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Is it possible to prove that a given signature is a part of an aggregated BLS signature? Specifically, given:

  • $m_1...m_n$ are $n$ distinct messages
  • $p_1...p_n$ are private keys with $P_1...P_n$ being the corresponding public keys
  • $S_1...S_n$ are BLS signatures such that $S_i = sig(m_i, p_i)$
  • $A = S_1 + S_2 + ... + S_n$ is the aggravated BLS signature

Is it possible to prove that a signature $S_i$ is contained within $A$ using only publicly available data: $A$, $S_i$, $P_i$, and $m_i$?

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Yes, it is possible. What you are referring to is called local aggregation. The proof is a small hint that is calculated from the set. The verifier can verify a signature on a message without knowing the full set. Thus, the runtime of the verifier is independent of the size of the set; unlike the other answer.

This paper, Locally Verifiable Signatures and Key Aggregation, from Goyal & Vaikuntanathan was published recently in CRYPTO22.

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    $\begingroup$ The first link is broken. I found the preprint eprint.iacr.org/2022/179.pdf $\endgroup$ Sep 29, 2022 at 17:46
  • $\begingroup$ oops thanks for telling me $\endgroup$
    – Wilson
    Sep 29, 2022 at 19:40

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