Abstract
A batch proof and verification technique by Chida and Yamamoto is extended to work in a more general scenario. The new batch proof and verification technique is more useful and can save more cost than the original technique. An application of the new batch proof and verification technique is range proof, which proves that a secret integer is in an interval range. Like the most resent and advanced range proof protocol by Camenisch, Chaabouni and Shelat in Asiacrypt2008, the new range proof technique is especially suitable for practical small ranges, but more efficient and stronger in security than the former. The new range proof technique is very efficient and more efficient than the existing solutions in practical small ranges. Moreover, it achieves stronger security and stronger privacy (perfect honest-verifier zero knowledge) than most of the existing range proof schemes.
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