Hiroshi Kai | Ehime University (original) (raw)

Papers by Hiroshi Kai

Research paper thumbnail of Hybrid Method for Solving Polynomial Equations

We discuss how to decompose the zero set of a multivariate polynomial system with inexact coecien... more We discuss how to decompose the zero set of a multivariate polynomial system with inexact coecien ts to a sequence of zero sets of reduced triangular sets in a numerically stable way.

Research paper thumbnail of Approximate computation of pseudovarieties

ACM SIGSAM Bulletin, 2003

Research paper thumbnail of Rational Interpolation and Its Ill-conditioned Property

Trends in Mathematics, 2007

A rational interpolation is obtained by solving a system of linear equations. However, when the s... more A rational interpolation is obtained by solving a system of linear equations. However, when the system is solved by floating point arithmetic, there appears a pathological feature such as undesired zeros and poles. In this paper, a method is described with the help from computer assisted proof to eliminate the feature.

Research paper thumbnail of Symbolic-numeric computation of Wu's method using stabilizing algorithm

A symbolic-numeric combined method to solve polynomial equations have been proposed by using Ritt... more A symbolic-numeric combined method to solve polynomial equations have been proposed by using Ritt-Wu's characteristic sets method. The method is extended 1) to solve a system of polynomial equations with floating point coecients and 2) to speed up by using parallel computations. Especially, in 1), above, the stabilization technique proposed by Shirayanagi and Sweedler is used. A parallelized method for

Research paper thumbnail of Cheater identification on a secret sharing scheme using GCD

ACM Communications in Computer Algebra, 2011

A method to identify cheaters on the Shamir's (k, n) threshold secret sh... more A method to identify cheaters on the Shamir's (k, n) threshold secret sharing scheme is proposed using rational interpolation. When a rational interpolant is computed for l shares Di, i = 1, ... , l, where l = k + 2s, then s unattainable points of the rational interpolant may identify s cheaters. The cheaters can be computed by GCD

Research paper thumbnail of Hybrid computation of bivariate rational interpolation

ACM SIGSAM Bulletin, 2000

ABSTRACT This paper shows how to solve homogeneous polynomial systems that contain parameters. Th... more ABSTRACT This paper shows how to solve homogeneous polynomial systems that contain parameters. The Hilbert function is used to check that the specialization of a 'generic' Gröbner basis of the parametric homogeneous polynomial system (computed in a polynomial ...

Research paper thumbnail of Hybrid computation of Cauchy-type singular integral equations

ACM SIGSAM Bulletin, 1998

ABSTRACT An abstract is not available.

Research paper thumbnail of Cauchy principal value integral using hybrid integral

ACM SIGSAM Bulletin, 1997

ABSTRACT Let P1 and P2 be polynomials, univariate or multivariate, and let (P1, P2, P3,…, Pi,…) b... more ABSTRACT Let P1 and P2 be polynomials, univariate or multivariate, and let (P1, P2, P3,…, Pi,…) be a polynomial remainder sequence. ...

Research paper thumbnail of Generating A Mathematical Web Service Client With xfy

Research paper thumbnail of Hybrid Rational Function Approximation and Its Accuracy Analysis

Reliable Computing, 2000

We propose a rational function approximation method combining numeric and symbolic computations. ... more We propose a rational function approximation method combining numeric and symbolic computations. Given functions or data are first interpolated by a rational function, i.e. the ratio of polynomials. Undesired poles appearing in the rational interpolant are removed by an approximate-GCD method. We call the rational approximation a Hybrid Rational Function Approximation and abbreviate it as HRFA. In this paper we give a short survey of the HRFA and then discuss its accuracy analysis by using the approximate-GCD proposed by Pan.

Research paper thumbnail of Hybrid rational approximation and its applications

Research paper thumbnail of Hybrid method for computing the nearest singular polynomials

Japan Journal of Industrial and Applied Mathematics, 2004

In this paper, we propose a combined symbolic-numeric algorithm for computing the nearest singula... more In this paper, we propose a combined symbolic-numeric algorithm for computing the nearest singular polynomial and its multiple zero. Explicit expressions of the minimal perturbation and the nearest singular polynomials are presented. A theoretical error bound and several numerical examples are given.

Research paper thumbnail of Security Flaw in SAS-2 Protocol

IEICE Transactions on Communications, 2005

ABSTRACT SAS-2 is an alternative of a one-time password authentication protocol SAS, and is devel... more ABSTRACT SAS-2 is an alternative of a one-time password authentication protocol SAS, and is developed in order to reduce overhead due to the use of hash functions. The idea of both algorithms is sharing a similar secret number called the verifier that allows a client to be authenticated and that is changed for each new session. However, some of the combinations proposed in [1] to transmit the verifier may contain a security flaw, and the insecure combination results in vulnerability to impersonation attacks.

Research paper thumbnail of A hybrid integral for parametrized rational functions

International Symposium on Symbolic and Algebraic Computation, 2007

We present a hybrid integral to obtain symbolic results of an indefinite integral where the integ... more We present a hybrid integral to obtain symbolic results of an indefinite integral where the integrand is an univariate rational function whose coeficients have a parameter. We consider calculating power series roots of the denominator polynomial by applying Hensel construction. Accurate numerical results for a definite integral are easily obtained by simple substitutions of upper and lower bounds of integral

Research paper thumbnail of Hybrid Method for Solving Polynomial Equations

We discuss how to decompose the zero set of a multivariate polynomial system with inexact coecien... more We discuss how to decompose the zero set of a multivariate polynomial system with inexact coecien ts to a sequence of zero sets of reduced triangular sets in a numerically stable way.

Research paper thumbnail of Approximate computation of pseudovarieties

ACM SIGSAM Bulletin, 2003

Research paper thumbnail of Rational Interpolation and Its Ill-conditioned Property

Trends in Mathematics, 2007

A rational interpolation is obtained by solving a system of linear equations. However, when the s... more A rational interpolation is obtained by solving a system of linear equations. However, when the system is solved by floating point arithmetic, there appears a pathological feature such as undesired zeros and poles. In this paper, a method is described with the help from computer assisted proof to eliminate the feature.

Research paper thumbnail of Symbolic-numeric computation of Wu's method using stabilizing algorithm

A symbolic-numeric combined method to solve polynomial equations have been proposed by using Ritt... more A symbolic-numeric combined method to solve polynomial equations have been proposed by using Ritt-Wu's characteristic sets method. The method is extended 1) to solve a system of polynomial equations with floating point coecients and 2) to speed up by using parallel computations. Especially, in 1), above, the stabilization technique proposed by Shirayanagi and Sweedler is used. A parallelized method for

Research paper thumbnail of Cheater identification on a secret sharing scheme using GCD

ACM Communications in Computer Algebra, 2011

A method to identify cheaters on the Shamir's (k, n) threshold secret sh... more A method to identify cheaters on the Shamir's (k, n) threshold secret sharing scheme is proposed using rational interpolation. When a rational interpolant is computed for l shares Di, i = 1, ... , l, where l = k + 2s, then s unattainable points of the rational interpolant may identify s cheaters. The cheaters can be computed by GCD

Research paper thumbnail of Hybrid computation of bivariate rational interpolation

ACM SIGSAM Bulletin, 2000

ABSTRACT This paper shows how to solve homogeneous polynomial systems that contain parameters. Th... more ABSTRACT This paper shows how to solve homogeneous polynomial systems that contain parameters. The Hilbert function is used to check that the specialization of a 'generic' Gröbner basis of the parametric homogeneous polynomial system (computed in a polynomial ...

Research paper thumbnail of Hybrid computation of Cauchy-type singular integral equations

ACM SIGSAM Bulletin, 1998

ABSTRACT An abstract is not available.

Research paper thumbnail of Cauchy principal value integral using hybrid integral

ACM SIGSAM Bulletin, 1997

ABSTRACT Let P1 and P2 be polynomials, univariate or multivariate, and let (P1, P2, P3,…, Pi,…) b... more ABSTRACT Let P1 and P2 be polynomials, univariate or multivariate, and let (P1, P2, P3,…, Pi,…) be a polynomial remainder sequence. ...

Research paper thumbnail of Generating A Mathematical Web Service Client With xfy

Research paper thumbnail of Hybrid Rational Function Approximation and Its Accuracy Analysis

Reliable Computing, 2000

We propose a rational function approximation method combining numeric and symbolic computations. ... more We propose a rational function approximation method combining numeric and symbolic computations. Given functions or data are first interpolated by a rational function, i.e. the ratio of polynomials. Undesired poles appearing in the rational interpolant are removed by an approximate-GCD method. We call the rational approximation a Hybrid Rational Function Approximation and abbreviate it as HRFA. In this paper we give a short survey of the HRFA and then discuss its accuracy analysis by using the approximate-GCD proposed by Pan.

Research paper thumbnail of Hybrid rational approximation and its applications

Research paper thumbnail of Hybrid method for computing the nearest singular polynomials

Japan Journal of Industrial and Applied Mathematics, 2004

In this paper, we propose a combined symbolic-numeric algorithm for computing the nearest singula... more In this paper, we propose a combined symbolic-numeric algorithm for computing the nearest singular polynomial and its multiple zero. Explicit expressions of the minimal perturbation and the nearest singular polynomials are presented. A theoretical error bound and several numerical examples are given.

Research paper thumbnail of Security Flaw in SAS-2 Protocol

IEICE Transactions on Communications, 2005

ABSTRACT SAS-2 is an alternative of a one-time password authentication protocol SAS, and is devel... more ABSTRACT SAS-2 is an alternative of a one-time password authentication protocol SAS, and is developed in order to reduce overhead due to the use of hash functions. The idea of both algorithms is sharing a similar secret number called the verifier that allows a client to be authenticated and that is changed for each new session. However, some of the combinations proposed in [1] to transmit the verifier may contain a security flaw, and the insecure combination results in vulnerability to impersonation attacks.

Research paper thumbnail of A hybrid integral for parametrized rational functions

International Symposium on Symbolic and Algebraic Computation, 2007

We present a hybrid integral to obtain symbolic results of an indefinite integral where the integ... more We present a hybrid integral to obtain symbolic results of an indefinite integral where the integrand is an univariate rational function whose coeficients have a parameter. We consider calculating power series roots of the denominator polynomial by applying Hensel construction. Accurate numerical results for a definite integral are easily obtained by simple substitutions of upper and lower bounds of integral