Replace fixed key for the random linear combination in aBit

[weikengchen]

This is likely left as a future TODO.

To obtain maliciously secure n-party authenticated bits, the parties, in a pairwise manner, run COT. This is followed by a random validity check.

• discussed in Step 3, Figure 14 of the AG-MPC paper: https://eprint.iacr.org/2017/189.pdf
• implemented in fpremp.h#L194

In practice, this linear combination has to be generated online, which requires a coin-tossing functionality.

This can be implemented by having each party commit to the random numbers (or a PRNG seed), broadcast the commitments, and open the commitments. See Appendix A.1 in https://eprint.iacr.org/2019/1104.pdf for more details.

[weikengchen]

A popular alternative, mentioned in Ferret and the new AG-MPC, is to hash the transcript, using the Fiat-Shamir heuristic. This could be done, but it might require some changes to the interface, as we need the COT to supply such a value.