8.6 Summary
In this chapter we learned about how to use elliptic curves in cryptography and especially within TLS. Elliptic curves are a special kind of mathematical structure that allows for a commutative group operation. It turns out that the discrete logarithm problem in these groups is harder than in other, more common groups such as 𝔽p∗. Moreover, they offer great flexibility via their curve parameters. We have seen how to perform Diffie-Hellman key exchange using these curves, and how secure curves are chosen to be used within the TLS handshake protocol.
In the next chapter, another application of asymmetric cryptography is introduced, namely digital signatures. Digital signatures are important tools for providing integrity protection and authenticity, but they can also serve yet another security service, namely non-repudiation. In this respect, they are very similar to physical, handwritten signatures.
