ABSTRACT
This chapter discusses the cryptographic building blocks where the use of a bilinear pairing is definitely an advantage, compared to the historical use of finite fields as in traditional constructions. The construction of these new cryptographic solutions requires the use of new mathematical tools, and, in this context, pairings are the most important and most often used ones in the current literature. Digital signatures are today one of the most famous cryptographic tools used in real-world applications. Since the introduction of public key cryptography, and the publication of RSA cryptosystem, many new signature schemes have been proposed, and one of the most challenging tasks for cryptographers has been to design such tools tailored for lightweight devices. In public key encryption schemes, as said previously, everyone can encrypt a message by using the public key and only the entity having access to the related secret key will be able to decrypt and read the initial message.
