# Prime extension field encoding ASN.1

ASN.1 encoding for elliptic curve cryptography is recommended by Certicom, as explained at a related question, covering curves over prime fields and binary extension fields.

I'm looking for known recommendations for encoding curves defined over prime extension fields that are suitable for pairing. At best, generally acceptable ASN.1 modules for target group elements, and $\mathbb G_1$ and $\mathbb G_2$ elements (points on curves over base prime field and over extension).

Google search returns nothing relevant. Any known recommendations please?

To refine the question, encoding is well-defined for two classes of curves: over a large extension of binary field and over a prime field. For pairing, popular choice is Barreto-Naehrig parameterized curves family defined over 12th extension of a prime field. MNT curves is another example. Both examples do not quite fit Appendix C of SEC1v2. In particular, trinomial or pentamonial polynomials do not make sense in this case.

Would it be reasonable to believe no agreement/consensus was attempted on encoding pairing-specific curves yet?

• Could you detail your question a bit more? What are you looking for exactly? For instance [SEC1v2](www.secg.org/sec1-v2.pdf#page=106) contains a lot of information regarding ASN.1 encoding and Elliptic curves and is usually used as the reference by many current implementations (OpenSSL, Go, mbedTLS, etc.) – Lery Jul 10 '17 at 16:39
• @Lery thank you. Prime field extension encoding probably is the major roadblock. Please take a look at the update. – Vadym Fedyukovych Jul 10 '17 at 20:58