NIST Elliptic Curves

Related Concepts

Elliptic Curve Cryptography

Definition

The NIST elliptic curves are a set of curves from the FIPS 186-3 standard that are recommended for US federal government use.

Applications

In FIPS 186-3, NIST recommended 15 elliptic curves of varying security levels for US federal government use. The curves are of three types: random elliptic curves over a prime field, random elliptic curves over a binary (characteristic 2) field, and Koblitz [2] elliptic curves over a binary field. Some of the selection criteria and parameters are described here; see [1] for details.

Table 1 lists the NIST-recommended elliptic curves. The curve parameters were chosen so that the corresponding elliptic curve groups have prime order (for curves over $\mathbb{F}_p$) or nearly prime order (two or four times a prime) for curves over binary fields.

NIST Elliptic Curves. Table 1 NIST-recommended curves