Privacy preserving pattern matching on remote encrypted data

In this paper we propose a solution to matching bitstrings in the bitstring encrypted by stream cipher. We consider the following problem setting. There is a bitstring encrypted with owner's secret key and allocated on the remote untrusted site. The owner of these data wants to find all occurrences of some pattern presented as a bit string in the string on the remote site without revealing either pattern string or the data string on the remote site. The owner knows the secret key but he/she is not allowed to reveal either data or the pattern to the remote site. We propose an efficient algorithm that solves the problem efficiently in amortized time.