Continuous Encryption Functions for Security Over Networks

Abstract

This paper presents a study of continuous encryption functions (CEFs) of secret feature vectors for security over networks, which include physical layer encryption for wireless communications and biometric template security for online Internet applications. While CEFs are defined here to include all prior continuous one-way functions, a good CEF is defined to be a continuous function that turns a random feature vector of limited dimension into a long sequence of numbers in such a way that it is hard to invert and hard to substitute, it has no or little amplification of noise, and its output samples have zero or near-zero correlations and have identical or nearly identical distributions. A number of prior CEFs, such as dynamic random projection, index-of-max hashing and higher-order polynomials, are all shown to fail on these criteria. Based on selected components of singular value decomposition (SVD) of randomly modulated matrices of the feature vector, a family of SVD-CEFs is proposed. Such a SVD-CEF is shown to meet all the criteria for a good CEF and outperform the prior CEFs significantly.