# Cancelable Multimodal Biometrics Based on Chaotic Maps
## 2 Overview of Related Work  
In the literature, cryptography and specifically chaos-based techniques have been employed for the generation of cancelable biometric templates. An overview of recent chaos-based approaches that have been proposed to protect biometric templates is presented in this section. A non-invertible chaotic map-based transformation for the protection of face templates was addressed in [6]. In this approach, the Logistic map metric is utilized to produce linearly independent vectors for random projection in a way that the constructed projection matrix depends on the identity of the individual to whom belongs the biometric template. The experimental results have shown the efficacy of the suggested technique to meet the requirements of biometric systems. An extension study of this approach that provided rigorous performance and security experiments and analysis using different biometric modalities was presented in [7]. In [8], the authors presented the design of an approach for the protection of biometric templates using the chaotic behavior of a Logistic map. The transform approach uses the user's secret key to mix the plain face features with a chaotic random matrix. The biometric authentication system satisfied the privacy, diversity, and revocability requirements. Furthermore, a reasonable level of performance was reached. In [9], the authors used biohashing in combination with chaos-based permutation to improve the privacy and security of biometric templates. The extracted face features using PCA or LDA are subjected to permutation before applying the biohashing. Their approach satisfied a good level of security and achieved comparable recognition accuracy to the traditional biohashing method. In [10], a chaos-based image cryptosystem was proposed to protect fingerprint templates. The proposed scheme design is composed of four chaotic algorithms: two 1D and two 3D chaotic maps. The advantage of the scheme is increasing the keyspace to thwart brute force attacks. The security analysis showed that the scheme satisfied the randomness characteristic of a secure cryptosystem. In [11], the authors introduced a chaos-based encryption algorithm that merges [PERSON]'s scheme and the Logistic map to ensure a higher security level of fingerprint templates. In addition, the statistical security analysis was entirely highlighted to prove the efficiency of the approach in real-world applications. However, the scheme fails to satisfy the revocability of the biometric data. [PERSON] et al. [12] developed an encryption-based method for biometric template protection using a combination of logistic mapping and dynamic Bernoulli mapping, hence allowing to improve the reliability of the cryptographic system in terms of volatility and correlation. The analysis of experimental results demonstrated that the scheme is simple to implement and yet resistant to attacks. [PERSON] et al. [13] proposed to protect face templates using a cryptosystem combining schemes of binarization transform, chaos-based feature permutation, and fuzzy commitment. The chaos-based feature permutation aimed to counter the cross-matching attacks against the fuzzy commitment scheme by generating cancelable templates, attaining better security and unlinkability features. Experimental results showed that the system gained improved discriminability, privacy, and security. [PERSON] et al. [14] suggested a nonlinear chaos-based cryptosystem approach to protect biometric templates stored in system databases. In their approach, a 2D Logistic Sine Map was used by joining the 2D Logistic map and 1D sine map to generate large dimension chaotic keys based on the confusion and diffusion stages of the encryption. Experimental results and analysis proved the swiftness, security, and efficiency of implementing the scheme in real-time applications. In [15], the authors presented a cancelable biometric approach that involved using chaotic maps to generate convolution kernels that are employed to extract encrypted Gabor features from iris images.