Paper 2019/119

On the security of the BCTV Pinocchio zk-SNARK variant

Ariel Gabizon

Abstract

The main result of this note is a severe flaw in the description of the zk-SNARK in [BCTV14]. The flaw stems from including redundant elements in the CRS, as compared to that of the original Pinocchio protocol [PHGR16], which are vital not to expose. The flaw enables creating a proof of knowledge for *any* public input given a valid proof for *some* public input. We also provide a proof of security for the [BCTV14] zk-SNARK in the generic group model, when these elements are excluded from the CRS, provided a certain linear algebraic condition is satisfied by the QAP polynomials.