Reference Work Entry

Encyclopedia of Cryptography and Security

pp 843-844

NIST Elliptic Curves

  • Darrel HankersonAffiliated withDepartment of Mathematics, Auburn University
  • , Alfred MenezesAffiliated withDepartment of Combinatorics and Optimization, University of Waterloo

Related Concepts

Elliptic Curve Cryptography


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


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.

For the curves over \(\mathbb{F}[p]\), the primes p are Mersenne-like and chosen to allow fast reduction of integers modul ...

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