Unconditionally provably secure cancellable biometrics based on a quotient polynomial ring

Cancelable indexing based on low-rank approximation of correlation-invariant random filtering for fast and secure biometric identification

“…In this section, we describe details of cancelable biometrics and CIRF [38,40,39]. We first explain an overview of cancelable biometrics in the case of verification and identification in Sections 2.1 and 2.2, respectively.…”

“…It is proved that the transformed template T leaks no information about the original template X: Pr(X|T ) = Pr(X) for any X ∈ Z h×w p and any T ∈ Z h×w p (i.e., perfect secrecy) [40,39]. Similarly, V leaks no information about Y : Pr(Y |V ) = Pr(Y ) for any Y ∈ Z h×w p and any V ∈ Z h×w p .…”

“…In this case, the system of equations (37) and (38) are quadratic simultaneous equations with (N + 2)hw unknown variables (i.e., X (1) , · · · , X (N ) , Y , and R * ) and (N + 1)hw equations. Similarly, the (39) and (40) are quadratic simultaneous equations with (N k + 2k + 1)(h + w) unknown variables (i.e., X…”

“…feature transformation) [34,38,40,39,46] and biometric cryptosystems [11,12,22,26]. Among them, a cancelable biometric scheme called correlation-invariant random filtering (CIRF) [38,40,39] is known as a promising template protection scheme. CIRF transforms biometric features via the 2D number theoretic transform (NTT) and random filtering.…”

“…CIRF can be applied to any kind of biometric traits whose score (distance or similarity) is measured via cross-correlation between biometric features (e.g., fingerprint [14], face [4], iris [9], finger-vein [25]) without affecting accuracy. In addition, it is proved in [40,39] that CIRF has perfect secrecy. Specifically, according to [5], a cryptosystem has perfect secrecy if any ciphertext c ∈ C (C: ciphertext space) provides no information about the plaintext m ∈ P (P: plaintext space); i.e., Pr(m|c) = Pr(m) for any m ∈ P and any c ∈ C. Similarly, it is proved in [40,39] that in CIRF, the transformed template T ∈ T (T: space of transformed templates) provides no information about the original template X ∈ X (X: space of original templates); i.e., Pr(X|T ) = Pr(X) for any X ∈ X and any T ∈ T.…”