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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)
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 with auxiliary input (DLP-wAI) is a problem to find α from G, αG, α d G in an additive cyclic group generated by G of prime order r and a positive integer d dividing r − 1. The infeasibility of DLPwAI assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLP-wAI. This paper(More)
—The discrete logarithm problem (DLP) is one of the familiar problem on which some cryptographic schemes rely. In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input which works better than conventional algorithms. In this paper, we show our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF(3(More)