A provably secure code‐based short signature scheme and its nontransferable variant

Signatures with partially message recovery in which some parts of messages are not transmitted with signatures to make them shorter are helpful where bandwidth is one of the critical concern. This primitive is especially used for signing short messages in applications such as time stamping, certified email services, and identity‐based cryptosystems. In this paper, to have quantum‐attack‐resistant short signatures, the first signature scheme with partially message recovery based on coding theory is presented. Next, it is shown that the proposal is secure under Goppa Parametrized Bounded Decoding and the Goppa Code Distinguishing assumptions in the random oracle model. Relying on the partially message recovery property, the proposal is shorter than Dallot signature scheme, the only provably secure and practical code‐based signature scheme, while it preserves Dallot signature efficiency. We should highlight that our scheme can be used as a building block to construct short code‐based signature schemes with special properties. To show this, we present a provably secure short designated verifier signature scheme, a nontransferable form of short signatures, which is used in electronic voting and deniable authentication protocols.