This paper presents a method to construct pairing-friendly elliptic curves of prime order and embedding degree \( k = 12 \). The authors describe an efficient algorithm to generate such curves, which are essential for pairing-based cryptosystems like short signatures with longer useful life. The proposed curves achieve a security ratio \( \rho \) close to 1, significantly improving over previous methods that typically achieve \( \rho \sim 2 \). The paper also discusses techniques to compress point and pairing values, reducing their length by up to one-third or one-sixth, and explores the use of large complex multiplication (CM) discriminants to minimize \( \rho \). Additionally, the authors consider the possibility of constructing curves with composite order over extension fields, though this remains an open problem. The paper concludes by highlighting the practical benefits of the proposed curves, including reduced bandwidth requirements and enhanced security levels.This paper presents a method to construct pairing-friendly elliptic curves of prime order and embedding degree \( k = 12 \). The authors describe an efficient algorithm to generate such curves, which are essential for pairing-based cryptosystems like short signatures with longer useful life. The proposed curves achieve a security ratio \( \rho \) close to 1, significantly improving over previous methods that typically achieve \( \rho \sim 2 \). The paper also discusses techniques to compress point and pairing values, reducing their length by up to one-third or one-sixth, and explores the use of large complex multiplication (CM) discriminants to minimize \( \rho \). Additionally, the authors consider the possibility of constructing curves with composite order over extension fields, though this remains an open problem. The paper concludes by highlighting the practical benefits of the proposed curves, including reduced bandwidth requirements and enhanced security levels.