Welcome to the resource topic for
**2022/179**

**Title:**

Locally Verifiable Signature and Key Aggregation

**Authors:**
Rishab Goyal, Vinod Vaikuntanathan

**Abstract:**

Aggregate signatures (Boneh, Gentry, Lynn, Shacham, Eurocrypt 2003) enable compressing a set of N signatures on N different messages into a short aggregate signature. This reduces the space complexity of storing the signatures from linear in N to a fixed constant (that depends only on the security parameter). However, verifying the aggregate signature requires access to all N messages, resulting in the complexity of verification being at least \Omega(N). In this work, we introduce the notion of locally verifiable aggregate signatures that enable efficient verification: given a short aggregate signature \sigma (corresponding to a set \mathcal{M} of N messages), the verifier can check whether a particular message m is in the set, in time independent of N. Verification does not require knowledge of the entire set \mathcal{M}. 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 N identities can be compressed into a single aggregate key, which can then be used to decrypt ciphertexts sent to any of the N identities.

**ePrint:**
https://eprint.iacr.org/2022/179

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