An enhancement of privacy-preserving wildcards pattern matching

We consider secure pattern matching for some alphabet set, where gaps are represented by the character ‘*’. Generally, we know that a wildcard character ‘*’ in the pattern is used to replace zero or more letters in the text. Yasuda et al. (ACISP 2014) proposed a new packing method for somewhat homomorphic encryption for handling wildcards pattern where the wildcards replace one letter in the text. We extend the secure pattern matching so that the wildcards are replaced with any sequences. We propose a method for privacy-preserving wildcards pattern matching using somewhat homomorphic encryption in the semi-honest model. At the same time, we also propose another packing method for executing homomorphic operations between plaintext and encrypted wildcards pattern in three homomorphic multiplications rather than 3k multiplications required by Yasuda et al. method to handle k sub-patterns. Moreover, we have been able to improve the communication complexity of Yasuda et al. method by a factor k denoting the total number of sub-patterns appearing in the pattern. In addition, our practical implementation shows that our method is about k-times faster than that of Yasuda et al. Here, we show some applications of our packing method to computing secure Hamming and Euclidean distances.