Improving logarithmic derivative lookups using GKR

ePrint Report: Improving logarithmic derivative lookups using GKR

Shahar Papini, Ulrich Haböck

In this informal note, we instantiate the Goldwasser-Kalai-Rothblum (GKR) protocol to prove fractional sumchecks as present in lookup arguments based on logarithmic derivatives, with the following impact on the prover cost of logUp (IACR eprint 2022/1530):
When looking up $M\geq 1$ columns in a (for the sake of simplicity) single column table, the prover has to commit only to a single extra column, i.e. the multiplicities of the …

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