Elliptic Curve Digital Signature Algorithm

Elliptic Curve DSA (EC-DSA) is a variant of the Digital Signature Algorithm which operates on elliptic curve groups.

One of the reasons this algorithm is preferred over DSA is for efficiency reasons. To be 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 Baby-step giant-step attack. In practical terms this means the DSA is slower than RSA as a signature scheme.

However elliptic curve groups are not vulnerable to a Number Field Sieve attack, so they can be securely implemented with smaller key sizes and can be faster than RSA.