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Are both of these concepts related in someway. Can a group signature scheme be transformed into a multi-signature scheme?

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Althogh the two signatures can be used as the authentication method, the security requirements between group signatures and multi-signature are different. The secure properties of the group signatures scheme are usually anonymity, traceability and non-frameability.

  1. Anonymity can keep one's identity anonymous;
  2. Traceability can make sure that illegal group memebers should be traced and revealed by a authority entity who owns the tracing/open key;
  3. Non-frameability means nobody, except itself, can generate a valid signature for anyone else.

What's more, the construction of a group signature is more complicated than that of a multi-signature. If you say "Can a multi-signature scheme be transformed into a group signatures scheme?", the answer will be 'Yes'. That's because a group signatures always is made up of some signatrue scheme (such as BLS, BBS, PS, CL, etc,. signatrue schemes), a commitment scheme and a zero knowledge proof/argument of knowledge. Thus, the multi-signature also can be used for constructing a group signatures scheme.

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