Efficient KZG-based Univariate Sum-check and Lookup Argument

ePrint Report: Efficient KZG-based Univariate Sum-check and Lookup Argument

Yuncong Zhang, Shi-Feng Sun, Dawu Gu

We propose a novel KZG-based sum-check scheme, dubbed $\mathsf{Losum}$, with optimal efficiency. Particularly, its proving cost is one multi-scalar-multiplication of size $k$---the number of non-zero entries in the vector, its verification cost is one pairing plus one group scalar multiplication, and the proof consists of only one group element.


Using $\mathsf{Losum}$ as a component, we then construct a new lookup argument, named $\mathsf{Locq}$, which enjoys …

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