ABSTRACT
The purpose of this chapter is to offer a brief review of all of the necessary cryptographic concepts needed in the following chapters. We start with mathematical background and the associated hard problems. The other aspect of this chapter is some facts regarding classical symmetric cryptography and the public-key cryptosystem. Finally, a concise description of provable security will be presented in the remainder of this chapter. We remark that this introduction is by no means exhaustive such that the approaches used to speed-up pairing computations or select suitable parameters of an elliptic curve is really beyond the scope of this book.
