The unlinkability of randomization-enhanced Chaum's blind signature scheme

The key issue in e-commerce security is digital signature. Chaum first proposed the concept of blind digital signature, and designed untraceable payments. To avoid threats from chosen-message attacks presented by Coron et al. (1999), Fan et al. (2000) proposed a randomization enhanced Chaum blind signature scheme, by injecting a random factor into messages. In this paper, we first formally define the unlinkability of the blind signature scheme. According to this definition, we prove that Fan's scheme does not possess the unlinkablity property: after the message and signature have been revealed to the public by the sender, the signer can trace the corresponding blinded message and signature by constructing a linkage between the message and the blind message. Therefore, Fan's scheme cannot provide true blind signatures.