TLS Cryptography In-Depth

8

Elliptic Curves

In the previous chapter, we got some first insights into how public-key cryptography can solve the key distribution problem even if Alice and Bob have never met before. More specifically, we learned how public-key cryptosystems can be built on two well-known problems from number theory: the discrete logarithm problem and the integer factorization problem.

Even after studying these problems for centuries – integer factorization, for example, was first investigated by the ancient Greeks – there are no known polynomial-time algorithms for these problems - at least not on conventional, non-quantum computers. For the time being, we therefore consider them to be computationally secure.

Nevertheless, to be secure in practice, cryptosystems ...