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There's no doubt that the BBS Signature was born from this classic Short Group Signature paper in 2004. It's capable of Zero-knowledge. In the paper, section 5, it describes how a member of a group, can sign a message, without revealing which member signed it. But, this group signature can be verified that it was signed by a member of a group (anonymously) through a group public key $gpk$.

However, later, there are some works improving BBS into BBS+. It was first modified and named in Constant-Size Dynamic k-TAA by Au et al. BBS+ was touched again in Anonymous Attestation Using the Strong Diffie Hellman Assumption Revisited. Nevertheless, in those two papers mentioned above, it seems the BBS+ scheme is a multi-messages signing protocol. It takes messages $m_1, m_2, m_3,..., m_L$ and produces a single signature $\sigma$. It can create a proof of knowledge $SPK$ on top of signature $\sigma$, with some messages $m_i$ revealed.

Yet, in work on Enhanced Privacy ID from Bilinear Pairing by intel, it seems their BBS+ scheme becomes as a member of a group signing the message anonymously, same as Short Group Signature paper in 2004.

Therefore, I'm confused about BBS+ protocol. Whether it is

  1. a multi-message $m_1, m_2, m_3,..., m_L$ signing protocol producing a single signature $\sigma$ with signature proof of knowledge $SPK$

or

  1. a group signature signed by a member of a group anonymously using a group public key $gpk$?
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I've always used it as #1. Hyperledger Ursa has an implementation in Rust (see https://github.com/hyperledger/ursa/tree/master/libzmix/bbs).

However, it is a type of group signature which allows the type of signing of multiple messages.

When someone says to me group signature I immediately think your #2. If we look at a paper written by David Chaum (https://chaum.com/publications/Group_Signatures.pdf), He mentions

group signatures are a "generalization" of the credential/ membership authentication schemes, in which one person proves that he belongs to a certain group.

So in effect, the proof being made is proving the messages belong to the signature and the signature allows for a proof of knowledge to be made. It's a different use of a crypto primitive.

Hope this helps

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