International Association
for Cryptologic Research

We introduce a new cryptographic primitive called symmetric signcryption, which differs from traditional signcryption because the sender and recipient share a secret key. We prove that a natural composition of symmetric encryption and signatures achieves strong notions of security against attackers that can learn and control many keys. We then identify that the core encryption algorithm of the Keybase encrypted messaging protocol can be modeled as a symmetric signcryption scheme. We prove the security of this algorithm, though our proof requires assuming non-standard, brittle security properties of the underlying primitives.

The Fuchsbauer, Kiltz, and Loss (Crypto 2018) claim that (some) hardness results in the algebraic group model imply the same hardness results in the generic group model was recently called into question by Katz, Zhang, and Zhou (Asiacrypt 2022). The latter gave an interpretation of the claim under which it is incorrect. We give an alternate interpretation under which it is correct, using natural frameworks for capturing generic and algebraic models for arbitrary algebraic structures. Most algebraic analyses in the literature can be captured by our frameworks, making the claim correct for them.

Anamorphic signature schemes (KPPYZ, Crypto 2023) allow users to hide encrypted messages in signatures to allow covert communication in a hypothesized scenario where encryption is outlawed by a "dictator" but authentication is permitted. We enhance the security of anamorphic signatures by proposing two parallel notions of unforgeability which close gaps in existing security definitions. The first notion considers a dictator who wishes to forge anamorphic signatures. This notion patches a divide between the definition and a stated security goal of robustness (BGHMR, Eurocrypt 2024). We port two related BGHMR constructions to the signature scheme setting and show that one is secure when built from unpredictable signature schemes while the other is broken. The second notion considers a recipient who wishes to forge signatures. To motivate this notion, we identify a gap in an existing security definition from KPPYZ and present attacks that allow parties to be impersonated when using schemes erroneously deemed secure. We then formalize our new unforgeability definition to close this gap. Interestingly, while the new definition is only modestly different from the old one, the change introduces subtle technical challenges that arise when proving security. We overcome these challenges in our reanalysis of existing anamorphic signature schemes by showing they achieve our new notion when built from chosen-randomness secure signatures or with encryption that satisfies a novel ideal-model simulatability property.

We show that the adaptive compromise security definitions of Jaeger and Tyagi (Crypto '20) cannot be applied in several natural use-cases. These include proving multi-user security from single-user security, the security of the cascade PRF, and the security of schemes sharing the same ideal primitive. We provide new variants of the definitions and show that they resolve these issues with composition. Extending these definitions to the asymmetric settings, we establish the security of the modular KEM/DEM and Fujisaki-Okamoto approaches to public key encryption in the full adaptive compromise setting. This allows instantiations which are more efficient and standard than prior constructions.

This paper continues the study of {\em memory-tight reductions} (Auerbach et al, CRYPTO '17). These are reductions that only incur minimal memory costs over those of the original adversary, allowing precise security statements for memory-bounded adversaries (under appropriate assumptions expressed in terms of adversary time and memory usage). Despite its importance, only a few techniques to achieve memory-tightness are known and impossibility results in prior works show that even basic, textbook reductions cannot be made memory-tight. This paper introduces a new class of memory-tight reductions which leverage random strings in the interaction with the adversary to hide state information, thus shifting the memory costs to the adversary. We exhibit this technique with several examples. We give memory-tight proofs for digital signatures allowing many forgery attempts when considering randomized message distributions or probabilistic RSA-FDH signatures specifically. We prove security of the authenticated encryption scheme Encrypt-then-PRF with a memory-tight reduction to the underlying encryption scheme. By considering specific schemes or restricted definitions we avoid generic impossibility results of Auerbach et al.~(CRYPTO '17) and Ghoshal et al.~(CRYPTO '20). As a further case study, we consider the textbook equivalence of CCA-security for public-key encryption for one or multiple encryption queries. We show two qualitatively different memory-tight versions of this result, depending on the considered notion of CCA security.

We give the first examples of public-key encryption schemes which can be proven to achieve multi-challenge, multi-user CCA security via reductions that are tight in time, advantage, and memory. Our constructions are obtained by applying the KEM-DEM paradigm to variants of Hashed ElGamal and the Fujisaki-Okamoto transformation that are augmented by adding uniformly random strings to their ciphertexts. The reductions carefully combine recent proof techniques introduced by Bhattacharyya'20 and Ghoshal-Ghosal-Jaeger-Tessaro'22. Our proofs for the augmented ECIES version of Hashed-ElGamal make use of a new computational Diffie-Hellman assumption wherein the adversary is given access to a pairing to a random group, which we believe may be of independent interest.

Should quantum computers become available, they will reduce the effective key length of basic secret-key primitives, such as blockciphers. To address this we will either need to use blockciphers with inherently longer keys or develop key-length extension techniques to amplify the security of a blockcipher to use longer keys. We consider the latter approach and revisit the FX and double encryption constructions. Classically, FX was proven to be a secure key-length extension technique, while double encryption fails to be more secure than single encryption due to a meet-in-the-middle attack. In this work we provide positive results, with concrete and tight bounds, for the security of both of these constructions against quantum attackers in ideal models. For FX, we consider a partially-quantum model, where the attacker has quantum access to the ideal primitive, but only classical access to FX. This is a natural model and also the strongest possible, since effective quantum attacks against FX exist in the fully-quantum model when quantum access is granted to both oracles. We provide two results for FX in this model. The first establishes the security of FX against non-adaptive attackers. The second establishes security against general adaptive attackers for a variant of FX using a random oracle in place of an ideal cipher. This result relies on the techniques of Zhandry (CRYPTO '19) for lazily sampling a quantum random oracle. An extension to perfectly lazily sampling a quantum random permutation, which would help resolve the adaptive security of standard FX, is an important but challenging open question. We introduce techniques for partially-quantum proofs without relying on analyzing the classical and quantum oracles separately, which is common in existing work. This may be of broader interest. For double encryption, we show that it amplifies strong pseudorandom permutation security in the fully-quantum model, strengthening a known result in the weaker sense of key-recovery security. This is done by adapting a technique of Tessaro and Thiruvengadam (TCC '18) to reduce the security to the difficulty of solving the list disjointness problem and then showing its hardness via a chain of reductions to the known quantum difficulty of the element distinctness problem.

We provide a new definitional framework capturing the multi-user security of encryption schemes and pseudorandom functions in the face of adversaries that can adaptively compromise users' keys. We provide a sequence of results establishing the security of practical symmetric encryption schemes under adaptive compromise in the random oracle or ideal cipher model. The bulk of analysis complexity for adaptive compromise security is relegated to the analysis of lower-level primitives such as pseudorandom functions. We apply our framework to give proofs of security for the BurnBox system for privacy in the face of border searches and the in-use searchable symmetric encryption scheme due to Cash et al. In both cases, prior analyses had bugs that our framework helps avoid.

This paper initiates the study of the provable security of authenticated encryption (AE) in the memory-bounded setting. Recent works -- Tessaro and Thiruvengadam (TCC '18), Jaeger and Tessaro (EUROCRYPT '19), and Dinur (EUROCRYPT '20) -- focus on confidentiality, and look at schemes for which trade-offs between the attacker's memory and its data complexity are inherent. Here, we ask whether these results and techniques can be lifted to the full AE setting, which additionally asks for integrity. We show both positive and negative results. On the positive side, we provide tight memory-sensitive bounds for the security of GCM and its generalization, CAU (Bellare and Tackmann, CRYPTO '16). Our bounds apply to a restricted case of AE security which abstracts the deployment within protocols like TLS, and rely on a new memory-tight reduction to corresponding restricted notions of confidentiality and integrity. In particular, our reduction uses an amount of memory which linearly depends on that of the given adversary, as opposed to only imposing a constant memory overhead as in earlier works (Auerbach et al, CRYPTO '17). On the negative side, we show that a large class of black-box reductions cannot generically lift confidentiality and integrity security to a joint definition of AE security in a memory-tight way.

This paper studies concrete security with respect to expected-time adversaries. Our first contribution is a set of generic tools to obtain tight bounds on the advantage of an adversary with expected-time guarantees. We apply these tools to derive bounds in the random-oracle and generic-group models, which we show to be tight. As our second contribution, we use these results to derive concrete bounds on the soundness of public-coin proofs and arguments of knowledge. Under the lens of concrete security, we revisit a paradigm by Bootle at al. (EUROCRYPT '16) that proposes a general Forking Lemma for multi-round protocols which implements a rewinding strategy with expected-time guarantees. We give a tighter analysis, as well as a modular statement. We adopt this to obtain the first quantitative bounds on the soundness of Bulletproofs (Bünz et al., S&P 2018), which we instantiate with our expected-time generic-group analysis to surface inherent dependence between the concrete security and the statement to be proved.

Concrete security proofs give upper bounds on the attacker’s advantage as a function of its time/query complexity. Cryptanalysis suggests however that other resource limitations – most notably, the attacker’s memory – could make the achievable advantage smaller, and thus these proven bounds too pessimistic. Yet, handling memory limitations has eluded existing security proofs.This paper initiates the study of time-memory trade-offs for basic symmetric cryptography. We show that schemes like counter-mode encryption, which are affected by the Birthday Bound, become more secure (in terms of time complexity) as the attacker’s memory is reduced.One key step of this work is a generalization of the Switching Lemma: For adversaries with S bits of memory issuing q distinct queries, we prove an n-to-n bit random function indistinguishable from a permutation as long as $$S \times q \ll 2^n$$S×q≪2n. This result assumes a combinatorial conjecture, which we discuss, and implies right away trade-offs for deterministic, stateful versions of CTR and OFB encryption.We also show an unconditional time-memory trade-off for the security of randomized CTR based on a secure PRF. Via the aforementioned conjecture, we extend the result to assuming a PRP instead, assuming only one-block messages are encrypted.Our results solely rely on standard PRF/PRP security of an underlying block cipher. We frame the core of our proofs within a general framework of indistinguishability for streaming algorithms which may be of independent interest.

We aim to understand the best possible security of a (bidirectional) cryptographic channel against an adversary that may arbitrarily and repeatedly learn the secret state of either communicating party. We give a formal security definition and a proven-secure construction. This construction provides better security against state compromise than the Signal Double Ratchet Algorithm or any other known channel construction. To facilitate this we define and construct new forms of public-key encryption and digital signatures that update their keys over time.