A fast algorithm for polynomial reconstruction of fuzzy fingerprint vault

Abstract

Abstract:In recent years, a cryptographic construct, called fuzzy vault, has been proposed, which aims to secure critical data (e.g., secret encryption key) with the fingerprint data in a way that only the authorized user can access the secret by providing the valid fingerprint, and some implementation results have been reported. However, all the previous results adopted the brute-force search to reconstruct the polynomial or skipped the procedure for the polynomial reconstruction. In this paper, we propose a fast polynomial reconstruction algorithm for the fuzzy fingerprint vault which can improve the execution time of the brute-force search by a factor of 300∼1,500.

Review of key‐binding‐based biometric data protection schemes

“…Other attacks to which the FV has been subjected to include a brute force attack [126], collusion attack [127] and fast polynomial reconstruction attack [128]. Especially, the last attack (fast polynomial reconstruction) is very much interesting as it claims that the original polynomial of the vault could be accurately reconstructed if the number of genuine points exceeded the degree of the polynomial by two.…”

Protection of the Fingerprint Minutiae

“…This gives exactly the same solution as the Gaussian elimination. The proof can be found on the reference (Choi et al, 2008).…”

“…In this section, we introduce a fast algorithm for the polynomial reconstruction (Choi et al, 2008). To begin with, let us consider the following theorem which provides the conditions under which a linear system of m equations in n unknowns is guaranteed to be consistent.…”

Subspace Fuzzy Vault

“…It was shown in [15] that certain reasonable parameters for the PFV scheme cause the system to be susceptible to a brute force attack. Choi et al in [2] speed up the attack by using a fast polynomial reconstruction algorithm. These attacks may indicate that additional security measures should be taken to prevent the loss of a user's features.…”

“…Lemma 2. In the above settings, let δ 0 be so that α 2 (k, δ 0 , n) < 1 from equation (2). On average, an attacker can recover the secret key in C • (r/t) δ 0 operations, where C < 0.55 • n(δ 2 0 − δ 0 ).…”