Faculty Profiles - NOGAMI Yasuyuki

A Binary Sequence Generated by Legendre Symbol and Primitive Polynomial over Odd Characteristic

Other Link： https://dblp.uni-trier.de/db/conf/pairing/pairing2013.html#MoriANS13

有限体上のロジスティック写像による生成系列に対する長周期を保証するための条件

土屋和由, 野上保之

日本応用数理学会年会講演予稿集(CD-ROM) 2014 2014

NOGAMI Yasuyuki, UEHARA Satoshi, TADA Kazuki

IEICE technical report. Information theory 113 ( 58 ) 5 - 8 2013.5

Language：English Publisher：The Institute of Electronics, Information and Communication Engineers

Let p be an odd characteristic and m be the degree of primitive polynomial f(x). Let ω be its zero, that is a primitive element in F^*_pm, then the sequence S={s_i}, s_i=Tr(w^i), i=0,1,2,… becomes a maximum length sequence, where Tr(・) is the trace function over F_p. On this fact, this paper proposes to binarize the sequence by using Legendre symbol. Then, it is shown that the obtained binary sequence has the period L=2(p^m-1)/(p-1) and a certain periodic autocorrelation. This paper also shows a small example.

A Smaller Final Exponentiation for Tate and Ate Pairings with Barreto-Naehrig Curve

Yuki Kono, Taichi Sumo, Yasuyuki Nogami

2013 16TH INTERNATIONAL CONFERENCE ON NETWORK-BASED INFORMATION SYSTEMS (NBIS 2013) 518 - 522 2013

Language：English Publisher：IEEE

This paper shows an approach for reducing the size of the exponent of final exponentiation with multiplying some extra terms. In the case of Tate and Ate pairings with Barreto-Naehrig curve whose embedding degree is 12, the exponent is reduced to (p(4) - p(2) + 1)/r, where p is the characteristic of the base field and r is the order of pairing.

DOI： 10.1109/NBiS.2013.86

A Binarization of Geometric Sequences with Legendre Symbol and Its Autocorrelation

Other Link： https://dblp.uni-trier.de/db/conf/nbis/nbis2013.html#KonoSN13

Yasuyuki Nogami, Kazuki Tada, Satoshi Uehara

SIXTH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS 28 - 31 2013

Language：English Publisher：IEEE

Let p be an odd characteristic and m be the degree of primitive polynomial f(x). Let omega be its zero, that is a primitive element in F-pm*, then the sequence S = {s(i)}, s(i) = Tr (omega(i)) for i = 0, 1, 2, ... becomes a maximum length sequence, where Tr (.) is the trace function over F-p. On this fact, this paper proposes to binarize the sequence by using Legendre symbol. It will be a class of geometric sequences but its properties such as the period and autocorrelation has not been discussed. Then, it is shown that the obtained binary sequence (geometric sequence with Legendre symbol) has the period L given by 2 (p(m) - 1)/(p-1) and a certain periodic autocorrelation. After that, this paper also shows the numbers of ones and minus ones in the proposed binary sequence per a period together with some small examples.

DOI： 10.1109/IWSDA.2013.6849054

A Property of Norm Pairs of Rational Point on A Twisted Elliptic Curve and Adapting Pollard's Rho Method

Other Link： https://dblp.uni-trier.de/db/conf/iwsda/iwsda2013.html#NogamiTU13

Safe Primeを法とした素体上のロジスティック写像による生成系列に関する一考察

宮崎武, 荒木俊輔, 上原聡, 野上保之

日本応用数理学会年会講演予稿集(CD-ROM) 2013 2013

2012 ( 3 ) 493 - 500 2012.10

Finding a Basis Conversion Matrix Using a Polynomial Basis Derived by a Small Multiplicative Cyclic Group

Yasuyuki Nogami, Hidehiro Kato, Kenta Nekado, Satoshi Uehara, Yoshitaka Morikawa

IEEE TRANSACTIONS ON INFORMATION THEORY 58 ( 7 ) 4936 - 4947 2012.7

Language：English Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

Several methods for finding a basis conversion matrix between two different bases in an extension field F-p(m) have been proposed. Among them, the one based on Gauss period normal basis (GNB) is on average the most efficient. However, since it needs to construct a certain tower field F-(pm)n, some inefficient cases in which the towering degree n becomes large have been reported. This paper first determines that such inefficient cases are caused by the GNB condition. In order to overcome this inefficiency, we propose a method that does not use any GNB in the target extension field F-p(m), but instead uses a certain polynomial basis in F-p(m) derived by a certain small cyclic group in F-(pm)n. This causes relaxation of the condition for the towering degree n. In addition, our experimental results show that the proposed method substantially accelerates the computation time for finding a basis conversion matrix.

DOI： 10.1109/TIT.2012.2191477

Finding a Basis Conversion Matrix Using a Polynomial Basis Derived by a Small Multiplicative Cyclic Group

Yasuyuki Nogami, Hidehiro Kato, Kenta Nekado, Satoshi Uehara, Yoshitaka Morikawa

IEEE TRANSACTIONS ON INFORMATION THEORY 58 ( 7 ) 4936 - 4947 2012.7

Authorship：Lead author Language：English Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

DOI： 10.1109/TIT.2012.2191477

An Approach for Constructing Primitive Polynomials of Degree 2^i over Odd Characteristic Prime Field

NOGAMI Yasuyuki, TAKAI Yusuke, KOBAYASHI Shigeki, SUGIMURA Tatsuo, UEHARA Satoshi

Technical report of IEICE. ISEC 112 ( 39 ) 19 - 24 2012.5

Language：Japanese Publisher：The Institute of Electronics, Information and Communication Engineers

This paper considers an approach to obtain primitive polynomials over odd characteristic field F_p for which a variable transformation x&map;x+αx^<-1> called "self α reciprocal transform" is used, where α is a certain element in F^*_<p^<2^j>> of j<i. Self α reciprocal transforms give irreducible polynomials of degree 2^i under a certain condition to which this paper considers their primitivities. If they are not primitive polynomials over F_p, this paper also touches an efficient approach for translating them to primitive polynomials.

SubBytes Transform for AES Adopting Basis Conversion with More Miscellaneously Mixed Basis in F_{(2^4)^2}

2011 ( 3 ) 349 - 354 2011.10

Freeman曲線を用いたXateおよびR–ateペアリングのための定義体における乗算アルゴリズム

根角健太, 湯浅達也, 野上保之, 森川良孝

コンピュータセキュリティシンポジウム2009 (CSS2009) 論文集 2009 1 - 6 2011.10

SubBytes Transform for AES Adopting Inversion in F_{(2^4)^2} with Redundantly Represented Basis

2011 ( 3 ) 343 - 348 2011.10

Memory Saving Implementation of Cyclic Vector Multiplication Algorithm

TAKAHASHI Ryosuke, NEKADO Kenta, TAKAI Yusuke, NOGAMI Yasuyuki, KAGOTANI Hiroto, NARITA Takashi

IEICE technical report 111 ( 125 ) 145 - 150 2011.7

Language：Japanese Publisher：The Institute of Electronics, Information and Communication Engineers

The authors have proposed a cyclic vector multiplication algorithm abbreviated as CVMA that is flexible to the parameters of extension field, that is extension degree and charasteristic. For the hardware implementation of CVMA, the authors have improved the double loop structure of CVMA to a single loop one, and it has been presented at SITA2010. However, it has a problem that it needs a lot of memory. Thus, this paper proposes a method to save the memory use of the single loop version of CVMA.

Memory Saving Implementation of Cyclic Vector Multiplication Algorithm

TAKAHASHI Ryosuke, NEKADO Kenta, TAKAI Yusuke, NOGAMI Yasuyuki, KAGOTANI Hiroto, NARITA Takashi

IEICE technical report 111 ( 124 ) 145 - 150 2011.7

Language：Japanese Publisher：The Institute of Electronics, Information and Communication Engineers

Memory Saving Implementation of Cyclic Vector Multiplication Algorithm

TAKAHASHI Ryosuke, NEKADO Kenta, TAKAI Yusuke, NOGAMI Yasuyuki, KAGOTANI Hiroto, NARITA Takashi

IEICE technical report 111 ( 126 ) 145 - 150 2011.7

Language：Japanese Publisher：The Institute of Electronics, Information and Communication Engineers

Memory Saving Implementation of Cyclic Vector Multiplication Algorithm

TAKAHASHI Ryosuke, NEKADO Kenta, TAKAI Yusuke, NOGAMI Yasuyuki, KAGOTANI Hiroto, NARITA Takashi

IEICE technical report 111 ( 123 ) 145 - 150 2011.7

Language：Japanese Publisher：The Institute of Electronics, Information and Communication Engineers