Authentication systems have been widely used in many security applications. One challenge in these systems is how to protect the private key. Recently, biometric-based authentication systems have been introduced for authentication systems due to the high level of security. In these systems, if biometrics are stolen, they will be lost forever, so preservation of biometric patterns is necessary. Different systems are designed to protect the biometric pattern, one of which is the fuzzy vault system. Although the fuzzy vault system can protect biometric patterns, it is vulnerable to a cross-matching attack. To overcome this problem in this study, firstly, the information extracted from the biometrics is passed through a non-invertible cancelable system, then it is encrypted by the Fuzzy vault system. With this, the proposed system is also resistant to cross-matching attacks, and also increases its security level. The cancelable system used in the proposed scheme is based on random distances and reduces the required memory by 50 %. 1- Fuzzy vault, 2- Cancelable biometric, 3- Biometric, 4- Biometric cryptosystem, 5- Cryptography