Elliptic Curve Digital Signature Algorithm

Elliptic Curve DSA is a variant of the Digital Signature Algorithm which operates in the elliptic curve group.

One of the reasons this algorithm is prefered over DSA is efficiqency reasons. To be as secure DSA requires that $p>2^{512}$ to be secure against a Number Field Sieve attack and $q>2^{160}$ to be secure against a BSGS attack. In practical terms this means the DSA is slower than RSA as a signature scheme.

However the elliptic curve group is not vulnerable to a Number Field Sieve attack so can be securely implemented with smaller key sizes and hence be faster than RSA.