Biometric authentication has attracted attention because of its high security and convenience. However, biometric feature such as fingerprint can not be revoked like passwords. Thus once the biometric data of a user stored in the system has been compromised, it can not be used for authentication securely for his/her whole life long. To address this issue, an authentication scheme called cancelable biometrics has been studied. However, there remains a major challenge to achieve both strong security and practical accuracy. In this paper, we propose a novel and fundamental algorithm for cancelable biometrics called correlation-invariant random filtering (CIRF) with provable security. Then we construct a method for generating cancelable fingerprint templates based on the chip matching algorithm and the CIRF. Experimental evaluation shows that our method has almost the same accuracy as the conventional fingerprint verification based on the chip matching algorithm.