On scrambling the Burrows–Wheeler transform to provide privacy in lossless compression

The usual way of ensuring the confidentiality of the compressed data is to encrypt it with a standard encryption algorithm. Although the computational cost of encryption is practically tolerable in most cases, the lack of flexibility to perform pattern matching on the compressed data due to the encryption level is the main disadvantage. Another alternative to provide privacy in compression is to alter the compression algorithms in such a way that the decompression requires the knowledge of some secret parameters. Securing the arithmetic and Huffman coders along with the dictionary based schemes have been previously studied, where Burrows–Wheeler transform (BWT) has not been addressed before in that sense. On BWT of an input data it is not possible to perform a successful search nor construct any part of it without the proper knowledge of the lexicographical ordering used in the construction. Based upon this observation, this study investigates methods to provide privacy in BWT by using a randomly selected permutation of the input symbols as the lexicographical order. The proposed technique aims to support pattern matching on compressed data, while still retaining the confidentiality. Unifying compression and security in a single step is also considered instead of the two-level compress-then-encrypt paradigm.