**Locally Verifiable Signature and Key Aggregation**

*Rishab Goyal and 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.

**Category / Keywords: **foundations / Aggregate Signatures, Local Verifiability, RSA, Pairing, Blockchains, Redactable, Certificate Transparency

**Date: **received 16 Feb 2022

**Contact author: **goyal at utexas edu, vinod nathan at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20220220:201358 (All versions of this report)

**Short URL: **ia.cr/2022/179

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