Summary

In this chapter, we have analyzed some of the most used elliptic curves. We have seen what an elliptic curve is and how it is designed to be used in cryptography.

ECC has algorithms and protocols designed mainly to cover secrets related to public/private encryption systems, such as the D–H key exchange and the digital signature.

In particular, we analyzed the discrete logarithm problem transposed into ECC, so we have familiarized ourselves with the operations at the core of ECC, such as adding points on the curve and scalar multiplications.

These kinds of operations are quite different from the addition and multiplication we are familiar with; here, indeed, lies the strength of elliptic curves.

After the experimentation done on D–H ECC, we analyzed in detail secp256k1, which is the elliptic curve used to implement digital signatures on Bitcoin protocol through the ECDSA.

So, now that you have learned about elliptic curves and systems as alternative...