Identity-Based Encryption from the Tate pairing on genus two curves

Abstract Identity Based Encryption is an approach to link the public key to an identity. It is an extremely useful asymmetric cryptography type in which public and private keys are computed from a known identifier such as an email address instead of being generated randomly. This allows more flexibility in managing ad-hoc public key encryption and ensuring secure communications. The aim of this work is to improve IBE scheme using the bilinear Tate pairing on genus two curves with ordinary Jacobian over large prime fields. In the first hand, we demonstrate how to compute and implement pairings efficiently over ordinary Jacobian curves of genus two over a large prime field. We introduce a new technique to avoid performing an evaluation of the Miller function at the reduced divisor, which provides a reduced Miller’s algorithm to compute pairings. Furthermore, the final exponentiation is simplified to a minimum computation using the structure of the pairing-friendly curves. Numerical results are obtained via our implementation in Python for different security levels. In the second hand, we present a full description of functional IBE scheme using the optimization of the Tate pairing computations. The proposed application answers a question of Boneh and Franklin [2] about the possibility of using the Tate pairing in IBE schemes and represents the first IBE exploiting pairings in genus two. We provide a full description of a functional IBE scheme using our optimization of the Tate pairing computations.