## 2 Related Works
In this paper, we are mainly focused on some issues as follows:  
* Decreasing recognition rate with increasing chaff points The fuzzy vault scheme is based on the polynomial reconstruction problem, which cannot determine polynomial \(P(x)\) without \(k+1\) genuine points, where \(k\) is the degree of \(P(x)\). The security of vault construction via \(P(x)\) for hiding secret \(S\) depends on the number of chaff points used [13], though increasing this number creates a trade-off between security and usability. To find the \(k+1\) genuine points in UNLOCK, if \(a^{\prime}_{i}\in f^{\prime}\) satisfies \(|a_{j}-a^{\prime}_{i}|<\varepsilon\) where \(a_{j}\in f\), point \(a_{j}\) can be recognized as a candidate for a genuine point from vault \(R\). If the \(k+1\) candidate points are recognized as elements of \(Q\), the polynomial can be constructed successfully, and secret \(S^{\prime}\) recovered because \(P^{\prime}(x)=P(x)\) and \(S^{\prime}=S\). However, if the number \(r\) of chaff points in \(C\subset R\) is increased to improve security, more chaff points \((a_{i},y_{i})\) exist that may satisfy \(|a_{j}-a^{\prime}_{i}|<\varepsilon\) and be misrecognized as genuine points despite having valid biometric features as follows: \(\{(\alpha_{i},y_{i})\
otin G\}\ \wedge\{(\alpha_{i},y_{i})\in C\}\ (1\leq i\leq t)\)
* Practical implementation of polynomial reconstruction using Reed-Solomon decoding The Reed-Solomon decoding algorithm confirms that \(P^{\prime}(x)=P(x)\). The complexity of validating this is \(C(t^{\prime},k+1)\) in the UNLOCK algorithm. To find a valid polynomial, the calculation is run \(C(t^{\prime},k+1)\) times in the worst case. If the cardinality \(t^{\prime}\) of \(Q\) is larger, the complexity increases, and the scheme's usability is reduced. In previous work on this problem, [PERSON] et al. [25], [PERSON] et al. [45], and [PERSON] et al. [46] have prescribed that special use of Reed-Solomon decoding in the UNLOCK algorithm is not appropriate. * Correlation attacks to reconstruct a polynomial using the similarity of biometric features If an attacker can acquire biometric features \(f^{\prime\prime}\approx f\) or \(f^{\prime\prime}\approx f^{\prime}\), given \(f^{\prime\prime}=\alpha_{1^{\prime\prime}},\ldots,\alpha^{\prime\prime}_{t^{ \prime\prime}}\) where \(t+r\leq t^{\prime\prime}\), the attacker can determine \(Q,P^{\prime}(x),S^{\prime}\). Features \(f^{\prime\prime}\) can be generated or cracked; the attacker can generate random numbers for \(t^{\prime\prime}\) points and use these to create \(f^{\prime\prime}\), or she can crack similar biometric features to serve as \(f^{\prime\prime}\). In either case, the attacker can calculate \(P^{\prime}(x)\) by including \(k+1\) candidate points in \(f^{\prime\prime}\). This problem also increases when the number of chaff points increases because more similar points exist. Many researchers, not only those studying fuzzy vaults, have tried to solve the correlation attack problem with cancelable biometrics. Researchers have also tried to solve these problems and improve the security of the fuzzy vault scheme by increasing the number of chaff points generated by using efficient methods [35; 36]. However, these attempts have yet to be successful.