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Elliptic curve signatures have many advantages, however. Current attacks against elliptic curves scale exponentially with key size. Therefore ECC key and signatures can be considerably smaller than their RSA counterparts, and key generation and signing are much faster. Still, elliptic curve signatures' historically slow verification has kept these signatures out of protocols such as DNSSEC (though a draft is in progress), and still makes them a difficult choice for less powerful systems such as embedded devices and smart phones. Elliptic curve cryptosystems have improved greatly in speed over the past few years. In this paper, the authors outline a new elliptic curve signature and key agreement implementation. They achieve record speeds for signatures while remaining relatively compact.
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