As we pointed out in the previous chapter, elliptic curves have various advantages in cryptosystems based on discrete logs. However, as we’ll see in this chapter, they also open up exciting new vistas for cryptographic applications. The existence of a bilinear pairing on certain elliptic curves is what makes this possible.

First, we’ll describe one of these pairings. Then we’ll give various applications, including identity-based encryption, digital signatures, and encrypted keyword searches.