Pairing Compression on Some Elliptic Curves with Subgroups of Embedding Degree 6 and Its Applications to Pairing-Based Cryptography

As a subfield of elliptic curve cryptography, pairing-based cryptography has gained significant attention due to its practical and flexible functionality. In pairing-based cryptographic systems, it is necessary to have elliptic curves defined over finite fields with an appropriate embedding degree and non-degenerate bilinear pairing maps. This paper primarily focuses on the pairing maps. When certain conditions are met, it becomes feasible to compress the pairing values simultaneously on specific elliptic curves, achieving a compression ratio of 1/6. Additionally, in pairing-based cryptography, it is feasible to represent the elliptic curve points only by their x-coordinate or y-coordinate through a compression function. This approach enables saving a significant amount of communication or storage in protocols such as BLS and IBE, thereby enhancing their efficiency.