Updated on 2021/03/26

写真b

 
YOKOYAMA Kazuhiro
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Graduate School of Science Field of Study: Mathematics
Graduate School of Science Field of Study: Mathematics
Title*
Professor
Degree
博士(理学) ( 九州大学 ) / Doctor(Science) ( Kyushu University )
Contact information
Mail Address
Research Theme*
  • 計算機代数と代数的組合せ論を研究テーマとする。主たるテーマの計算機代数では、高度な数学の諸概念・数学的な操作を計算機上でどこまで実現できるのかについて研究を行っている。同時に計算可能になったものを計算を通して数学研究支援や工学などの実学に応用することも試みている。

  • Research Interests
  • Computer Algebra

  • 代数的組合せ論

  • Algebraic Combinatorics

  • 計算環論

  • Campus Career*
    • 4 2005 - Present 
      College of Science   Department of Mathematics   Professor
    • 4 2005 - Present 
      Graduate School of Science   Field of Study: Mathematics   Professor
    • 4 2005 - Present 
      Graduate School of Science   Field of Study: Mathematics   Professor
     

    Research Areas

    • Natural Science / Basic mathematics

    • Natural Science / Applied mathematics and statistics

    • Natural Science / Algebra

    Research History

    • 4 2005 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Professor

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    • 4 2005 - Present 
      RIKKYO UNIVERSITY   College of Science Department of Mathematics   Professor

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    • 4 2005 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Professor

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    • 12 2000 - 3 2005 
      Kyushu University   Faculty of Mathematics

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    • 4 1999 - 11 2000 
      富士通研究所 セキュアコンピューティング研究部   研究員

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    • 4 1999 - 11 2000 
      富士通研究所 セキュアコンピューティング研究部   研究員

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    • 11 1996 - 3 1999 
      Fujitsu Laboratories LTD.   Researcher

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    • 11 1996 - 3 1999 
      Fujitsu Laboratories LTD.   Researcher

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    • 4 1995 - 3 1996 
      Fujitsu Laboratories LTD.   Chief Researcher

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    • 4 1995 - 3 1996 
      Fujitsu Laboratories LTD.   Chief Researcher

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    • 12 1990 - 3 1995 
      Fujitsu Laboratories LTD.   Researcher

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    • 12 1990 - 3 1995 
      Fujitsu Laboratories LTD.   Researcher

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    • 4 1985 - 11 1990 
      Fujitsu   Researcher

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    Education

    • 4 1983 - 3 1983 
      The University of Tokyo   Graduate School, Division of Science

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      Country: Japan

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    • - 3 1983 
      The University of Tokyo   Graduate School, Division of Science

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      Country: Japan

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    • - 3 1981 
      The University of Tokyo   Faculty of Science

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      Country: Japan

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    Committee Memberships

    • 1 1992 
      日本数式処理学会   監事

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      Committee type:Academic society

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    Papers

    • On affine tropical F5 algorithms Peer-reviewed

      Tristan Vaccon, Thibaut Verron, Kazuhiro Yokoyama

      Journal of Symbolic Computation102   132 - 152   2021

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Elsevier  

      Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gröbner bases taking into account the valuation of K. Because of the use of the valuation, the theory of tropical Gröbner bases has proved to provide settings for computations over polynomial rings over a p-adic field that are more stable than that of classical Gröbner bases.

      Beforehand, these strategies were only available for homogeneous polynomials. In this article, we extend the F5 strategy to a new definition of tropical Gröbner bases in an affine setting. We also provide a competitor with an adaptation of the F4 strategy to tropical Gröbner bases computations.

      We provide numerical examples to illustrate time-complexity and p-adic stability of this tropical F5 algorithm. We also illustrate its merits as a first step before an FGLM algorithm to compute (classical) lex bases over p-adics.

      DOI: 10.1016/j.jsc.2019.10.012

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    • Hybrid meet-in-the-middle attacks for the isogeny path-finding problem Peer-reviewed

      Yasuhiko Ikematsu, Ryoya Fukasaku, Momonari Kudo, Masaya Yasuda, Katsuyuki Takashima, Kazuhiro Yokoyama

      to appear in Proceedings of The 7th ACM ASIA Public-Key Cryptography Workshop (APKC 2020)   10 2020

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      Language:English   Publishing type:Research paper (international conference proceedings)  

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    • On FGLM algorithms with tropical Gröbner bases Peer-reviewed

      Yuki Ishihara, Tristan Vaccon, Kazuhiro Yokoyama

      Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation   20 7 2020

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      Publishing type:Research paper (international conference proceedings)   Publisher:ACM  

      DOI: 10.1145/3373207.3404037

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    • Algebraic approaches for solving isogeny problems of prime power degrees Peer-reviewed International journal

      Yasushi Takahashi, Momonari Kudo, Yasuhiko Ikematsu, Masaya Yasuda, Kazuhiro Yokoyama

      accepted at MathCrypt 2019, Santa Barbara, USA, August 18, 2019   8 2019

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      Language:English   Publishing type:Research paper (international conference proceedings)  

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    • Complexity Bound on Semaev’s Naive Index Calculus Method for ECDLP Peer-reviewed

      Kazuhiro Yokoyama, Masaya Yasuda, Yasushi Takahashi, Jun Kogure

      accepted at Number-Theoretic Methods in Cryptology 2019   2019

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    • On Affine Tropical F5 Algorithms Peer-reviewed

      Tristan Vaccon, Thibaut Verron, Kazuhiro Yokoyama

      Proceedings of ISSAC 2018   383 - 390   7 2018

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACM  

      Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gröbner bases taking into account the valuation of K . Because of the use of the valuation, the theory of tropical Gröbner bases has proved to provide settings for computations over polynomial rings over a p -adic field that are more stable than that of classical Gröbner bases. Beforehand, these strategies were only available for homogeneous polynomials. In this article, we extend the F5 strategy to a new definition of tropical Gröbner bases in an affine setting. We provide numerical examples to illustrate time-complexity and p -adic stability of this tropical F5 algorithm. We also illustrate its merits as a first step before an FGLM algorithm to compute (classical) lex bases over p -adics.

      DOI: 10.1145/3208976.3209012

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    • Usage of Modular Techniques for Efficient Computation of Ideal Operations Peer-reviewed

      Masayuki Noro, Kazuhiro Yokoyama

      Mathematics in Computer Science12 ( 1 ) 1 - 32   1 3 2018

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Birkhauser Verlag AG  

      Modular techniques are widely applied to various algebraic computations. In this paper, we discuss how modular techniques can be efficiently applied to computation of Gröbner basis of the ideal generated by a given set, and extend the techniques for further ideal operations such as ideal quotient, saturation and radical computation. In order to make modular techniques very efficient, we focus on the most important issue, how to efficiently guarantee the correctness of computed results. Unifying notions of luckiness of primes proposed by several authors, we give precise and comprehensive explanation on the techniques which shall be a certain basis for further development.

      DOI: 10.1007/s11786-017-0325-1

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    • Effective Localization Using Double Ideal Quotient and Its Implementation. Peer-reviewed

      Yuki Ishihara, Kazuhiro Yokoyama

      Proceedings of CASC 2018, Lecture Notes in Computer Science11077   272 - 287   2018

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer  

      In this paper, we propose a new method for localization of polynomial ideal, which we call “Local Primary Algorithm”. For an ideal I and a prime ideal P, our method computes a P-primary component of I after checking if P is associated with I by using double ideal quotient (I : (I : P)) and its variants which give us a lot of information about localization of I.

      DOI: 10.1007/978-3-319-99639-4_19

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    • A Tropical F5 algorithm Peer-reviewed

      Tristan Vaccon, Kazuhiro Yokoyama

      Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC129312   429 - 436   23 7 2017

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Association for Computing Machinery  

      Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gröbner bases taking into account the valuation of K. While generalizing the classical theory of Gröbner bases, it is not clear how modern algorithms for computing Gröbner bases can be adapted to the tropical case. Among them, one of the most e.cient is the celebrated F5 Algorithm of Faugère. In this article, we prove that, for homogeneous ideals, it can be adapted to the tropical case. We prove termination and correctness. Because of the use of the valuation, the theory of tropical Gröbner bases is promising for stable computations over polynomial rings over a p-adic field. We provide numerical examples to illustrate time-complexity and p-adic stability of this tropical F5 algorithm.

      DOI: 10.1145/3087604.3087630

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    • Analysis of decreasing squared-sum of Gram-Schmidt lengths for short lattice vectors. Peer-reviewed

      Masaya Yasuda, Kazuhiro Yokoyama, Takeshi Shimoyama, Jun Kogure, Takeshi Koshiba

      J. Mathematical Cryptology11 ( 1 ) 1 - 24   2017

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:De Gruyter  

      In 2015, Fukase and Kashiwabara proposed an efficient method to find a very short lattice vector. Their method has been applied to solve Darmstadt shortest vector problems of dimensions 134 to 150. Their method is based on Schnorr’s random sampling, but their preprocessing is different from others. It aims to decrease the sum of the squared lengths of the Gram–Schmidt vectors of a lattice basis, before executing random sampling of short lattice vectors. The effect is substantiated from their statistical analysis, and it implies that the smaller the sum becomes, the shorter sampled vectors can be. However, no guarantee is known to strictly decrease the sum. In this paper, we study Fukase–Kashiwabara’s method in both theory and practice, and give a heuristic but practical condition that the sum is strictly decreased. We believe that our condition would enable one to monotonically decrease the sum and to find a very short lattice vector in fewer steps.

      DOI: 10.1515/jmc-2016-0008

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    • Secure statistical analysis using RLWE-based homomorphic encryption Peer-reviewed

      Masaya Yasuda, Takeshi Shimoyama, Jun Kogure, Kazuhiro Yokoyama, Takeshi Koshiba

      Lecture Notes in Computer Science (ACISP 2015)9144   471 - 487   6 2015

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      DOI: 10.1007/978-3-319-19962-7_27

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    • New packing method in somewhat homomorphic encryption and its applications. Peer-reviewed

      Masaya Yasuda, Takeshi Shimoyama, Jun Kogure, Kazuhiro Yokoyama, Takeshi Koshiba

      Security and Communication Networks8 ( 13 ) 2194 - 2213   2015

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:John Wiley and Sons  

      Somewhat homomorphic encryption is public key encryption supporting a limited number of additions and multiplications on encrypted data. This encryption gives a powerful tool in performing meaningful computations with protecting data confidentiality, whose property is suitable mainly in cloud computing. In this paper, we focus on the scheme proposed by Brakerski and Vaikuntanathan, and present two types of packed ciphertexts in order to improve performance and reduce size of the encrypted data. One type of our packed ciphertexts is based on the message encoding technique proposed by Lauter, Naehrig and Vaikuntanathan. While their technique empowers efficient secure computation of sums and products over the integers, our second type of packed ciphertexts enables efficient secure computation of more complex functionalities such as multiple inner products and multiple Hamming distances. We apply our packing method to construct several protocols for secure biometric authentication and secure pattern matching computations. Our implementation shows that our method gives faster performance than the state‐of‐the‐art work in such applications.

      DOI: 10.1002/sec.1164

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    • Secure Data Devolution: Practical Re-encryption with Auxiliary Data in LWE-based Somewhat Homomorphic Encryption. Peer-reviewed

      Masaya Yasuda, Array, Takeshi Shimoyama, Jun Kogure, Kazuhiro Yokoyama

      Proceedings of the 3rd International Workshop on Security in Cloud Computing, SCC@ASIACCS '15, Singapore, Republic of Singapore, April 14, 2015   53 - 61   2015

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    • On the exact decryption range for Gentry-Halevi's implementation of fully homomorphic encryption. Peer-reviewed

      Masaya Yasuda, Kazuhiro Yokoyama, Takeshi Shimoyama, Jun Kogure, Takeshi Koshiba

      J. Mathematical Cryptology8 ( 3 ) 305 - 329   2014

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:De Gruyter  

      In this paper, we revisit the fully homomorphic encryption (FHE) scheme implemented by Gentry and Halevi, which is just an instantiation of Gentry's original scheme based on ideal lattices. Their FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, and its decryption range is deeply related with the FHE construction. Gentry and Halevi gave an experimental evaluation of the decryption range, but theoretical evaluations have not been given so far. Moreover, we give a theoretical upper bound, and reconsider suitable parameters for theoretically obtaining an FHE scheme. In particular, while Gentry and Halevi use the Euclidean norm evaluation in the noise management of ciphertexts, our theoretical bound enables us to use the ∞-norm evaluation, and hence it helps to lower the difficulty of controlling the noise density of ciphertexts.

      DOI: 10.1515/jmc-2013-0024

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    • Practical Packing Method in Somewhat Homomorphic Encryption Peer-reviewed

      Yasuda Masaya, Shimoyama Takeshi, Kogure Jun, Yokoyama Kazuhiro, Koshiba Takeshi

      DATA PRIVACY MANAGEMENT AND AUTONOMOUS SPONTANEOUS SECURITY, DPM 20138247   34 - 50   2014

    • Privacy-Preserving Wildcards Pattern Matching Using Symmetric Somewhat Homomorphic Encryption Peer-reviewed

      Yasuda Masaya, Shimoyama Takeshi, Kogure Jun, Yokoyama Kazuhiro, Koshiba Takeshi

      INFORMATION SECURITY AND PRIVACY, ACISP 20148544   338 - 353   2014

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      Publisher:Springer  

      DOI: 10.1007/978-3-319-08344-5_22

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    • Verification of Gröbner basis candidates Peer-reviewed

      Masayuki Noro, Kazuhiro Yokoyama

      Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)8592   419 - 424   2014

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer Verlag  

      We propose a modular method for verifying the correctness of a Gröbner basis candidate. For an inhomogeneous ideal I, we propose to check that a Gröbner basis candidate G is a subset of I by computing an exact generating relation for each g in G by the given generating set of I via a modular method. The whole procedure is implemented in Risa/Asir, which is an open source general computer algebra system. By applying this method we succeeded in verifying the correctness of a Gröbner basis candidate computed in Romanovski et al (2007). In their paper the candidate was computed by a black-box software system and it has been necessary to verify the candidate for ensuring the mathematical correctness of the paper. © 2014 Springer-Verlag.

      DOI: 10.1007/978-3-662-44199-2_64

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    • An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination Peer-reviewed

      Hidenao Iwane, Hitoshi Yanami, Hirokazu Anai, Kazuhiro Yokoyama

      THEORETICAL COMPUTER SCIENCE479 ( 1 ) 43 - 69   4 2013

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

      With many applications in engineering and scientific fields, quantifier elimination (QE) has received increasing attention. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. In this paper we present an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm for QE incorporating several new devices, which we call "quick tests". The simple quick tests are run beforehand to detect an unnecessary procedure that might be skipped without violating the correctness of results and they thus considerably reduce the computing time. The effectiveness of the SNCAD algorithm is examined in a number of experiments including practical engineering problems, which also reveal the quality of the implementation. Experimental results show that our implementation has significantly improved efficiency compared with our previous work. (c) 2012 Elsevier B.V. All rights reserved.

      DOI: 10.1016/j.tcs.2012.10.020

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    • Packed Homomorphic Encryption Based on Ideal Lattices and Its Application to Biometrics. Peer-reviewed

      Masaya Yasuda, Takeshi Shimoyama, Jun Kogure, Kazuhiro Yokoyama, Takeshi Koshiba

      Proceedings of CD-ARES 2013, Lecture Notes in Computer Science8128   55 - 74   2013

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer  

      Among many approaches for privacy-preserving biometric authentication, we focus on the approach with homomorphic encryption, which is public key encryption supporting some operations on encrypted data. In biometric authentication, the Hamming distance is often used as a metric to compare two biometric feature vectors. In this paper, we propose an efficient method to compute the Hamming distance on encrypted data using the homomorphic encryption based on ideal lattices. In our implementation of secure Hamming distance of 2048-bit binary vectors with a lattice of 4096 dimension, encryption of a vector, secure Hamming distance, and decryption respectively take about 19.89, 18.10, and 9.08 milliseconds (ms) on an Intel Xeon X3480 at 3.07 GHz. We also propose a privacy-preserving biometric authentication protocol using our method, and compare it with related protocols. Our protocol has faster performance and shorter ciphertext size than the state-of-the-art prior work using homomorphic encryption.

      DOI: 10.1007/978-3-642-40588-4_5

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    • Secure pattern matching using somewhat homomorphic encryption. Peer-reviewed

      Masaya Yasuda, Takeshi Shimoyama, Jun Kogure, Kazuhiro Yokoyama, Takeshi Koshiba

      CCSW'13, Proceedings of the 2013 ACM Cloud Computing Security Workshop, Co-located with CCS 2013, Berlin, Germany, November 4, 2013   65 - 76   2013

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      Publishing type:Research paper (international conference proceedings)   Publisher:ACM  

      DOI: 10.1145/2517488.2517497

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    • Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries Peer-reviewed

      Sébastien Orange, Guénaël Renault, Kazuhiro Yokoyama

      Mathematics in Computer Science6 ( 3 ) 217 - 233   9 2012

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Birkhaeser/Springer  

      In this article, we present new results for efficient arithmetic operations in a number field K represented by successive extensions. These results are based on multi-modular and evaluation-interpolation techniques. We show how to use intrinsic symmetries in order to increase the efficiency of these techniques. Applications to splitting fields of univariate polynomials are presented. © 2012 Springer Basel AG.

      DOI: 10.1007/s11786-012-0112-y

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    • Usage of Modular Techniques for Efficient Computation of Ideal Operations Invited

      Kazuhiro Yokoyama

      COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, CASC 20127442   361 - 362   2012

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER-VERLAG BERLIN  

      Modular techniques are widely applied to various algebraic computations. (See [5] for basic modular techniques applied to polynomial computations.) In this talk, we discuss how modular techniques are efficiently applied to computation of various ideal operations such as Gröbner base computation and ideal decompositions. Here, by modular techniques we mean techniques using certain projections for improving the efficiency of the total computation, and by modular computations, we mean corresponding computations applied to projected images.

      DOI: 10.1007/978-3-642-32973-9\_30

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    • Optimizing a Particular Real Root of a Polynomial by a Special Cylindrical Algebraic Decomposition Peer-reviewed

      Silvia Gandy, Masaaki Kanno, Hirokazu Anai, Kazuhiro Yokoyama

      Mathematics in Computer Science5 ( 2 ) 209 - 221   6 2011

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Birkhaeuser/Springer  

      We study the problem of optimizing over parameters a particular real root of a polynomial with parametric coefficients. We propose an efficient symbolic method for solving the optimization problem based on a special cylindrical algebraic decomposition algorithm, which asks for a semi-algebraic decomposition into cells in terms of number-of-roots-invariance. © 2011 Springer Basel AG.

      DOI: 10.1007/s11786-011-0090-5

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    • Development of QC2AS- A computer algebra system for symbolic quantum chemical computations Peer-reviewed

      Takeshi Osoekawa, Yuji Mochizuki, Kazuhiro Kyokoyama

      Proceedings - 2011 International Conference on Computational Science and Its Applications, ICCSA 2011   102 - 109   2011

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE Computer Society  

      This paper introduces QC2AS which is a newly designed and developed computer algebra system for symbolic quantum chemical computations. With the rapid advancement of computer, the concern with high-level model chemistry has been growing. To handle such models, it is necessary to manipulate huge algebraic formulas. QC2AS has been designed to handle algebraic formulas appeared in quantum chemistry and it provides an access to our computer algebraic techniques without knowing the background theories. In this paper, we introduce its features and the architecture with some illustrative examples. This is the first report about the development of QC2AS. © 2011 IEEE.

      DOI: 10.1109/ICCSA.2011.39

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    • Gröbner Basis Technique for Algebraic Formulas in Electron Correlation Theories Peer-reviewed

      Takeshi Osoekawa, Yuji Mochizuki, Kazuhiro Yokoyama

      Proceedings of ICCSA 2010   17 - 23   2010

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:IEEE Computer Society  

      This paper describes an algorithm to simplify algebraic formulas appear in electron correlation theories using Grobner basis.The algorithm is designed to sum up the equivalent terms under a set of rewriting rules so that we obtain the simplest representation of the formula.This paper also discusses improvements of our algorithm.

      DOI: 10.1109/ICCSA.2010.30

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    • Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem Peer-reviewed

      Hirokazu Anai, Shinji Hara, Masaaki Kanno, Kazuhiro Yokoyama

      JOURNAL OF SYMBOLIC COMPUTATION44 ( 7 ) 703 - 725   7 2009

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

      This paper presents an algebraic approach to polynomial spectral factorization, an important mathematical tool in signal processing and control. The approach exploits an intriguing relationship between the theory of Grobner bases and polynomial spectral factorization which can be observed through the sum of roots, and allows us to perform polynomial spectral factorization in the presence of real parameters. It is discussed that parametric polynomial spectral factorization enables us to express quantities Such as the optimal cost in terms of parameters and the sum of roots. Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs two quantifier elimination techniques. This proposed approach is demonstrated in a numerical example of a particular control problem. (C) 2008 Elsevier Ltd. All rights reserved.

      DOI: 10.1016/j.jsc.2008.04.015

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    • An Effective Implementation of a Symbolic-Numeric Cylindrical Algebraic Decomposition for Quantifier Elimination Peer-reviewed

      Hidenao Iwane, Hitoshi Yanami, Hirokazu Anai, Kazuhiro Yokoyama

      SNC'09: PROCEEDINGS OF THE 2009 INTERNATIONAL WORKSHOP ON SYMBOLIC-NUMERIC COMPUTATION   55 - 64   2009

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:ASSOC COMPUTING MACHINERY  

      Recently quantifier elimination (QE) has been of great interest in many fields of science and engineering. In this paper an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm and its variant specially designed for QE are proposed based on the authors' previous work and our implementation of those is reported. Based on analysing experimental performances, we are improving our design/synthesis of the SNCAD for its practical realization with existing efficient computational techniques and several newly introduced ones. The practicality of the SNCAD is now examined by a number of experimental results including practical engineering problems, which also reveals the quality of the implementation.

      DOI: 10.1145/1577190.1577203

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    • Computation Schemes for Splitting Fields of Polynomials Peer-reviewed

      Sebastien Orange, Guenael Renault, Kazuhiro Yokoyama

      ISSAC2009: PROCEEDINGS OF THE 2009 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION   279 - 286   2009

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:ASSOC COMPUTING MACHINERY  

      In this article, we present new results about the computation of a general shape of a triangular basis generating the splitting ideal of an irreducible polynomial given with the permutation representation of its Galois group G. We provide some theoretical results and a new general algorithm based on the study of the non redundant bases of permutation groups. These new results deeply increase the efficiency of the computation of the splitting field of a polynomial.

      DOI: 10.1145/1576702.1576741

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    • Solution of Algebraic Riccati Equations Using the Sum of Roots Peer-reviewed

      Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai, Shinji Hara

      ISSAC2009: PROCEEDINGS OF THE 2009 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION   215 - 222   2009

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:ASSOC COMPUTING MACHINERY  

      This paper constructs an algebraic solution approach to the algebraic Riccati equation, an important equation in signal processing and control system design. Key features of the proposed approach are the exploitation of useful structures inherent in the problem and the avoidance of Grobner basis computation by generic algorithms. The approach extends the algebraic approach to polynomial spectral factorization by means of the Sum of Roots. The approach further finds an effective symbolic expression of the eigenvector of the associated Hamiltonian matrix in a simple way. An example is presented to demonstrate the proposed algorithm.

      DOI: 10.1145/1576702.1576733

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    • Symbolic optimization of algebraic function Peer-reviewed

      Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai, Shinji Hara

      Proceedings of the 2008 International Symposium on Symbolic and Algebraic Computation   247 - 254   7 2008

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    • Multi-modular algorithm for computing the splitting field of a polynomial Peer-reviewed

      Guénaël Renault, Kazuhiro Yokoyama

      Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC   247 - 254   2008

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:ACM  

      Let f be a univariate monic integral polynomial of degree n and let (α1...,αn) be an n-tuple of its roots in an algebraic closure ℚ̄ of ℚ. Obtaining an algebraic representation of the splitting field ℚ (α1...,αn) of f is a question of first importance in effective Galois theory. For instance, it allows us to manipulate symbolically the roots of f. In this paper, we propose a new method based on multi-modular strategy. Actually, we provide algorithms for this task which return a triangular set encoding the splitting ideal of f. We examine the ability/practicality of the method by experiments on a real computer and study its complexity.

      DOI: 10.1145/1390768.1390803

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    • Solution of the algebraic riccati equation using the sum of roots Peer-reviewed

      Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai

      ACM Comm. Computer Algebra42 ( 3 ) 144 - 145   2008

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACM  

      DOI: 10.1145/1504347.1504359

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    • Symbolic optimization of algebraic functions Peer-reviewed

      Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai, Shinji Hara

      Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC   147 - 154   2008

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      Language:English   Publishing type:Research paper (international conference proceedings)  

      This paper attempts to establish a new framework of symbolic optimization of algebraic functions that is relevant to possibly a wide variety of practical application areas. The crucial aspects of the framework are (i) the suitable use of algebraic methods coupled with the discovery and exploitation of structural properties of the problem in the conversion process into the framework, and (ii) the feasibility of algebraic methods when performing the optimization. As an example an algebraic approach is developed for the discrete-time polynomial spectral factorization problem that illustrates the significance and relevance of the proposed framework. A numerical example of a particular control problem is also included to demonstrate the development.

      DOI: 10.1145/1390768.1390791

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    • On systems of algebraic equations with parametric exponents II Peer-reviewed

      Kazuhiro Yokoyama

      APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING18 ( 6 ) 603 - 630   12 2007

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      We deal with ideals generated by polynomials with parametric exponents, and discuss certain stability of forms of Grobner bases of those ideals. Based on the author's previous work, we investigate techniques by "slack variables" and succeed in obtaining further useful notions and new techniques using elimination ideals and ring homomorphisms. We also apply those techniques to cases, where a single parameter appears only on a single variable as its exponent, with help of univariate GCD computation of polynomials with parametric exponent. Moreover, as the original method for GCD computation could not handle some subcase and so it was not complete, we complete the method by adding a concrete procedure for handling the subcase.

      DOI: 10.1007/s00200-007-0055-8

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    • On the relationship between the sum of roots with positive real parts and polynomial spectral factorization Peer-reviewed

      Masaaki Kanno, Hirokazu Anai, Kazuhiro Yokoyama

      Numerical Methods and Applications4310   320 - 328   2007

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      This paper is concerned with the relationship between the sum of roots with positive real parts (SORPRP) of an even polynomial and the polynomial spectral factor of the even polynomial. The SORPRP and its relationship to Grobner bases are firstly reviewed. Then it is shown that the system of equations satisfied by the coefficients of the polynomial spectral factor is directly related to a Grobner basis. It is then demonstrated by means of an H-2 optimal control problem that the above fact can be used to facilitate guaranteed accuracy computation.

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    • Parametric Optimization in Control Using the Sum of Roots for Parametric Polynomial Spectral Factorization Peer-reviewed

      Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai, Shinji Hara

      ISSAC 2007: PROCEEDINGS OF THE 2007 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION   211 - +   2007

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      This paper proposes an algebraic approach for parametric optimization which can be utilized for various problems in signal processing and control. The approach exploits the relationship between the sum of roots and polynomial spectral factorization and solves parametric polynomial spectral factorization by means of the sum of roots and the theory of Grobner basis. This enables us to express quantities such as the optimal cost in terms of parameters and the sum of roots. Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs quantifier elimination. The proposed approach is demonstrated on a numerical example of a particular control problem.

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    • Sum of roots, polynomial spectral factorization, and control performance limitations Peer-reviewed

      Masaaki Kanno, Shinji Hara, Hirokazu Anai, Kazuhiro Yokoyama

      Proceedings of the IEEE Conference on Decision and Control   2968 - 2973   2007

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      It has been pointed out that the notion of the sum of roots can be utilized for solving (parametric) polynomial spectral factorization. This paper reveals another aspect of the sum of roots as an indicator of achievable performance limitations. It is shown that performance limitations for some ℋ2 control problems can be expressed as the difference of two sums of roots. An optimization approach combining the two aspects of the sum of roots is also demonstrated that minimizes the achievable performance limitation over plant parameters. © 2007 IEEE.

      DOI: 10.1109/CDC.2007.4434562

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    • On polynomial curves in the affine plane Peer-reviewed

      Mitsushi Fujimoto, Masakazu Suzuki, Kazuhiro Yokoyama

      OSAKA JOURNAL OF MATHEMATICS43 ( 3 ) 597 - 608   9 2006

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      A curve that can be parametrized by polynomials is called a polynomial curve. It is well-known that a polynomial curve has only one place at infinity. Let C be a curve with one place at infinity. Sathaye presented the following question raised by Abhyankar: Is there a polynomial curve associated with the semigroup generated by pole orders of C at infinity? In this paper, we give a negative answer to this question using Grobner basis computation.

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    • A modular method for computing the splitting field of a polynomial Peer-reviewed

      Guenael Renault, Kazuhiro Yokoyama

      ALGORITHMIC NUMBER THEORY, PROCEEDINGS4076   124 - 140   2006

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      We provide a modular method for computing the splitting field K-f of an integral polynomial f by suitable use of the byproduct of computation of its Galois group G(f) by p-adic Stauduhar's method. This method uses the knowledge of G(f) with its action on the roots of f over a p-adic number field, and it reduces the computation of K-f to solving systems of linear equations modulo some powers of p and Hensel liftings. We provide a careful treatment on reducing computational difficulty. We examine the ability/practicality of the method by experiments on a real computer and study its complexity.

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    • Stability of parametric decomposition Peer-reviewed

      Kazuhiro Yokoyama

      MATHEMATICAL SOFTWARE-ICMS 2006, PROCEEDINGS4151   391 - 402   2006

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      We deal with ideals generated by polynomials with parametric coefficients, and introduce "stabilities on ideal structures" based on stability of forms of Grobner bases. Then, we extend those stabilities to radicals and irreducible decompositions and show the computational tractability on those computations by integrating existing techniques.

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    • Sum of roots with positive real parts Peer-reviewed

      Hirokazu Anai, Shinji Hara, Kazuhiro Yokoyama

      Proceedings of ISSAC 2005   21 - 28   7 2005

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    • Cylindrical algebraic decomposition via numerical computation with validated symbolic reconstruction Peer-reviewed

      Hirokazu Anai, Kazuhiro Yokoyama

      Algorithmic Algebra and Logic (A3L2005)   25 - 30   2005

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    • Implementation of prime decomposition of polynomial ideals over small finite fields Peer-reviewed

      M Noro, K Yokoyama

      JOURNAL OF SYMBOLIC COMPUTATION38 ( 4 ) 1227 - 1246   10 2004

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

      An algorithm for the prime decomposition of polynomial ideals over small finite fields is proposed and implemented on the basis of previous work of the second author. To achieve better performance, several improvements are added to the existing algorithm, with strategies for computational flow proposed, based on experimental results. The practicality of the algorithm is examined by testing the implementation experimentally, which also reveals information about the quality of the implementation. (C) 2004 Elsevier Ltd. All rights reserved.

      DOI: 10.1016/j.jsc.2003.08.004

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    • On systems algebraic equations with parametric exponents Peer-reviewed

      Kazuhiro Yokoyama

      Proceedings of ISSAC 2004   312 - 319   7 2004

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    • Z(3) symmetry and W-3 algebra in lattice vertex operator algebras Peer-reviewed

      CY Dong, CH Lam, K Tanabe, H Yamada, K Yokoyama

      PACIFIC JOURNAL OF MATHEMATICS215 ( 2 ) 245 - 296   6 2004

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      The W-3 algebra of central charge 6/5 is realized as a sub-algebra of the vertex operator algebra V (root2A2) associated with a lattice of type root2A(2) by using both coset construction and orbifold theory. It is proved that W-3 is rational. Its irreducible modules are classified and constructed explicitly. The characters of those irreducible modules are also computed.

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    • Yet another practical implementation of polynomial factorization over finite fields Peer-reviewed

      Masayuki Noro, Kazuhiro Yokoyama

      Proceedings of ISSAC 2002   200 - 206   7 2002

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    • Order counting of elliptic curves defined over finite fields of characteristic 2 Peer-reviewed

      T Izu, J Kogure, M Noro, K Yokoyama

      ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE85 ( 1 ) 62 - 70   2002

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SCRIPTA TECHNICA-JOHN WILEY & SONS  

      Algorithms for counting the order of the rational points group are indispensable for the random selection of secure elliptic curves used in cryptosystems. In the case of curves over fields having large characteristics, it is possible to use the SEA (Schoof-Elkies-Atkin) algorithm [3, 5, 16], but in the case of elliptic curves defined over finite fields of characteristic 2, the SEA algorithm can be applied only in a modified form. In the case of characteristic 2, the authors implemented the Lercier [10] and Couveignes [2] algorithms, and combined them with an improved Intelligent Choice System [7, 8] proposed by the authors earlier. It was confirmed that in the case of characteristic 2 the combination of these methods allows for a fast generation of secure curves. (C) 2001 Scripta. Technica.

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    • Prime decomposition of polynomial ideals over finite fields Peer-reviewed

      K Yokoyama

      MATHEMATICAL SOFTWARE, PROCEEDINGS   217 - 227   2002

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      In this paper we propose new algorithm for prime decomposition of polynomial ideals over finite fields. Aiming for practical computation, we employ the strategy by Gianni et al., and modify "decomposition using generic position" with special treatment for positive characteristic.

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    • Radical representation of polynomial roots Peer-reviewed

      Hirokazu Anai, Kazuhiro Yokoyama

      JSSAC(日本数式処理学会誌)9 ( 1 ) 53 - 79   2002

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    • The block cipher SC2000 Peer-reviewed

      T Shimoyama, H Yanami, K Yokoyama, M Takenaka, K Itoh, J Yajima, N Torii, H Tanaka

      FAST SOFTWARE ENCRYPTION2355   312 - 327   2002

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      In this paper, we propose a new symmetric key block cipher SC2000 with 128-bit block length and 128-,192-,256-bit key lengths. The block cipher is constructed by piling two layers: one is a Feistel structure layer and the other is an SPN structure layer. Each operation used in two layers is S-box or logical operation, which has been well studied about security. It is a strong feature of the cipher that the fast software implementations are available by using the techniques of putting together S-boxes in various ways and of the Bitslice implementation.

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    • Efficient implementation of Schoof's algorithm in case of characteristic 2 Peer-reviewed

      T Izu, J Kogure, K Yokoyama

      PUBLIC KEY CRYTOGRAPHY1751   210 - 222   2000

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      In order to choose a secure elliptic curve for Elliptic Curve Cryptosystems, it is necessary to count the order of a randomly selected elliptic curve. Schoof's algorithm and its variants by Elkies and Atkin are known as efficient methods to count the orders of elliptic curves. Intelligent Choice System(ICS) was proposed to combine these methods efficiently. In this paper, we propose an improvement on the ICS. Further, we propose several implementation techniques in the characteristic 2 case.

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    • Order counting of elliptic curves defined over finite fields of characteristic 2 Peer-reviewed

      Tetsuya Izu, Jun Kogure, Masayuki Noro, Kazuhiro Yokoyama

        82 ( 8 ) 1253 - 1260   8 1999

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    • A modular method to compute the rational univariate representation of zero-dimensional ideals Peer-reviewed

      M Noro, K Yokoyama

      JOURNAL OF SYMBOLIC COMPUTATION28 ( 1-2 ) 243 - 263   7 1999

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

      To give an efficiently computable representation of the zeros of a zero-dimensional ideal I, Rouillier (1996) introduced the rational univariate representation (RUR) as an extension of the generalized shape lemma (GSL) proposed by Alonso et al. (1996). In this paper, we propose a new method to compute the RUR of the radical of I, and report on its practical implementation. In the new method, the RUR of the radical of I is computed efficiently by applying modular techniques to solving the systems of linear equations. The performance of the method is examined by practical experiments. We also discuss its theoretical efficiency. (C) 1999 Academic Press.

      DOI: 10.1006/jsco.1999.0275

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    • Factoring polynomials over algebraic extension fields Peer-reviewed

      Masayuki Noro, Kazuhiro Yokoyama

      城西大学情報科学研究紀要(Josai Information Science Researches)9 ( 1 ) 11 - 33   1 1998

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    • Efficient implementation of Schoof's algorithm Peer-reviewed

      T Izu, J Kogure, M Noro, K Yokoyama

      ADVANCES IN CRYPTOLOGY - ASIACRYPT'981514   66 - 79   1998

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER-VERLAG BERLIN  

      Schoof's algorithm is used to find a secure elliptic curve for cryptosystems, as it can compute the number of rational points on a randomly selected elliptic curve defined over a finite field. By realizing efficient combination of several improvements, such as Atkin-Elkies's method, the isogeny cycles method, and trial search by match-and-sort techniques, we can count the number of rational points on an elliptic curve over GF(p) in a reasonable time, where p is a prime whose size is around 240-bits.

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    • Parameters for secure elliptic curve cryptosystem -improvements on schoof’s algorithm Peer-reviewed

      Tetsuya Izu, Jun Kogure, Masayuki Noro, Kazuhiro Yokoyama

      Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)1431   253 - 257   1998

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer Verlag  

      The security of elliptic curve cryptosystem depends on the choice of an elliptic curve on which cryptographic operations are performed. Schoof's algorithm is used to define a secure elliptic curve, as it can compute the number of rational points on a randomly selected elliptic curve defined over a finite field. By realizing efficient combination of several improvements, such as Atkin-Elkies’s method, isogeny cycles method, and baby-step-giant-step algorithm, we can count the number of rational points on an elliptic curve over GF(p) in a reasonable time, where p is a prime whose size is around 240-bit.

      DOI: 10.1007/BFb0054030

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    • A modular method for computing the Galois groups of polynomials Peer-reviewed

      K. Yokoyama

      Journal of Pure and Applied Algebra117-118   617 - 636   1997

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      We propose a new method to compute the Galois group of an integral polynomial based on resolvent computation by modular techniques. We developed an exact method to find integral roots of relative resolvents by direct evaluation of invariants over some p-adic number field or its extension. Experiments on a set of test polynomials suggest that the presented method is quite practical by virtue of efficient evaluation of invariants based on modular techniques introduced here. © 1997 Elsevier Science B.V.

      DOI: 10.1016/S0022-4049(97)00030-3

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    • Computation of the splitting fields and the Galois groups of polynomials

      H Anai, M Noro, K Yokoyama

      ALGORITHMS IN ALGEBRAIC GEOMETRY AND APPLICATIONS143   29 - 50   1996

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:BIRKHAUSER VERLAG  

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    • Localization and primary decomposition of polynomial ideals Peer-reviewed

      Takeshi Shimoyama, Kazuhiro Yokoyama

      Journal of Symbolic Computation22 ( 3 ) 247 - 277   1996

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Academic Press  

      In this paper, we propose a new method for primary decomposition of a polynomial ideal, not necessarily zero-dimensional, and report on a detailed study for its practical implementation. In our method, we introduce two key techniques, effective localization and fast elimination of redundant components, by which we can get a good performance for several examples. The performance of our method is examined by comparison with other existing methods based on practical experiments. © 1996 Academic Press Limited.

      DOI: 10.1006/jsco.1996.0052

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    • Finding roots of unity among quotients of the roots of an integral polynomial Peer-reviewed

      Kazuhiro Yokoyama, Ziming Li, Istvan Nemes

      Proceedings of ISSAC 1995   85 - 89   7 1995

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    • MULTI-MODULAR APPROACH TO POLYNOMIAL-TIME FACTORIZATION OF BIVARIATE INTEGRAL POLYNOMIALS Peer-reviewed

      K YOKOYAMA, M NORO, T TAKESHIMA

      JOURNAL OF SYMBOLIC COMPUTATION17 ( 6 ) 545 - 563   6 1994

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      Efficient algorithms to factorize bivariate integral polynomials are discussed. As a key technique to provide the most efficient algorithms in theory, an approach, named multi-modular approach, is proposed and its implication is discussed intensively. The approach uses combined information from several modular factorizations of different types. Although essentially the same idea was already proposed by Chistov and Grigoryev in 1982, the concept is presented independently in detail but in a more intelligible form. Effectiveness of the multi-modular approach is proved by affording two new algorithms superior to any other existing algorithms.

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    • On Hensel construction of eigenvalues and eigenvectors of matrices with polynomial entries Peer-reviewed

      Kazuhiro Yokoyama, Taku Takeshima

      Proceedings of ISSAC 1993   218 - 224   7 1993

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    • SOLUTIONS OF SYSTEMS OF ALGEBRAIC EQUATIONS AND LINEAR-MAPS ON RESIDUE CLASS RINGS Peer-reviewed

      K YOKOYAMA, M NORO, T TAKESHIMA

      JOURNAL OF SYMBOLIC COMPUTATION14 ( 4 ) 399 - 417   10 1992

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    • ON DISTANCE TRANSITIVE GRAPHS WHOSE AUTOMORPHISM-GROUPS ARE AFFINE Peer-reviewed

      K YOKOYAMA

      JOURNAL OF COMBINATORIAL THEORY SERIES B55 ( 2 ) 190 - 235   7 1992

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS  

      By Praeger, Saxl, and Yokoyama, the classification problem of finite primitive distance transitive graphs is reduced to the case where the automorphism group is either almost simple or affine. Here we study graphs in the affine case, that is, we classify some classes of distance transitive graphs whose automorphism groups are affine.

      DOI: 10.1016/0095-8956(92)90041-U

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    • 代数制約の処理 Peer-reviewed

      竹島 卓, 横山 和弘

      コンピューターソフトウェア9 ( 6 ) 16 - 30   1992

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    • ON DETERMINING THE SOLVABILITY OF POLYNOMIALS Peer-reviewed

      K YOKOYAMA, M NORO, T TAKESHIMA

      ISSAC 90 : PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION   127 - 134   1990

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:ASSOC COMPUTING MACHINERY  

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    • ON FACTORING MULTI-VARIATE POLYNOMIALS OVER ALGEBRAICALLY CLOSED FIELDS Peer-reviewed

      K YOKOYAMA, M NORO, T TAKESHIMA

      ISSAC 90 : PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION   297 - 297   1990

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    • Computing primitive elements of extension fields Peer-reviewed

      Kazuhiro Yokoyama, Masayuki Noro, Taku Takeshima

      Journal of Symbolic Computation8 ( 6 ) 553 - 580   1989

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      Several mathematical results and new computational methods are presented for primitive elements and their minimal polynomials of algebraic extension fields. For a field Q(α1,…,αt) obtained by adjoining algebraic numbers α1,…αt to the rational number field Q, it is shown that there exists at least one vector =(s1,…,st) of integers in a specially selected set of (−1)N vectors such that s1α1+s2α2+…+stαt is a primitive element, where N is the degree of Q(α1,…,αt) over Q. Furthermore, a method is presented for directly calculating such a vector, that gives a primitive element. Finally, for a given polynomial f over Q, a new method is presented for computing a primitive element of the splitting field of f and its minimal polynomial over Q. © 1989, Academic Press Limited. All rights reserved.

      DOI: 10.1016/S0747-7171(89)80061-6

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    • Euclid環上の因数分解およびGCDについて-格子算法の応用 Peer-reviewed

      横山 和弘

      コンピュータソフトウェア ( 5 ) 42 - 61   1 1 1988

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    • On Distance Transitive Graphs in Which the Stabilizer of a Point Contains an Alternating Group Peer-reviewed

      Kazuhiro Yokoyama

      European Journal of Combinatorics9 ( 4 ) 379 - 390   1988

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Elsevier  

      Distance transitive graphs with some local properties are completely classified under the following condition: the diameter d of the graph is at least 2, the valency υ of the graph is at least 7 and the stabilizer of a point acts (υ — 2)-transitively on its neighborhood, i.e. the stabilizer contains an alternating group. © 1988, Academic Press Limited. All rights reserved.

      DOI: 10.1016/S0195-6698(88)80069-6

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    • DISTANCE TRANSITIVE GRAPHS AND FINITE SIMPLE-GROUPS Peer-reviewed

      CE PRAEGER, J SAXL, K YOKOYAMA

      PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY55   1 - 21   7 1987

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    Misc.

    • QEのための積分式の簡約化

      外川拓真, 横山和弘, 岩根秀直, 松崎拓也

      RIMS研究集会「数式処理とその周辺分野の研究 — Computer Algebra and Related Topics」   12 2016

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    • Computer algebra, its history and current state-with the Gröbner basis and quantifier elimination as the center Invited Peer-reviewed

      Masayuki Noro, Kazuhiro Yokoyama

        66 ( 3 ) 298 - 309   2014

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      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)  

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    • RL-003 A customer information analysis between enterprises using homomorphic encryption

      Yasuda Masaya, Shimoyama Takeshi, Yokoyama Kazuhiro, Kogure Jun

        12 ( 4 ) 15 - 22   20 8 2013

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      Language:Japanese   Publisher:Forum on Information Technology  

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    • 計算実代数幾何入門(第5回)CAD による QE

      穴井 宏和, 横山 和弘

      数学セミナー47 ( 4 ) 82 - 88   4 2008

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      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)   Publisher:日本評論社  

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    • 計算実代数幾何入門(第4回)CAD アルゴリズム(後半)

      穴井 宏和, 横山 和弘

      数学セミナー47 ( 3 ) 79 - 85   3 2008

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    • 計算実代数幾何入門(第3回)CAD アルゴリズム(前半)

      穴井 宏和, 横山 和弘

      数学セミナー47 ( 1 ) 76 - 82   1 2008

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      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)   Publisher:日本評論社  

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    • 計算実代数幾何入門(第2回)QE による最適化とその応用

      穴井 宏和, 横山 和弘

      数学セミナー46 ( 12 ) 75 - 81   12 2007

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      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)   Publisher:日本評論社  

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    • 計算実代数幾何入門(第1回) CAD と QE の概要

      穴井 宏和, 横山 和弘

      数学セミナー46 ( 11 ) 64 - 71   11 2007

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    • 多項式環上の素イデアル分解について(数式処理における理論とその応用の研究)

      下山 武司, 野呂 正行, 横山 和弘

      数理解析研究所講究録 ( 941 ) 7 - 14   3 1996

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      Language:Japanese   Publisher:京都大学数理解析研究所  

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    Books and Other Publications

    • Algorithms of Quantifier Elimination and their Applications

      Hirokazu Anai, Kazuhiro Yokoyama( Role: Joint author)

      8 2011  ( ISBN:9784130614061

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      Language:Japanese Book type:Scholarly book

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    • 岩波数学辞典第4版

      横山 和弘( Role: Other)

      岩波書店  3 2007 

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      Language:Japanese Book type:Dictionary, encyclopedia

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    • グレブナー基底の計算 基礎篇,計算代数入門

      横山 和弘, 野呂正行( Role: Joint author)

      東京大学出版会  6 2003 

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    Works

    • 計算機代数の暗号および制御、設計への応用 Other

      4 2000
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      Present

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    • Application of Computer Algebra to Engineering Other

      4 2000
      -
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    • オーストリア ヨハネスケプラー大学記号計算研究所(RISC-Linz) 文部科学省在外研究員 Other

      7 2003
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      9 2003

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    • フランス パリ第6大学 情報研究所(LIP6) 招聘教育研究者 Other

      5 2000
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      7 2000

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      Work type:Other  

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    • オーストリア ヨハネスケプラー大学記号計算研究所(RISC-Linz) 客員講師 Other

      11 1994
      -
      11 1995

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      Work type:Other  

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    Research Projects

    • 記号代数的近似と数値的近似の組合せによる数値数式融合計算の研究

      科学研究費助成事業 

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      4 2006 - 3 2009

      Grant type:Competitive

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    • 記号・代数計算に基づく計算技法の一般的適用方法論の確立と適用規模の拡大

      (独)科学技術振興機構  受託研究(一般受託研究) 

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      4 2005 - 3 2007

      Grant type:Competitive

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    • 種々の代数構造に現われる分解計算の計算機上での実現の研究

      日本学術振興会  科学研究費助成事業 

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      4 2003 - 3 2006

      Grant type:Competitive

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    • 数理モデリングの基礎技術

      富士通研究所  受託研究 

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      4 2004 - 3 2005

      Grant type:Competitive

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    • 記号・代数計算による最適化問題解法と定理自動証明の研究

      科学研究費助成事業 

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      4 2002 - 3 2004

      Grant type:Competitive

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    • 代数的算法に関する研究

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      Grant type:Competitive

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    • 代数的算法の工学(暗号等)への応用に関する研究

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      Grant type:Competitive

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    • 代数的組合せ論に関する研究

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      Grant type:Competitive

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    • Study on Algebraic Algorithms

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      Grant type:Competitive

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    • Study on Algebraic Combinatorics

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      Grant type:Competitive

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    • Study on Application of Algebraic Algorithm to Engineering

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      Grant type:Competitive

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    Social Contribution

    • 計算機代数国際会議 ISSAC

      1 2005 - 12 2005

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      プログラム委員

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    • 計算数学国際会議 ASCM

      1 2003 - 12 2003

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      プログラム委員

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    • 計算数学国際会議 ICMS

      1 2002 - 12 2002

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      プログラム委員

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    • 計算数学国際会議 ASCM

      1 2001 - 12 2001

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      プログラム委員長

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    • 計算数学国際会議 ASCM

      1 2000 - 12 2000

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      プログラム委員

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    • Journal of Symbolic Computation 計算ガロア理論特集号

      1 1997 - 12 1997

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      visiting editor(発行 Volume 30 Number 6, December 2000)

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    • 計算機代数国際会議 ISSAC

      1 1997 - 12 1997

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      プログラム委員

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    • 計算機代数国際会議 ISSAC

      1 1995 - 12 1995

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      ポスタープログラム委員

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    • ACM ISSAC Steering Committee

      1 1900

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    • 計算機代数国際会議 ICPSS

      1 1900

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      プログラム委員

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