In the binary case of Elliptic-Curve-Diffie-Hellman (ECDH) exchange protocol the domain parameters are $T = (m,f(x),a,b,G,n,h)$. What is the meaning of parameter $f(x)$?

You may find the definition of the protocol in wikipedia I've gone trough other books and materials but found nothing.

  • $\begingroup$ please if you think this question is not suitable for the site provide some feedback so that i can improve it or removing it $\endgroup$
    – Rodrigo
    Nov 5, 2016 at 22:23
  • 1
    $\begingroup$ As it's listed as "in the binary case" on Wikipedia I'm fairly confident that this is the field-defining polynomial. $\endgroup$
    – SEJPM
    Nov 6, 2016 at 0:22

1 Answer 1


This Wikipedia article is simply not complete. They refer to the NIST Special Publication 800-56A (http://csrc.nist.gov/publications/nistpubs/800-56A/SP800-56A_Revision1_Mar08-2007.pdf), which is now replaced by a new version (http://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Ar2.pdf).

It seems the Wikipedia article refers to the domain parameters as indicated on page 41 for ECC CDH, of the form $\left(q,FR,a,b,G,n,h\right)$. The explanation of $FR$ is stated on page 10 of the same document:

"Field Representation indicator (an ECC domain parameter); an indication of the basis used for representing field elements. FR is NULL if the field has odd prime order or if a Gaussian normal basis is used. If a polynomial basis representation is used for a field of order $2^m$, then FR indicates the reduction polynomial (a trinomial or a pentanomial)."

As SEJPM commented, this is the polynomial which defines the field $GF(q)$. Note that up to isomorphism there is only one field $GF(q)$, but there are many ways to represent it (by choosing different $FR$). Hence it is important to specify which $FR$ was chosen for compatibility.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.