Cryptography and biometrics are widely used in providing information security. Cryptographic systems rely on keys for secure information. Unlike biometric systems, the keys in cryptographic systems must be exactly reproducible and not strongly linked to the user identity. Each of the two systems has some issue associated with it. Combining cryptography and biometrics in a secure way can mitigate these issues. This paper presents a secure cryptographic authentication method based on the discrete logarithm problem. Through the security analysis of the proposed scheme, we prove that the security characteristics of the proposed scheme relative to the properties of the discrete logarithm problem. Based on the proposed scheme, a biometric cryptosystem is constructed. The proposed system evaluated using CASIA iris database from 70 different eyes, with 7 samples of each eye. Experimental results demonstrate that the proposed system is more effective, promising in terms of cope up to 21.41% percent of error bits within an iris code, and can generate up to 98 bits of the cryptographic key from the iris codes.