International Association for Cryptologic Research

International Association
for Cryptologic Research


Guilherme Rito


Revisiting (R)CCA Security and Replay Protection 📺
This paper takes a fresh approach to systematically characterizing, comparing, and understanding CCA-type security definitions for public-key encryption (PKE), a topic with a long history. The justification for a concrete security definition X is relative to a benchmark application (e.g. confidential communication): Does the use of a PKE scheme satisfying X imply the security of the application? Because unnecessarily strong definitions may lead to unnecessarily inefficient schemes or unnecessarily strong computational assumptions, security definitions should be as weak as possible, i.e. as close as possible to (but above) the benchmark. Understanding the hierarchy of security definitions, partially ordered by the implication (i.e. at least as strong) relation, is hence important, as is placing the relevant applications as benchmark levels within the hierarchy. CCA-2 security is apparently the strongest notion, but because it is arguably too strong, Canetti, Krawczyk, and Nielsen (Crypto 2003) proposed the relaxed notions of Replayable CCA security (RCCA) as perhaps the weakest meaningful definition, and they investigated the space between CCA and RCCA security by proposing two versions of Detectable RCCA (d-RCCA) security which are meant to ensure that replays of ciphertexts are either publicly or secretly detectable (and hence preventable). The contributions of this paper are three-fold. First, following the work of Coretti, Maurer, and Tackmann (Asiacrypt 2013), we formalize the three benchmark applications of PKE that serve as the natural motivation for security notions, namely the construction of certain types of (possibly replay-protected) confidential channels (from an insecure and an authenticated communication channel). Second, we prove that RCCA does not achieve the confidentiality benchmark and, contrary to previous belief, that the proposed d-RCCA notions are not even relaxations of CCA-2 security. Third, we propose the natural security notions corresponding to the three benchmarks: an appropriately strengthened version of RCCA to ensure confidentiality, as well as two notions for capturing public and secret replay detectability.
Giving an Adversary Guarantees (Or: How to Model Designated Verifier Signatures in a Composable Framework)
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 (CC) 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 (Damg{\r a}rd et al., TCC 2020). As we prove, however, these notions are still strictly stronger than necessary.