How to pair small fields with elliptic curve groups

[armfazh]

Usually, the target field for splitting secrets (such as in threshold signatures) is the field of scalars of an elliptic curve group. This allows to play with Discrete Log to ensure verifiability and other properties.

However, how to pair small fields, e.g. those of size 64 or 128 bits, with an elliptic curve group of similar size?

[chris-wood]

This is precisely why I enumerated specific fields and restricted the scheme to those fields. I think that restriction is important for security and interoperability, so I think we ought to close this and #3.