On the security of the BCTV Pinocchio zk-SNARK variant

Ariel Gabizon

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.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint. MINOR revision.
Keywords: zk-SNARKs
Contact author(s): ariel gabizon @ gmail com
History: 2019-02-13: revised; 2019-02-13: received; See all versions
Short URL: https://ia.cr/2019/119
License: CC BY

BibTeX

@misc{cryptoeprint:2019/119,
      author = {Ariel Gabizon},
      title = {On the security of the {BCTV} Pinocchio zk-{SNARK} variant},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/119},
      year = {2019},
      url = {https://eprint.iacr.org/2019/119}
}