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1. The Power of Abstract MAC Layer: A Fault-Tolerance Perspective

   https://doi.org/10.4230/LIPICS.DISC.2024.39  

   Zhang, Qinzi; Tseng, Lewis (January 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Alistarh, Dan (Ed.)

   This paper studies the power of the "abstract MAC layer" model in a single-hop asynchronous network. The model captures primitive properties of modern wireless MAC protocols. In this model, Newport [PODC '14] proves that it is impossible to achieve deterministic consensus when nodes may crash. Subsequently, Newport and Robinson [DISC '18] present randomized consensus algorithms that terminate with O(n³ log n) expected broadcasts in a system of n nodes. We are not aware of any results on other fault-tolerant distributed tasks in this model. We first study the computability aspect of the abstract MAC layer. We present a wait-free algorithm that implements an atomic register. Furthermore, we show that in general, k-set consensus is impossible. Second, we aim to minimize storage complexity. Existing algorithms require Ω(n log n) bits. We propose two wait-free approximate consensus and two wait-free randomized binary consensus algorithms that only need constant storage complexity (except for the phase index). One randomized algorithm terminates with O(n log n) expected broadcasts. All our algorithms are anonymous, meaning that at the algorithm level, nodes do not need to have a unique identifier. 

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2. Mycielski Graphs and PR Proofs

   https://doi.org/10.1007/978-3-030-51825-7_15  

   Yolcu, Emre; Wu, Xinyu; Heule, Marijn (June 2020, Theory and Applications of Satisfiability Testing – SAT 2020)

   Mycielski graphs are a family of triangle-free graphs 𝑀_𝑘 with arbitrarily high chromatic number. 𝑀_𝑘 has chromatic number k and there is a short informal proof of this fact, yet finding proofs of it via automated reasoning techniques has proved to be a challenging task. In this paper, we study the complexity of clausal proofs of the uncolorability of 𝑀_𝑘 with 𝑘−1 colors. In particular, we consider variants of the PR (propagation redundancy) proof system that are without new variables, and with or without deletion. These proof systems are of interest due to their potential uses for proof search. As our main result, we present a sublinear-length and constant-width PR proof without new variables or deletion. We also implement a proof generator and verify the correctness of our proof. Furthermore, we consider formulas extended with clauses from the proof until a short resolution proof exists, and investigate the performance of CDCL in finding the short proof. This turns out to be difficult for CDCL with the standard heuristics. Finally, we describe an approach inspired by SAT sweeping to find proofs of these extended formulas. 

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3. Stabbing Planes

   https://doi.org/10.48550/arXiv.1710.03219  

   Beame, Paul; Fleming, Noah; Impagliazzo, Russell; Pankratov, Denis; Pitassi, Toniann; Robere, Robert (May 2022, ArXivorg)

   We develop a new semi-algebraic proof system called Stabbing Planes which formalizes modern branch-and-cut algorithms for integer programming and is in the style of DPLL-based modern SAT solvers. As with DPLL there is only a single rule: the current polytope can be subdivided by branching on an inequality and its “integer negation.” That is, we can (non-deterministically choose) a hyperplane ax ≥ b with integer coefficients, which partitions the polytope into three pieces: the points in the polytope satisfying ax ≥ b, the points satisfying ax ≤ b, and the middle slab b − 1 < ax < b. Since the middle slab contains no integer points it can be safely discarded, and the algorithm proceeds recursively on the other two branches. Each path terminates when the current polytope is empty, which is polynomial-time checkable. Among our results, we show that Stabbing Planes can efficiently simulate the Cutting Planes proof system, and is equivalent to a tree-like variant of the R(CP) system of Krajicek [54]. As well, we show that it possesses short proofs of the canonical family of systems of F_2-linear equations known as the Tseitin formulas. Finally, we prove linear lower bounds on the rank of Stabbing Planes refutations by adapting lower bounds in communication complexity and use these bounds in order to show that Stabbing Planes proofs cannot be balanced. 

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4. Komodo: Using verification to disentangle secure-enclave hardware from software

   https://doi.org/10.1145/3132747.3132782  

   Ferraiuolo, Andrew; Baumann, Andrew; Hawblitzel, Chris; Parno, Bryan (January 2017, SOSP '17 Proceedings of the 26th Symposium on Operating Systems Principles)

   Intel SGX promises powerful security: an arbitrary number of user-mode enclaves protected against physical attacks and privileged software adversaries. However, to achieve this, Intel extended the x86 architecture with an isolation mechanism approaching the complexity of an OS microkernel, implemented by an inscrutable mix of silicon and microcode. While hardware-based security can offer performance and features that are difficult or impossible to achieve in pure software, hardware-only solutions are difficult to update, either to patch security flaws or introduce new features. Komodo illustrates an alternative approach to attested, on-demand, user-mode, concurrent isolated execution. We decouple the core hardware mechanisms such as memory encryption, address-space isolation and attestation from the management thereof, which Komodo delegates to a privileged software monitor that in turn implements enclaves. The monitor's correctness is ensured by a machine-checkable proof of both functional correctness and high-level security properties of enclave integrity and confidentiality. We show that the approach is practical and performant with a concrete implementation of a prototype in verified assembly code on ARM TrustZone. Our ultimate goal is to achieve security equivalent to or better than SGX while enabling deployment of new enclave features independently of CPU upgrades. The Komodo specification, prototype implementation, and proofs are available at https://github.com/Microsoft/Komodo. 

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5. How to Record Quantum Queries, and Applications to Quantum Indifferentiability

   https://doi.org/10.1007/978-3-030-26951-7_9  

   Zhandry, Mark (August 2019, CRYPTO 2019)

   The quantum random oracle model (QROM) has become the standard model in which to prove the post-quantum security of random-oracle-based constructions. Unfortunately, none of the known proof techniques allow the reduction to record information about the adversary’s queries, a crucial feature of many classical ROM proofs, including all proofs of indifferentiability for hash function domain extension. In this work, we give a new QROM proof technique that overcomes this “recording barrier”. We do so by giving a new “compressed oracle” which allows for efficient on-the-fly simulation of random oracles, roughly analogous to the usual classical simulation. We then use this new technique to give the first proof of quantum indifferentiability for the Merkle-Damgård domain extender for hash functions. We also give a proof of security for the Fujisaki-Okamoto transformation; previous proofs required modifying the scheme to include an additional hash term. Given the threat posed by quantum computers and the push toward quantum-resistant cryptosystems, our work represents an important tool for efficient post-quantum cryptosystems. 

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