Secure proof of the sum of all the elements of a matrix of finite field elements in zero-knowledge

Abstract

Interactive zero-knowledge arguments for some fundamental linear algebraic operations have been formulated. Using those proofs for operations involving vectors or matrices requires certain reductions and additional communication rounds. In this paper, we explore the possibility of using various principles of discrete mathematics to formulate a method for a prover to securely prove to the verifier that he knows the sum of all the elements of a matrix, while both the sum and the original matrix remain unknown to the verifier.