We introduce compact certificate schemes, which allow any party to take a large number of signatures on a message M, by many signers of different weights, and compress them to a much shorter certificate. This certificate convinces the verifiers that signers with sufficient total weight signed M, even though the verifier will not see—let alone verify—all of the signatures. Thus, for example, a compact certificate can be used to prove that parties who jointly have a sufficient total account balance have attested to a given block in a blockchain.After defining compact certificates, we demonstrate an effi-cient compact certificate scheme. We then show how to implement such a scheme in a decentralized setting over an unreliable network and in the presence of adversarial parties who wish to disrupt certificate creation. Our evaluation shows that compact certificates are 50–280× smaller and 300–4000 cheaper to verify than a natural baseline approach.

Algorand is a new cryptocurrency that confirms transactions with latency on the order of a minute while scaling to many users. Algorand ensures that users never have divergent views of confirmed transactions, even if some of the users are malicious and the network is temporarily partitioned. In contrast, existing cryptocurrencies allow for temporary forks and therefore require a long time, on the order of an hour, to confirm transactions with high confidence.