Verifiably Encrypted Signatures from RSA without NIZKs

Verifiably encrypted signature (VES) schemes allow a signer to encrypt a signature under the public key of a trusted party, the adjudicator, while maintaining public signature verifiability without interactive proofs. A popular application for this concept is fair online contract signing. This paper answers the question of whether it is possible to implement a VES without pairings and zero-knowledge proofs. Our construction is based on RSA signatures and a Merkle hash tree. Hence, the scheme is stateful but relies on relatively mild assumptions in the random oracle model. Thus, we provide an alternative that does not rely on pairing-based assumptions. The advantage of our approach over previous schemes is that widespread efficient hard- and software implementations of hash functions and RSA signatures can be easily reused for VES, i.e., we can avoid costly redevelopment. Furthermore, in contrast to using non-interactive zero-knowledge proofs, we only need a constant, small number of modular exponentiations.

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