Synopsis
This book will be devoted to efficient pairing computations and implementations. Pairings are a very interesting tool for cryptographers; they provide new protocols such as Identity Based Cryptography and allow the simplification of existing protocols such as signature schemes. The implementation of a pairing involves several levels of arithmetic: the arithmetic of finite fields, extensions of finite fields, the arithmetic of elliptic curves and several algorithmic problems. Various pairings available for cryptographic use will be provided, as well as the necessary mathematical background about finite fields and elliptic curves.
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