More Efficient Digital Signatures with Tight Multi-User Security 📺
We construct the currently most efficient signature schemes with tight multi-user security against adaptive corruptions. It is the first generic construction of such schemes, based on lossy identification schemes (Abdalla etal; JoC 2016), and the first to achieve strong existential unforgeability. It also has significantly more compact signatures than the previously most efficient construction by Gjosteen and Jager (CRYPTO 2018). When instantiated based on the decisional Diffie-Hellman assumption, a signature consists of only three exponents. We propose a new variant of the generic construction of signatures from sequential OR-proofs by Abe, Ohkubo, and Suzuki (ASIACRYPT 2002) and Fischlin, Harasser, and Janson (EUROCRYPT 2020). In comparison to Fischlin etal, who focus on constructing signatures in the non-programmable random oracle model (NPROM), we aim to achieve tight security against adaptive corruptions, maximize efficiency, and to directly achieve strong existential unforgeability (also in the NPROM). This yields a slightly different construction and we use slightly different and additional properties of the lossy identification scheme. Signatures with tight multi-user security against adaptive corruptions are a commonly-used standard building block for tightly-secure authenticated key exchange protocols. We also show how our construction improves the efficiency of all existing tightly-secure AKE protocols.
Symmetric Key Exchange with Full Forward Security and Robust Synchronization
We construct lightweight authenticated key exchange protocols based on pre-shared keys, which achieve full forward security and rely only on simple and efficient symmetric-key primitives. All of our protocols have rigorous security proofs in a strong security model, all have low communication complexity, and are particularly suitable for resource-constrained devices. We describe three protocols that apply linear key evolution to provide different performance and security properties. Correctness in parallel and concurrent protocol sessions is difficult to achieve for linearly key-evolving protocols, emphasizing the need for assurance of availability alongside the usual confidentiality and authentication security goals. We introduce synchronization robustness as a new formal security goal, which essentially guarantees that parties can re-synchronize efficiently. All of our new protocols achieve this property. Since protocols based on linear key evolution cannot guarantee that all concurrently initiated sessions successfully derive a key, we also propose two constructions with non-linear key evolution based on puncturable PRFs. These are instantiable from standard hash functions and require O( C log(|CTR|)) memory, where C is the number of concurrent sessions and |CTR| is an upper bound on the total number of sessions per party. These are the first protocols to simultaneously achieve full forward security, synchronization robustness, and concurrent correctness.
Digital Signatures with Memory-Tight Security in the Multi-Challenge Setting
The standard security notion for digital signatures is "single-challenge" (SC) EUF-CMA security, where the adversary outputs a single message-signature pair and "wins" if it is a forgery. Auerbach et al. (CRYPTO 2017) introduced memory-tightness of reductions and argued that the right security goal in this setting is actually a stronger "multi-challenge" (MC) definition, where an adversary may output many message-signature pairs and "wins" if at least one is a forgery. Currently, no construction from simple standard assumptions is known to achieve full tightness with respect to time, success probability, and memory simultaneously. Previous works showed that memory-tight signatures cannot be achieved via certain natural classes of reductions (Auerbach et al., CRYPTO 2017; Wang et al., EUROCRYPT 2018). These impossibility results may give the impression that the construction of memory-tight signatures is difficult or even impossible. We show that this impression is false, by giving the first constructions of signature schemes with full tightness in all dimensions in the MC setting. To circumvent the known impossibility results, we first introduce the notion of canonical reductions in the SC setting. We prove a general theorem establishing that every signature scheme with a canonical reduction is already memory-tightly secure in the MC setting, provided that it is strongly unforgeable, the adversary receives only one signature per message, and assuming the existence of a tightly-secure pseudorandom function. We then achieve memory-tight many-signatures-per-message security in the MC setting by a simple additional generic transformation. This yields the first memory-tightly, strongly EUF-CMA-secure signature schemes in the MC setting. Finally, we show that standard security proofs often already can be viewed as canonical reductions. Concretely, we show this for signatures from lossy identification schemes (Abdalla et al., EUROCRYPT 2012), two variants of RSA Full-Domain Hash (Bellare and Rogaway, EUROCRYPT 1996), and two variants of BLS signatures (Boneh et al., ASIACRYPT 2001).
Session Resumption Protocols and Efficient Forward Security for TLS 1.3 0-RTT 📺
The TLS 1.3 0-RTT mode enables a client reconnecting to a server to send encrypted application-layer data in “0-RTT” (“zero round-trip time”), without the need for a prior interactive handshake. This fundamentally requires the server to reconstruct the previous session’s encryption secrets upon receipt of the client’s first message. The standard techniques to achieve this are Session Caches or, alternatively, Session Tickets. The former provides forward security and resistance against replay attacks, but requires a large amount of server-side storage. The latter requires negligible storage, but provides no forward security and is known to be vulnerable to replay attacks.In this paper, we first formally define session resumption protocols as an abstract perspective on mechanisms like Session Caches and Session Tickets. We give a new generic construction that provably provides forward security and replay resilience, based on puncturable pseudorandom functions (PPRFs). This construction can immediately be used in TLS 1.3 0-RTT and deployed unilaterally by servers, without requiring any changes to clients or the protocol.We then describe two new constructions of PPRFs, which are particularly suitable for use for forward-secure and replay-resilient session resumption in TLS 1.3. The first construction is based on the strong RSA assumption. Compared to standard Session Caches, for “128-bit security” it reduces the required server storage by a factor of almost 20, when instantiated in a way such that key derivation and puncturing together are cheaper on average than one full exponentiation in an RSA group. Hence, a 1 GB Session Cache can be replaced with only about 51 MBs of storage, which significantly reduces the amount of secure memory required. For larger security parameters or in exchange for more expensive computations, even larger storage reductions are achieved. The second construction combines a standard binary tree PPRF with a new “domain extension” technique. For a reasonable choice of parameters, this reduces the required storage by a factor of up to 5 compared to a standard Session Cache. It employs only symmetric cryptography, is suitable for high-traffic scenarios, and can serve thousands of tickets per second.