Efficient Algorithms for Pairing-Based Cryptosystems

We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable to that of RSA in larger characteristics. We also propose much faster algorithms for scalar multiplication and square root extraction, the latter technique being also useful in contexts other than that of pairing-based cryptography