1] や ID-based 暗号 [3] といった楕円曲線上の双線形写像（ペアリング) [2] に基づく暗号方式が注目されている．これらの暗号方式は暗号化・復号・署名などの処理の際に，ペアリング計算後の拡大上の乗法群 Gt における演算（べき乗算）を必要とする．暗号に用いられるべき乗算は指数部が大きく計算に時間を要するため，本稿では Barreto-Naehrig (BN) 曲線 [9] とよばれる，埋坊込み次数 k=12 をもつ非超特異なペアリングフレンドリ曲線を用いた場合に組織的に与えられる整数 x で指数部を展開することでべき乗算を高速化する手法を提案する．加えて，本稿ではこれまでに提案されている Bynary 法やＮＡＦ法、 Window 法， Avanzi 法 [12] [15] といった拡大体上のべき乗算アルゴリズムと提案法を組み合わせた実装および検証を行う．とくに NAF 法との組み合わせによってべき乗する際の指数部のハミング重みに大きく依存せず高速に計算できることを示す．In recent years, pairing-baaed cryptographies [2] such as ID-base cryptography |3] and group signature [1] have been studied. These cryptographies require exponentiations in multiplicative group Gt- In this paper, the author proposes an efficient exponentiation method for the case of Barreto-Naehrig (BN) curve [9] . Additionally, the author shows implementation results of the proposed method with conventional techniques such as binary method, window method, NAF method and Avanzi method [12] [15]. Then, the author shows the proposed method carries out exponentiation fast.

A Necessary Condition for Gauss Period Normal Bases to Be the Same Normal Basis

その他リンク： http://id.nii.ac.jp/1001/00044301/

A Basis Translation Matrix between Two Isomorphic Extension Fields via Optimal Normal Basis

R.Namba, *Y.Nogami, Y.Morikawa

The 1st Joint Workshop on Information Security JWIS2006 30 ( 2 ) 326 - 334 2008年4月

Yasuyuki NOGAMI , Ryo NAMBA, and Yoshitaka MORIKAWA

IEICE Trans. E91A ( 4 ) 1229 - 1231 2008年4月

Extension Field for Ate Pairing with Freeman Curve

K.Nekado, H.Kato, M.Akane, Y.Nogami, Y.Morikawa

ITC-CSCC2008 653 - 656 2008年

Fast Exponentiation in Extension Field with Frobenius Mappings

H. Kato, K. Nekado, Y. Nogami, Y.Morikawa

Memoirs of the Faculty of Engineering, Okayama Universit 42 ( 4 ) 36 - 43 2008年

記述言語：英語出版者・発行元：Faculty of Engineering, Okayama University

This paper proposes an exponentiation method with Frobenius mappings. Our method is closely related to so-called interleaving exponentiation. Different from the interleaving exponentiation methods, our method can carry out several exponentiations using same base at the same time. The efficiency to use Frobenius mappings for an exponentiation in extension field is well introduced by Avanzi and Mihailescu. This exponentiation method is based on so-called simultaneous exponentiation and uses many Frobenius mappings. Their method more decreased the number of multiplications; however, the number of Frobenius mappings inversely increased. Compared to their method , the number of multiplications needed for the proposed method becomes about 20% larger; however, that of Frobenius mappings becomes small enough.