Studying a range proof technique - Exception and optimisation

Abstract

A batch proof and verification technique is employed to design efficient range proof with practical small ranges in AFRICACRYPT 2010. It is shown in this paper that the batch proof and verification technique is not always sound in its application to range proof. We demonstrate that their batch proof and verification technique causes a concern such that in some cases a malicious prover without the claimed knowledge may pass the verification. As a result their range proof scheme to prove that a secret committed integer is in an interval range is not so reliable and cannot guarantee that the committed integer is in the range in some special cases. To ease the concern, we employ an efficient membership proof technique to replace the batch proof and verification technique in their range proof scheme and re-design it to achieve the claimed high efficiency with practical small ranges. © 2013 Springer-Verlag Berlin Heidelberg.