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Simplier TurboPlonk relation

Open alxiong opened this issue 1 year ago • 0 comments

Currently, our customized gate formula is:

Screenshot 2022-11-10 at 12 58 41 AM

@zhenfeizhang has suggested that since currently the gadgets we use either use linear combination selectors q_lc := (q1~q4) or hash (degree 5) selectors q_hash:=(qH1~qH4), but not at the same time, maybe we can simplify the formula to (... are remaining parts that stays unchanged):

$$ \textcolor{red}{(1 - q_H) \cdot} (q_1 \cdot w_1 + q_2 \cdot w_2 + q_3 \cdot w_3 + q_4 \cdot w_4 ) + \textcolor{red}{q_H \cdot (q_1 \cdot w_1^5 + q_2 \cdot w_2^5 + q_3 \cdot w_3^5 + q_4 \cdot w_4^5)} + \ldots $$

In this way, we can save 3 q_H selectors which translate to 3 group elements in verification keys and 3 field elements in proof size.

Current WIP: https://github.com/EspressoSystems/jellyfish/tree/simpler-turboplonk

alxiong avatar Nov 09 '22 17:11 alxiong