Aggregate signatures (Boneh, Gentry, Lynn, Shacham, Eurocrypt 2003) enable compressing a set of signatures on different messages into a short aggregate signature. This reduces the space complexity of storing the signatures from linear in to a fixed constant (that depends only on the security parameter). However, verifying the aggregate signature requires access to all messages, resulting in the complexity of verification being at least .
In this work, we introduce the notion of locally verifiable aggregate signatures that enable efficient verification: given a short aggregate signature (corresponding to a set of messages), the verifier can check whether a particular message is in the set, in time independent of . Verification does not require knowledge of the entire set . We demonstrate many natural applications of locally verifiable aggregate signature schemes: in the context of certificate transparency logs; in blockchains; and for redacting signatures, even when all the original signatures are produced by a single user.
We provide two constructions of single-signer locally verifiable aggregate signatures, the first based on the RSA assumption and the second on the bilinear Diffie-Hellman inversion assumption, both in the random oracle model.
As an additional contribution, we introduce the notion of compressing cryptographic keys in identity-based encryption (IBE) schemes, show applications of this notion, and construct an IBE scheme where the secret keys for identities can be compressed into a single aggregate key, which can then be used to decrypt ciphertexts sent to any of the identities.