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The basic pattern matching problem is to find the locations where a pattern occurs in a text. Recently, secure pattern matching has been received much attention in various areas, including privacy-preserving DNA matching and secure biometric authentication. The aim of this paper is to give a practical solution for this problem using homomorphic encryption,(More)
In this paper, the uncertain transition matrices for inhomogeneous Markov decision processes are described by use of fuzzy sets. Introducing a ν-step contractive property, called a minorization condition, for the average case, we fined a Pareto optimal policy maximizing the average expected fuzzy rewards under some partial order. The Pareto optimal policies(More)
A discrete logarithm problem with auxiliary input (DLP-wAI) is a problem to find α from G, αG, α d G in an additive cyclic group generated by an element G of prime order r, and a positive integer d satisfying d|(r − 1). The infeasibility of this problem assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving(More)
The discrete logarithm problem (DLP) is one of the familiar problem on which cryptographic schemes rely. In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input which works better than conventional algorithms. This paper firstly reports experimental results on Cheon's algorithm for DLP on a super singular elliptic curve defined over(More)
Based on temporal difference method in neuro-dynamic programming , an adaptive policy for finite state Markov decision processes with the average reward is constructed under the minorization condition. We estimate the value function by a learning iteration algorithm. And the adaptive policy is specified as an ε-forced modification of the greedy policy for(More)