Analysing a Batch Range Proof to Address a Security Concern

In Africacrypt 2010, Peng and Bao propose a batch proof and verification technique and apply it to design efficient range proof with practical small ranges. Their range proof employs a batch proof and verification technique by Chida and Yamamoto. We show that the batch proof and verification fails in security such that a malicious prover without the claimed knowledge can pass the verification. As a result, there is security concern for the range proof scheme as it may be vulnerable to the attack. However, it is illustrated in this paper that the attack must work under a condition and a simple countermeasure can fail the condition and prevent the attack in the range proof scheme.