Abstract
The generalized compact knapsack function is defined as fa(x)=∑iai.xi, where a=(a1,…,am)∈R for some ring R and x=(x1,…,xm)∈S for a specified subset S ⊂ R. It is known that, for appropriate choice of R and S, inverting this function is at least as hard as solving certain worst-case problems on cyclic lattices. In this paper, we exploit collision-resistance as well as homomorphic properties of this function to propose a threshold verifiable secret sharing scheme with two distinguished features: first, the security of the scheme is completely based on lattice problems and second, upon receiving shares, participants can verify consistency of their shares with the secret without any communication.
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