Cryptanalysis of an Off-Line Electronic Cash Scheme Based on Proxy Blind Signature

Abstract

Proxy blind signature is an important cryptographic primitive and plays an essential role in construction of the electronic cash (e-cash). Recently, Tan (2001, An offline electronic cash scheme based on proxy blind signature. Comput. J., 54, 505–512) proposed a new proxy blind signature scheme and applied it to electronic cash. The scheme was claimed as being provably secure under the Discrete Log assumption, DBDH assumption and Chosen–Target CDH assumption in the random oracle model. In this paper, we show that Tan's proxy blind signature scheme is insecure by demonstrating several attacks in which a malicious original signer can forge both valid proxy signature keys of arbitrary proxy signers and a proxy blind signature on an arbitrary message with respect to any proxy signer directly. We also discuss some weaknesses in the e-cash scheme proposed by Tan.