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When defining a security notion, one typically specifies what dishonest parties cannot achieve. For example, communication is confidential if a third party cannot learn anything about the messages being transmitted, and it is authentic if a third party cannot impersonate the real (honest) sender. For certain applications, however, security crucially relies on giving dishonest parties certain capabilities. As an example, in Designated Verifier Signature (DVS) schemes, one captures that only the designated verifier can be convinced of the authenticity of a message by guaranteeing that any dishonest party can forge signatures which look indistinguishable (to a third party) from original ones created by the sender. However, composable frameworks cannot typically model such guarantees as they are only designed to bound what a dishonest party can do. In this paper we show how to model such guarantees-that dishonest parties must have some capability-in the Constructive Cryptography framework (Maurer and Renner, ICS 2011). More concretely, we give the first composable security definitions for Multi-Designated Verifier Signature (MDVS) schemes-a generalization of DVS schemes. The ideal world is defined as the intersection of two worlds. The first captures authenticity in the usual way. The second provides the guarantee that a dishonest party can forge signatures. By taking the intersection we have an ideal world with the desired properties. We also compare our composable definitions to existing security notions for MDVS schemes from the literature. We find that only recently, 23 years after the introduction of MDVS schemes, sufficiently strong security notions were introduced capturing the security of MDVS schemes (Damgård et al., TCC 2020). As we prove, however, these notions are still strictly stronger than necessary.

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Deniable Authentication is a highly desirable property for secure messaging protocols: it allows a sender Alice to authentically transmit messages to a designated receiver Bob in such a way that only Bob gets convinced that Alice indeed sent these messages. In particular, it guarantees that even if Bob tries to convince a (non-designated) party Judy that Alice sent some message, and even if Bob gives Judy his own secret key, Judy will not be convinced: as far as Judy knows, Bob could be making it all up! In this paper we study Deniable Authentication in the setting where Judy can additionally obtain Alice's secret key. Informally, we want that knowledge of Alice's secret key does not help Judy in learning whether Alice sent any messages, even if Bob does not have Alice's secret key and even if Bob cooperates with Judy by giving her his own secret key. This stronger flavor of Deniable Authentication was not considered before and is particularly relevant for Off-The-Record Group Messaging as it gives users stronger deniability guarantees. Our main contribution is a scalable "MDRS-PKE" (Multi-Designated Receiver Signed Public Key Encryption) scheme-a technical formalization of Deniable Authentication that is particularly useful for secure messaging for its confidentiality guarantees-that provides this stronger deniability guarantee. At its core lie new MDVS (Multi-Designated Verifier Signature) and PKEBC (Public Key Encryption for Broadcast) scheme constructions: our MDVS is not only secure with respect to the new deniability notions, but it is also the first to be tightly secure under standard assumptions; our PKEBC-which is also of independent interest-is the first with ciphertext sizes and encryption and decryption times that grow only linearly in the number of receivers. This is a significant improvement upon the construction given by Maurer et al. (EUROCRYPT '22), where ciphertext sizes and encryption and decryption times are quadratic in the number of receivers.Motivation. More than 3 billion people currently use messaging apps. 3 Naturally, there is a demand for secure messaging which guarantees, e.g., the secrecy ⋆ All of the work was done while author was at ETH Zurich.