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Today, due to the progress of technology in daily life, a variety of data security issues emerge one after another (Dong et al.,2022). People begin to pay attention to data security and privacy protection (Turesson et al., 2021), and information security has become increasingly important in daily life (Bollle et al., 2002; Lin et al., 2020). In identity management, people are also paying increasing attention to the identification and protection of biometrics. Common biometrics include fingerprint (Yang et al., 2022), iris (Lai et al., 2017), finger vein (Kirchgasser et al., 2019), and so on. Fingerprint identification technology (Wang & Hu, 2016) is the most convenient and widely used biometric technology with strong adaptability, easy operation, and high stability. At the same time, there are some problems with biometric templates that are worth noting: because biometric features are irrevocable, they cannot be reissued once they are damaged, and the authors need to ensure that the generated cancellable biological template is reproducible; in addition, biometrics are unique, and new biometrics cannot be generated if user characteristics are stolen (Ratha et al., 2001). Therefore, biometric template protection is a pivotal and urgent matter.
Biometric template protection falls into two types, including the two-factor cancellable method and the one-factor cancellable method. The two-factor cancellable biometric template protection algorithm needs an extra specific parameter from the user, which is a token or password, along with biometrics as input, to guarantee the unlinkability and revocability of the converted template. For example, reference (Teoh et al., 2004, 2006) generated a binary vector by the inner product of a feature vector and a user-specific nonsquare orthogonal random matrix and then performed threshold binarization to generate a scheme of cancellable biometric template, Biohash. Reference (Wang et al., 2017) proposed a cancellable fingerprint template using the local Hadamard transform method, which used a randomly generated token to construct a submatrix of a Hadamard matrix for local Hadamard transformation to obtain a cancellable biometric template. An original approach is proposed in the reference (Wang & Hu, 2017) and used a randomly generated token matrix to further hide the original biometric information. In a typical two-factor cancellable scheme, user-specific parameters (password or token) are important input factors, but there are also some problems caused by external factors (user-specific parameters): (i) it is necessary to keep the token or remember the password. (ii) External factors may be lost, forgotten, or stolen. (iii) The exposure of user-specific parameters may lead to the risk of conversion template intrusion, especially for some salt-based schemes.