Efficient Lattice-Based Polynomial Evaluation and Batch ZK Arguments

In this paper we provide an efficient construction of a lattice-based polynomial argument and a polynomial batch-protocol, where the latter contains the polynomial argument as a building block. Our contribution is motivated by the discrete log based construction (EUROCRYPT'16), where in our case we employ different techniques to obtain a communication efficient lattice-based scheme. In the zero-knowledge polynomial batch-protocol, we prove the knowledge of an easy relation between two polynomials which also allows batching of several instances of the same relation. Our batch-protocol is applicable to an efficient lattice-based range proof construction which represents a useful application in cryptocurrencies. In contrast to the existing range proof (CRYPTO'19), our proof is more efficient for large number of batched instances.