  This paper presents a study of continuous encryption functions (CEFs) of
secret feature vectors for security over networks such as physical layer
encryption for wireless communications and biometric template security for
online Internet applications. CEFs are defined to include all prior continuous
"one-way" functions. It is shown that dynamic random projection and
index-of-max (IoM) hashing algorithm 1 are not hard to attack, IoM algorithm 2
is not as hard to attack as it was thought to be, and higher-order polynomials
are easy to attack via substitution. Also presented is a new family of CEFs
based on selected components of singular value decomposition (SVD) of a
randomly modulated matrix of feature vector. Detailed empirical evidence
suggests that SVD-CEF is hard to attack. Statistical analysis of SVD-CEF
reveals its useful properties including its sensitivity to noise. The
bit-error-rate performance of a quantized SVD-CEF is shown to exceed that of
IoM algorithm 2.
