Interdisciplinary Information Sciences

Regular Papers

Construction, Randomness and Security of New Hash Functions Derived from Chaos Mappings

Hirotake YAGUCHI, Sumie UEDA

2012 年 18 巻 1 号 p. 1-11
発行日: 2012年
公開日: 2012/03/28

DOIhttps://doi.org/10.4036/iis.2012.1

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We introduce new hash functions SSInhash, n=160, 192, 256, 384, 512, 1024 and 2048, whose algorithm is, differently from many other hash functions, consisting of multiplication and shift of multiple-precision integers. The base of algorithm is a repetition of piecewise linear chaos mappings called SSR computations. We first construct a tiny hash function SSRhash which is derived from SSR algorithm directly, and then translate it into all-integer version SSInhash whose hash value is n bits. After constructing hash functions we verify randomness of hash values generated by SSInhash by applying the NIST statistical test suite and TestU01. We further discuss the security of our hash function by deriving algebraic equation of high degree.

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Development of a Japanese Version of the Object-Spatial Imagery Questionnaire (J-OSIQ)

Masahiro KAWAHARA, Kazuo MATSUOKA

2012 年 18 巻 1 号 p. 13-18
発行日: 2012年
公開日: 2012/03/28

DOIhttps://doi.org/10.4036/iis.2012.13

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The Object-Spatial Imagery Questionnaire (OSIQ) is a measure of individual differences in visual imagery preferences. In the present study, we attempted to develop a Japanese version of the OSIQ (J-OSIQ). On the basis of principal components analysis, we obtained two factors in the questionnaire. An object imagery scale (15 items) assesses preferences for representing colorful, pictorial, high-resolution images of individual objects or scenes. A spatial imagery scale (15 items) assesses preferences for representing schematic images of objects and spatial locations of objects. The reliabilities of these factors were similar to those of the original version. Additionally, we showed that the object imagery scale was selectively correlated with object imagery measures, whereas the spatial imagery scale was selectively correlated with spatial imagery tests. These results demonstrate that the J-OSIQ is useful for measuring preferences for object and spatial imagery in Japanese.

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A Remark on Löwner's Theorem

Toshiyuki SUGAWA

2012 年 18 巻 1 号 p. 19-22
発行日: 2012年
公開日: 2012/05/16

DOIhttps://doi.org/10.4036/iis.2012.19

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We give a refinement of Löwner's inequality with argument of the equality case. To this end, we establish a complete univalence criterion for meromorphic functions of special type. We also give applications of the refinement.

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A Note on Super Catalan Numbers

Evangelos GEORGIADIS, Akihiro MUNEMASA, Hajime TANAKA

2012 年 18 巻 1 号 p. 23-24
発行日: 2012年
公開日: 2012/06/21

DOIhttps://doi.org/10.4036/iis.2012.23

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We show that the super Catalan numbers are special values of the Krawtchouk polynomials by deriving an expression for the super Catalan numbers in terms of a signed set.

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Distributed Construction of Trust Anchor with the Hyper-Powering Signature Scheme

Eisuke KOIZUMI, Marika MINAGAWA, Hiroki SHIZUYA

2012 年 18 巻 1 号 p. 25-36
発行日: 2012年
公開日: 2012/06/21

DOIhttps://doi.org/10.4036/iis.2012.25

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In this paper, we explore a strategy for recovering a PKI system without reconstructing the whole one when the trust anchor has been broken. Specifically, we propose two distributed signature schemes based on the hyper-powering discrete logarithm problem, which is a two-dimensional extension of the discrete logarithm problem. We show that these schemes are existentially unforgeable against the adaptively chosen message attack.

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Deciding Nonconstructibility of 3-Balls with Strict Spanning Edges

Satoshi KAMEI

2012 年 18 巻 1 号 p. 37-41
発行日: 2012年
公開日: 2012/10/04

DOIhttps://doi.org/10.4036/iis.2012.37

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In this paper, we consider constructibility of simplicial 3-balls. Examining 1-dimensional subcomplexes of a simplicial 3-ball is efficient to solve the decision problem whether the simplicial 3-ball is constructible or not. From the point of view, we consider the case where a simplicial 3-ball has spanning edges and present a sufficient condition for nonconstructibility.

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Spectra of Manhattan Products of Directed Paths P_n#P₂

Nobuaki OBATA

2012 年 18 巻 1 号 p. 43-54
発行日: 2012年
公開日: 2012/10/30

DOIhttps://doi.org/10.4036/iis.2012.43

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The Manhattan product of directed paths P_n and P_m is a digraph, where the underlying graph is the n×m lattice and each edge is given direction in such a way that left and right directed horizontal lines are placed alternately, and so are up and down directed vertical lines. Unless both m and n are even, the Manhattan product of P_n and P_m is unique up to isomorphisms, which is called standard and denoted by P_n#P_m. If both m and n are even, there is a Manhattan product which is not isomorphic to the standard one. It is called non-standard and denoted by P_n#^′P_m. The characteristic polynomials of P_n#P₂ and P_n#^′P₂ are expressed in terms of the Chebychev polynomials of the second kind, and their spectra (eigenvalues with multiplicities) are thereby determined explicitly. In particular, it is shown that ev (P_2n-1#P₂)=ev (P_2n#P₂) and ev (P_2n#^′P₂)=ev (P_2n+2#P₂). The limit of the spectral distribution of P_n#P2 as n→∞ exists in the sense of weak convergence and its concrete form is obtained.

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Learning Algorithm for Boltzmann Machines Using Max-Product Algorithm and Pseudo-Likelihood

Muneki YASUDA, Junya TANNAI, Kazuyuki TANAKA

2012 年 18 巻 1 号 p. 55-63
発行日: 2012年
公開日: 2012/12/05

DOIhttps://doi.org/10.4036/iis.2012.55

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Boltzmann machines are parametric probabilistic models for the statistical machine learning, forming Markov random fields. Owing to their normalization constant, inference and learning in Boltzmann machines are generally classified under NP-hard problems. Maximum pseudo-likelihood estimation is an effective approximate learning method for Boltzmann machines. However, in principle, we cannot use this method for incomplete data sets, except for some special cases. In this paper, we propose a new learning algorithm for Boltzmann machines with incomplete data sets by generating a pseudo-complete data set from a given incomplete data using the max-product algorithm and the Markov chain Monte Carlo method, and then, by applying maximum pseudo-likelihood estimation to the pseudo-complete data set.

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