Security in biometry is a prime concern of modern society. Identity theft is a growing problem in today’s interconnected world. To ensure a safe and secure environment biometrics is used today in many commercial, government and forensic applications. To ensure a high level of security of a biometric system we use Cryptographic algorithms. Though a number of bio-crypto algorithms have been proposed, they have limited practical applicability due to the trade-off between recognition performance and security of the template. Overall, these are very secure, however, they do have a weak point in terms of the procedure and storage of the crypto keys. Biometric authentication systems should have many exploitable crypto secure points that can be used to compromise the identification system within the optimization process. Biometric encryption with Jacobean Genus 2 Hyperelliptic curves is a security scheme that combines strong cryptographic algorithms with biometric authentication to provide enhanced security. This paper discusses the simple implementation Co-Z divisor addition formulae in a weighted representation of encryption systems for biometric software application. In this article the authors show a newly developed Co-Z approach to divisor scalar multiplication in Jacobean of Genus 2 Hyperelliptic curves over fields with odd characteristics in weighted coordinates for application in biometric-based authentication systems. We assess the performance of these biometric generation algorithms using Co-Z divisor. This approach is based upon improved additional formulae of weight 2 divisors in weighted divisor representation which, in the most frequent cases are well suited to exponentiation algorithms based on Euclidean addition chains.