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We generalise and improve the security and efficiency of the verifiable encryption scheme of Asokan et al., such that it can rely on more general assumptions, and can be proven secure without relying on random oracles. We show a new application of verifiable encryption to group signatures with separability, these schemes do not need special purpose keys but can work with a wide range of signature and encryption schemes already in use. Finally, we extend our basic primitive to verifiable threshold and group encryption. By encrypting digital signatures this way, one gets new solutions to the verifiable signature sharing problem.

Verifiable Encryption and Applications to Group Signatures and Signature Sharing