## 1 Introduction  
Mutual communication environments based on wired, wireless, and mobile networks give us various service models for convenience in many domains, such as communication, education, banking, payments, entertainment, shopping, etc. Security systems are organized with devices, protocols, algorithms, and various security policies and procedures to apply more powerful security to eliminate vulnerabilities in these service models. Specifically, end-to-end or application layers in the security systems are mainly based on authentication and authorization factors (what users remember, such as a password, and what users have, such as a security card) and modern cryptographic algorithms (e.g., AES, RSA, and ECC). In these systems, the most general thought is that more security is associated with less convenience because security improvements generally require a user to possess and remember additional factors with complicated secret keys. However, these security solutions do not prevent illegal sharing and proxies. These are severe vulnerabilities in which root or increased permissions can be passed to an unauthorized user, such as an attacker, despite a system equipped with robust security solutions. Fortunately, adding biometrics to an authentication system and biometrics-based keys to cryptographic algorithms have become good solutions for added security in any system [1; 2; 3; 4; 5]. Applying biometrics to a general cryptographic algorithm-based security system protects against illegitimate sharing and proxies while improving security and usability [6]. Although using biometrics confers a significant security advantage, combining them with traditional cryptographic algorithms because all acquired biometrics from a sensor have different bit sequences, while those in a cryptographic key are the same. The fusion of biometrics and cryptography--using biometric features in conventional cryptographic algorithms--is generally referred to as bio-cryptography, and there has been increasing interest in this concept [7; 8; 9]. The initial purpose of bio-cryptography is to protect the biometrics themselves, and recently, the technique has been extended to the generation and sharing of a biometrics-based secret key [10; 11; 12; 13]. Two general approaches exist to the relationship between a biometric and its secret key: key binding and key generation. In key generation, the secret key is generated from biometrics, which includes biometric information; however, in the key binding approach, the secret key is generated from another resource or by a cryptographic mechanism, so it does not include any information from biometrics. Only biometrics is used to hide it by binding, shielding, etc. Whereas notable solutions, such as the fuzzy vault scheme, have been proposed as key binding solutions, applicable key generation schemes have not yet been proposed--despite several attempts--to the best of our knowledge [7]. The fuzzy vault scheme is the most practical key binding scheme based on the polynomial reconstruction problem [13]. Some researchers have applied it to protect biometric templates because they are irreplaceable. The template is hidden in the polynomial in the fuzzy vault for biometric template protection. Well-known fuzzy vault schemes are mainly based on fingerprints [14; 15; 16; 17; 18]. In addition to fingerprints, the fuzzy vault for variable biometrics such as faces, irises, signatures, and palmprints has also been proposed [19; 20; 21; 22; 23; 24; 25].