Handling Adaptive Compromise for Practical Encryption Schemes 📺 ★
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.
The Memory-Tightness of Authenticated Encryption 📺
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.
Expected-Time Cryptography: Generic Techniques and Applications to Concrete Soundness 📺
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.
Tight Time-Memory Trade-Offs for Symmetric Encryption 📺
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.
Optimal Channel Security Against Fine-Grained State Compromise: The Safety of Messaging 📺
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.