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Does an anonymous signature hide the sender's identity from the receiver, or simply just hide the sender's identity from an eavesdropper or third party?

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It is perhaps more complicated.

Signer anonymity for anonymous signatures means anyone who has the signature but not the message (or does not know enough about the message) cannot reveal the identity of the signer.

Thus it really depends on, in your model, what the receiver or eavesdropper knows. For example, if one sends the signature and the message (in plaintext) together, then even the eavesdropper can know the signer's identity. For receivers, often they are supposed to verify a signature, so they know the identity of the signer. However, if your receivers are not verifiers (e.g. they just receive and store the signatures), then they may not need to know the messages, and if the messages are hidden from them, then they don't know the identity of the signer.

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  • $\begingroup$ Will anonymous IBE(Identity based encryption) serve the purpose (hiding sender's identity) then? $\endgroup$ – user2035863 Jun 6 '18 at 10:58
  • $\begingroup$ IBE uses identities are public keys. The receiver, if can decrypt, must be the owner of the identity (because he/she possess the private key corresponding to the ID). There are anonymous IBE and non-anonymous IBE schemes, for the former, the ciphertext does not leak information about the identity used in encryption to eavesdroppers. $\endgroup$ – Changyu Dong Jun 6 '18 at 14:44

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