Bio-cryptographic systems provide security by securing a cryptographic key with biometric data. To secure the cryptographic key, biometric data should be significantly consistent. However, the uncertainty of biometrics makes it complicated to achieve highly accurate authentication. In this paper, we propose a novel bio-cryptographic authentication scheme that improves the security of Public Key Infrastructure. To confirm authenticity of a public key and make authentication information using biometric features consistent, we created a one-way, bio-hash function by using a public-key bitstream and Zernike moments extracted from fingerprint images. Experimental results and analysis show that the proposed method prevents attackers from modifying public-key certificates and getting access to biometric data. Moreover, the results prove that the proposed method achieves very high accuracy.