Logarithmic derivatives translate products of linear factors into sums of their reciprocals,
turning zeroes into simple poles of same multiplicity. Based on this simple fact, we construct …

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 …

We present a protocol for checking the values of a committed polynomial $ f\in\mathbb {F} _
{< n}[X] $ over a multiplicative subgroup $ H\subset\mathbb {F} $ of size $ n $, are contained …

We present a protocol for checking the values of a committed polynomial $\phi (X) $ over a
multiplicative subgroup $ H\subset\mathbb {F} $ of size $ m $ are contained in a table …

We present a protocol called $\mathsf {cq} $ for checking the values of a committed
polynomial $ f (X)\in\mathbb {F} _ {< n}(X) $ over a multiplicative subgroup …

This paper introduces Lasso, a new family of lookup arguments, which allow an untrusted
prover to commit to a vector a∈ F m and prove that all entries of a reside in some …

We present position-hiding linkability for vector commitment schemes: one can prove in zero
knowledge that one or m values that comprise commitment\cm all belong to the vector of …

The field of information security deals with methods and mechanisms to protect sensitive
information. Some of these methods and mechanisms deal with the problem of main taining …

In the framework of Wegman and Carter, ak-independent hash function maps any k keys
independently. It is known that 5-independent hashing provides good expected performance …

We propose a novel KZG-based sum-check scheme, dubbed Losum, with optimal efficiency.
Particularly, its proving cost is one multi-scalar-multiplication of size k—the number of non …