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brave / sta-rs

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Use power-of-two field for secret sharing #9

Open alxdavids opened 3 years ago

alxdavids commented 3 years ago

Overview

Currently we use the default prime-order field that is provided in the https://github.com/zkcrypto/ff crate, i.e. the 255-bit that is used by the JubJub curve: https://github.com/brave-experiments/sta-rs/blob/main/sharks/src/share_ff.rs#L11-L15. We need to use such a large field to ensure that there are not collisions during the sharing process in the sta-rs protocol.

For the Shamir-based secret sharing approach we use, we could also the finite Galois field GF(2^256) which would provide us with a cleaner modulus that allows us to fit in 32 bytes of data into a single share. Unfortunately I couldn't previously find instantiations of this field anywhere.

Task

Replace the usage of the current prime-order field with an implementation of GF(2^256).

alxdavids commented 2 years ago

After doing an investigation, I wasn't able to find a power-of-two field implementation in rust that would really work for what we need. Personally, I think this is low-priority because the field itself does not impact security, and the implementations that we have seem efficient enough.