# ecc

4 articles with this tag

## Elliptic Curve Cryptography: breaking security and a comparison with RSA

This post is the fourth and last in the series ECC: a gentle introduction.

In the last post we have seen two algorithms, ECDH and ECDSA, and we have seen how the discrete logarithm problem for elliptic curves plays an important role for their security. But, if you remember, we said that we have no mathematical proofs for the complexity of the discrete logarithm …

## Elliptic Curve Cryptography: finite fields and discrete logarithms

This post is the second in the series ECC: a gentle introduction.

In the previous post, we have seen how elliptic curves over the real numbers can be used to define a group. Specifically, we have defined a rule for point addition: given three aligned points, their sum is zero ($P + Q + R = 0$). We have derived a geometric method and an algebraic method …

## Elliptic Curve Cryptography: a gentle introduction

Those of you who know what public-key cryptography is may have already heard of ECC, ECDH or ECDSA. The first is an acronym for Elliptic Curve Cryptography, the others are names for algorithms based on it.

Today, we can find elliptic curves cryptosystems in TLS, PGP and SSH, which are just three of the main technologies on which the modern web and IT world …