Password-Authenticated Key Exchange from Group Actions
We present two provably secure password-authenticated key exchange (PAKE) protocols based on a commutative group action. To date the most important instantiation of isogeny-based group actions is given by CSIDH. To model the properties more accurately, we extend the framework of cryptographic group actions (Alamati et al., ASIACRYPT 2020) by the ability of computing the quadratic twist of an elliptic curve. This property is always present in the CSIDH setting and turns out to be crucial in the security analysis of our PAKE protocols. Despite the resemblance, the translation of Diffie-Hellman based PAKE protocols to group actions either does not work with known techniques or is insecure (``How not to create an isogeny-based PAKE'', Azarderakhsh et al. ACNS 20). We overcome the difficulties mentioned in previous work by using a ``bit-by-bit'' approach, where each password bit is considered separately. Our first protocol X-GA-PAKE can be executed in a single round. Both parties need to send two set elements for each password bit in order to prevent offline dictionary attacks. The second protocol Com-GA-PAKE requires only one set element per password bit, but one party has to send a commitment on its message first. We also discuss different optimizations that can be used to reduce the computational cost. We provide comprehensive security proofs for our base protocols and deduce security for the optimized versions.
Tightly-Secure Authenticated Key Exchange, Revisited 📺
We introduce new tightly-secure authenticated key exchange (AKE) protocols that are extremely efficient, yet have only a constant security loss and can be instantiated in the random oracle model both from the standard DDH assumption and a subgroup assumption over RSA groups. These protocols can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate a security loss with increased parameters and thus decreased computational efficiency. We use the standard “Single-Bit-Guess” AKE security (with forward secrecy and state corruption) requiring all challenge keys to be simultaneously pseudo-random. In contrast, most previous papers on tightly secure AKE protocols (Bader et al., TCC 2015; Gjøsteen and Jager, CRYPTO 2018; Liu et al., ASIACRYPT 2020) concentrated on a non-standard “Multi-Bit-Guess” AKE security which is known not to compose tightly with symmetric primitives to build a secure communication channel. Our key technical contribution is a new generic approach to construct tightly-secure AKE protocols based on non-committing key encapsulation mechanisms. The resulting DDH-based protocols are considerably more efficient than all previous constructions.
Analysing the HPKE Standard 📺
The Hybrid Public Key Encryption (HPKE) scheme is an emerging standard currently under consideration by the Crypto Forum Research Group (CFRG) of the IETF as a candidate for formal approval. Of the four modes of HPKE, we analyse the authenticated mode HPKE_Auth in its single-shot encryption form as it contains what is, arguably, the most novel part of HPKE. HPKE_Auth’s intended application domain is captured by a new primitive which we call Authenticated Public Key Encryption (APKE). We provide syntax and security definitions for APKE schemes, as well as for the related Authenticated Key Encapsulation Mechanisms (AKEMs). We prove security of the AKEM scheme DH-AKEM underlying HPKE Auth based on the Gap Diffie-Hellman assumption and provide general AKEM/DEM composition theorems with which to argue about HPKE_Auth’s security. To this end, we also formally analyse HPKE_Auth’s key schedule and key derivation functions. To increase confidence in our results we use the automatic theorem proving tool CryptoVerif. All our bounds are quantitative and we discuss their practical implications for HPKE_Auth. As an independent contribution we propose the new framework of nominal groups that allows us to capture abstract syntactical and security properties of practical elliptic curves, including the Curve25519 and Curve448 based groups (which do not constitute cyclic groups).
Authenticated Key Exchange and Signatures with Tight Security in the Standard Model 📺
We construct the first authenticated key exchange protocols that achieve tight security in the standard model. Previous works either relied on techniques that seem to inherently require a random oracle, or achieved only “Multi-Bit-Guess” security, which is not known to compose tightly, for instance, to build a secure channel. Our constructions are generic, based on digital signatures and key encapsulation mechanisms (KEMs). The main technical challenges we resolve is to determine suitable KEM security notions which on the one hand are strong enough to yield tight security, but at the same time weak enough to be efficiently instantiable in the standard model, based on standard techniques such as universal hash proof systems. Digital signature schemes with tight multi-user security in presence of adaptive corruptions are a central building block, which is used in all known constructions of tightly-secure AKE with full forward security. We identify a subtle gap in the security proof of the only previously known efficient standard model scheme by Bader et al. (TCC 2015). We develop a new variant, which yields the currently most efficient signature scheme that achieves this strong security notion without random oracles and based on standard hardness assumptions.