Bio-cryptographic systems provide security by securing a cryptographic key with biometric data. To secure the crypto-graphic 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 authentic- ity 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 biomet- ric data. Moreover, the results prove that the proposed method achieves very high accuracy.