@article{18961, abstract = {Automated contact tracing (ACT) emerged as a promising measure to curb the spread of Covid-19. Users enable ACT on their smartphones to automatically record contacts with other users. If a user tests positive for the disease, they report their diagnosis to alert their contacts. Designing effective ACT protocols is challenging since they need to be efficient and secure while also ensuring users' privacy. As ACT protocols necessarily leak some information by design, defining privacy is difficult. For example, a user cannot deny having met another user. Ideally, however, the user can plausibly deny everything else, in particular, when they met. We call this privacy property contact-time deniability. While some early works discussed contact-time deniability informally, it has received little attention since then. We investigate deniability from a rigorous, theoretical point of view and arrive at the following impossibility result: A decentralized protocol with unidirectional communication cannot be contact-time deniable and replay-secure. This holds even if malicious users treat smartphones as black-boxes. Unidirectional protocols are usually very efficient and many proposals are unidirectional, e.g., the widely-deployed Google-Apple Exposure Notifications. So the impossibility result considerably constrains the design space of efficient, secure, and private ACT protocols. However, it can also be used as a guide; we discuss several possibilities to achieve contact-time deniability in practice.}, author = {Günther, Christoph Ullrich and Pietrzak, Krzysztof Z}, issn = {2299-0984}, journal = {Proceedings on Privacy Enhancing Technologies}, location = {Bristol, UK/Virtual}, number = {4}, pages = {636--648}, publisher = {Privacy Enhancing Technologies Symposium Advisory Board}, title = {{Deniability in automated contact tracing: Impossibilities and possibilities}}, doi = {10.56553/popets-2024-0134}, volume = {2024}, year = {2024}, } @article{14820, abstract = {We consider a natural problem dealing with weighted packet selection across a rechargeable link, which e.g., finds applications in cryptocurrency networks. The capacity of a link (u, v) is determined by how many nodes u and v allocate for this link. Specifically, the input is a finite ordered sequence of packets that arrive in both directions along a link. Given (u, v) and a packet of weight x going from u to v, node u can either accept or reject the packet. If u accepts the packet, the capacity on link (u, v) decreases by x. Correspondingly, v's capacity on increases by x. If a node rejects the packet, this will entail a cost affinely linear in the weight of the packet. A link is “rechargeable” in the sense that the total capacity of the link has to remain constant, but the allocation of capacity at the ends of the link can depend arbitrarily on the nodes' decisions. The goal is to minimise the sum of the capacity injected into the link and the cost of rejecting packets. We show that the problem is NP-hard, but can be approximated efficiently with a ratio of (1+E) . (1+3) for some arbitrary E>0.}, author = {Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, issn = {0304-3975}, journal = {Theoretical Computer Science}, keywords = {General Computer Science, Theoretical Computer Science}, publisher = {Elsevier}, title = {{Weighted packet selection for rechargeable links in cryptocurrency networks: Complexity and approximation}}, doi = {10.1016/j.tcs.2023.114353}, volume = {989}, year = {2024}, } @inproceedings{15007, abstract = {Traditional blockchains grant the miner of a block full control not only over which transactions but also their order. This constitutes a major flaw discovered with the introduction of decentralized finance and allows miners to perform MEV attacks. In this paper, we address the issue of sandwich attacks by providing a construction that takes as input a blockchain protocol and outputs a new blockchain protocol with the same security but in which sandwich attacks are not profitable. Furthermore, our protocol is fully decentralized with no trusted third parties or heavy cryptography primitives and carries a linear increase in latency and minimum computation overhead.}, author = {Alpos, Orestis and Amores-Sesar, Ignacio and Cachin, Christian and Yeo, Michelle X}, booktitle = {27th International Conference on Principles of Distributed Systems}, isbn = {9783959773089}, issn = {1868-8969}, location = {Tokyo, Japan}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Eating sandwiches: Modular and lightweight elimination of transaction reordering attacks}}, doi = {10.4230/LIPIcs.OPODIS.2023.12}, volume = {286}, year = {2024}, } @inproceedings{17051, abstract = {Memory-hard functions (MHF) are functions whose evaluation provably requires a lot of memory. While MHFs are an unkeyed primitive, it is natural to consider the notion of trapdoor MHFs (TMHFs). A TMHF is like an MHF, but when sampling the public parameters one also samples a trapdoor which allows evaluating the function much cheaper. Biryukov and Perrin (Asiacrypt’17) were the first to consider TMHFs and put forth a candidate TMHF construction called Diodon that is based on the Scrypt MHF (Percival, BSDCan’09). To allow for a trapdoor, Scrypt’s initial hash chain is replaced by a sequence of squares in a group of unknown order where the order of the group is the trapdoor. For a length n sequence of squares and a group of order N, Diodon’s cumulative memory complexity (CMC) is O(n2log N) without the trapdoor and O(n log(n) log(N)2) with knowledge of it. While Scrypt is proven to be optimally memory-hard in the random oracle model (Alwen et al., Eurocrypt’17), Diodon’s memory-hardness has not been proven so far. In this work, we fill this gap by rigorously analyzing a specific instantiation of Diodon. We show that its CMC is lower bounded by Ω( n2log nlog N) which almost matches the upper bound. Our proof is based Alwen et al.’s lower bound on Scrypt’s CMC but requires non-trivial modifications due to the algebraic structure of Diodon. Most importantly, our analysis involves a more elaborate compression argument and a solvability criterion for certain systems of Diophantine equations.}, author = {Auerbach, Benedikt and Günther, Christoph Ullrich and Pietrzak, Krzysztof Z}, booktitle = {43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques}, isbn = {9783031587337}, issn = {1611-3349}, location = {Zurich, Switzerland}, pages = {315--344}, publisher = {Springer Nature}, title = {{Trapdoor memory-hard functions}}, doi = {10.1007/978-3-031-58734-4_11}, volume = {14653}, year = {2024}, } @inproceedings{17126, abstract = {Functional encryption (FE) is a primitive where the holder of a master secret key can control which functions a user can evaluate on encrypted data. It is a powerful primitive that even implies indistinguishability obfuscation (iO), given sufficiently compact ciphertexts (Ananth-Jain, CRYPTO’15 and Bitansky-Vaikuntanathan, FOCS’15). However, despite being extensively studied, there are FE schemes, such as function-hiding inner-product FE (Bishop-Jain-Kowalczyk, AC’15, Abdalla-Catalano-Fiore-Gay-Ursu, CRYPTO’18) and compact quadratic FE (Baltico-Catalano-Fiore-Gay, Lin, CRYPTO’17), that can be only realized using pairings. This raises the question if there are some mathematical barriers that hinder us from realizing these FE schemes from other assumptions. In this paper, we study the difficulty of constructing lattice-based compact FE. We generalize the impossibility results of Ünal (EC’20) for lattice-based function-hiding FE, and extend it to the case of compact FE. Concretely, we prove lower bounds for lattice-based compact FE schemes which meet some (natural) algebraic restrictions at encryption and decryption, and have ciphertexts of linear size and secret keys of minimal degree. We see our results as important indications of why it is hard to construct lattice-based FE schemes for new functionalities, and which mathematical barriers have to be overcome.}, author = {Tairi, Erkan and Ünal, Akin}, booktitle = {Advances in Cryptology – EUROCRYPT 2024}, isbn = {9783031587221}, issn = {1611-3349}, location = {Zurich, Switzerland}, pages = {249--279}, publisher = {Springer Nature}, title = {{Lower bounds for lattice-based compact functional encryption}}, doi = {10.1007/978-3-031-58723-8_9}, volume = {14652}, year = {2024}, } @inproceedings{17328, abstract = {We study selfish mining attacks in longest-chain blockchains like Bitcoin, but where the proof of work is replaced with efficient proof systems - like proofs of stake or proofs of space - and consider the problem of computing an optimal selfish mining attack which maximizes expected relative revenue of the adversary, thus minimizing the chain quality. To this end, we propose a novel selfish mining attack that aims to maximize this objective and formally model the attack as a Markov decision process (MDP). We then present a formal analysis procedure which computes an ϵ-tight lower bound on the optimal expected relative revenue in the MDP and a strategy that achieves this ϵ-tight lower bound, where ϵ > 0 may be any specified precision. Our analysis is fully automated and provides formal guarantees on the correctness. We evaluate our selfish mining attack and observe that it achieves superior expected relative revenue compared to two considered baselines. In concurrent work [Sarenche FC'24] does an automated analysis on selfish mining in predictable longest-chain blockchains based on efficient proof systems. Predictable means the randomness for the challenges is fixed for many blocks (as used e.g., in Ouroboros), while we consider unpredictable (Bitcoin-like) chains where the challenge is derived from the previous block.}, author = {Chatterjee, Krishnendu and Ebrahimzadeh, Amirali and Karrabi, Mehrdad and Pietrzak, Krzysztof Z and Yeo, Michelle X and Zikelic, Dorde}, booktitle = { Proceedings of the 43rd Annual ACM Symposium on Principles of Distributed Computing}, isbn = {9798400706684}, location = {Nantes, France}, pages = {268--278}, publisher = {Association for Computing Machinery}, title = {{Fully automated selfish mining analysis in efficient proof systems blockchains}}, doi = {10.1145/3662158.3662769}, year = {2024}, } @unpublished{20701, abstract = {A Proof of Exponentiation (PoE) allows a prover to efficiently convince a verifier that 𝑦 = 𝑥 𝑒 in some group of unknown order. PoEs are the basis for practical constructions of Verifiable Delay Functions (VDFs), which, in turn, are important for various higher-level protocols in distributed computing. In applications such as distributed consensus, many PoEs are generated regularly, motivating protocols for secure aggregation of batches of statements into a few statements to improve the efficiency for both parties. Rotem (TCC 2021) recently presented two such generic batch PoEs. In this work, we introduce two batch PoEs that outperform both proposals of Rotem and we evaluate their practicality. First, we show that the two batch PoEs of Rotem can be combined to improve the overall efficiency by at least a factor of two. Second, we revisit the work of Bellare, Garay, and Rabin (EUROCRYPT 1998) on batch verification of digital signatures and show that, under the low order assumption, their bucket test can be securely adapted to the setting of groups of unknown order. The resulting batch PoE quickly outperforms the state of the art in the expected number of group multiplications with the growing number of instances, and it decreases the cost of batching by an order of magnitude already for hundreds of thousands of instances. Importantly, it is the first batch PoE that significantly decreases both the proof size and complexity of verification. Our experimental evaluations show that even a nonoptimized implementation achieves such improvements, which would match the demands of real-life systems requiring large-scale PoE processing. Finally, even though our proof techniques are conceptually similar to Rotem, we give an improved analysis of the application of the low order assumption towards secure batching of PoE instances, resulting in a tight reduction, which is important when setting the security parameter in practice.}, author = {Hoffmann, Charlotte and Hubáček, Pavel and Ivanova, Svetlana}, booktitle = {Cryptology ePrint Archive}, publisher = {International Association for Cryptologic Research }, title = {{Practical batch proofs of exponentiation}}, year = {2024}, } @phdthesis{18088, abstract = {Instant messaging applications like Whatsapp, Signal or Telegram have become ubiquitous in today's society. Many of them provide not only end-to-end encryption, but also security guarantees even when the key material gets compromised. These are achieved through frequent key update performed by users. In particular, the compromise of a group key should preserve confidentiality of previously exchanged messages (forward secrecy), and a subsequent key update will ensure security for future ones (post-compromise security). Though great protocols for one-on-one communication have been known for some time, the design of ones that scale efficiently for larger groups while achieving akin security guarantees is a hard problem. A great deal of research has been aimed at this topic, much of it under the umbrella of the Messaging Layer Security (MLS) working group at the IETF. Started in 2018, this joint effort by academics and industry culminated in 2023 with the publication of the first standard for secure group messaging [IETF, RFC9420]. At the core of secure group messaging is a cryptographic primitive termed Continuous Group Key Agreement, or CGKA [Alwen et al. 2021], that essentially allows a changing group of users to agree on a common key with the added functionality security against compromises is achieved by users asynchronously issuing a key update. In this thesis we contribute to the understanding of CGKA across different angles. First, we present a new technique to effect dynamic operations in groups, i.e., add or remove members, that can be more efficient that the one employed by MLS in certain settings. Considering the setting of users belonging to multiple overlapping groups, we then show lowerbounds on the communication cost of constructions that leverage said overlap, at the same time showing protocols that are asymptotically optimal and efficient for practical settings, respectively. Along the way, we show that the communication cost of key updates in MLS is average-cost optimal. An important feature in CGKA protocols, particularly for big groups, is the possibility of executing several group operations concurrently. While later versions of MLS support this, they do at the cost of worsening the communication efficiency of future group operations. In this thesis we introduce two new protocols that permit concurrency without any negative effect on efficiency. Our protocols circumvent previously existing lower bounds by satisfying a new notion of post-compromise security that only asks for security to be re-established after a certain number of key updates have taken place. While this can be slower than MLS in terms of rounds of communication, we show that it leads to more efficient overall communication. Additionally, we introduce a new technique that allows group members to decrease the information they need to store and download, which makes one of our protocols enjoy much lower download cost than any other existing CGKA constructions. }, author = {Pascual Perez, Guillermo}, issn = {2663-337X}, pages = {239}, publisher = {Institute of Science and Technology Austria}, title = {{On the efficiency and security of secure group messaging}}, doi = {10.15479/at:ista:18088}, year = {2024}, } @inproceedings{18086, abstract = {Abstract. Continuous group key agreement (CGKA) allows a group of users to maintain a continuously updated shared key in an asynchronous setting where parties only come online sporadically and their messages are relayed by an untrusted server. CGKA captures the basic primitive underlying group messaging schemes. Current solutions including TreeKEM (“Messaging Layer Security” (MLS) IETF RFC 9420) cannot handle concurrent requests while retaining low communication complexity. The exception being CoCoA, which is concurrent while having extremely low communication complexity (in groups of size n and for m concurrent updates the communication per user is log(n), i.e., independent of m). The main downside of CoCoA is that in groups of size n, users might have to do up to log(n) update requests to the server to ensure their (potentially corrupted) key material has been refreshed. In this work we present a “fast healing” concurrent CGKA protocol, named DeCAF, where users will heal after at most log(t) requests, with t being the number of corrupted users. While also suitable for the standard central-server setting, our protocol is particularly interesting for realizing decentralized group messaging, where protocol messages (add, remove, update) are being posted on some append-only data structure rather than sent to a server. In this setting, concurrency is crucial once the rate of requests exceeds, say, the rate at which new blocks are added to a blockchain. In the central-server setting, CoCoA (the only alternative with concurrency, sub-linear communication and basic post-compromise security) enjoys much lower download communication. However, in the decentralized setting – where there is no server which can craft specific messages for different users to reduce their download communication – our protocol significantly outperforms CoCoA. DeCAF heals in fewer epochs (log(t) vs. log(n)) while incurring a similar per epoch per user communication cost.}, author = {Alwen, Joel F and Auerbach, Benedikt and Cueto Noval, Miguel and Klein, Karen and Pascual Perez, Guillermo and Pietrzak, Krzysztof Z}, booktitle = {Security and Cryptography for Networks: 14th International Conference}, editor = {Galdi, Clemente and Phan, Duong Hieu}, isbn = {9783031710728}, issn = {1611-3349}, location = {Amalfi, Italy}, pages = {294–313}, publisher = {Springer Nature}, title = {{DeCAF: Decentralizable CGKA with fast healing}}, doi = {10.1007/978-3-031-71073-5_14}, volume = {14974}, year = {2024}, } @article{12164, abstract = {A shared-memory counter is a widely-used and well-studied concurrent object. It supports two operations: An Inc operation that increases its value by 1 and a Read operation that returns its current value. In Jayanti et al (SIAM J Comput, 30(2), 2000), Jayanti, Tan and Toueg proved a linear lower bound on the worst-case step complexity of obstruction-free implementations, from read-write registers, of a large class of shared objects that includes counters. The lower bound leaves open the question of finding counter implementations with sub-linear amortized step complexity. In this work, we address this gap. We show that n-process, wait-free and linearizable counters can be implemented from read-write registers with O(log2n) amortized step complexity. This is the first counter algorithm from read-write registers that provides sub-linear amortized step complexity in executions of arbitrary length. Since a logarithmic lower bound on the amortized step complexity of obstruction-free counter implementations exists, our upper bound is within a logarithmic factor of the optimal. The worst-case step complexity of the construction remains linear, which is optimal. This is obtained thanks to a new max register construction with O(logn) amortized step complexity in executions of arbitrary length in which the value stored in the register does not grow too quickly. We then leverage an existing counter algorithm by Aspnes, Attiya and Censor-Hillel [1] in which we “plug” our max register implementation to show that it remains linearizable while achieving O(log2n) amortized step complexity.}, author = {Baig, Mirza Ahad and Hendler, Danny and Milani, Alessia and Travers, Corentin}, issn = {1432-0452}, journal = {Distributed Computing}, keywords = {Computational Theory and Mathematics, Computer Networks and Communications, Hardware and Architecture, Theoretical Computer Science}, pages = {29--43}, publisher = {Springer Nature}, title = {{Long-lived counters with polylogarithmic amortized step complexity}}, doi = {10.1007/s00446-022-00439-5}, volume = {36}, year = {2023}, } @inproceedings{14428, abstract = {Suppose we have two hash functions h1 and h2, but we trust the security of only one of them. To mitigate this worry, we wish to build a hash combiner Ch1,h2 which is secure so long as one of the underlying hash functions is. This question has been well-studied in the regime of collision resistance. In this case, concatenating the two hash function outputs clearly works. Unfortunately, a long series of works (Boneh and Boyen, CRYPTO’06; Pietrzak, Eurocrypt’07; Pietrzak, CRYPTO’08) showed no (noticeably) shorter combiner for collision resistance is possible. In this work, we revisit this pessimistic state of affairs, motivated by the observation that collision-resistance is insufficient for many interesting applications of cryptographic hash functions anyway. We argue the right formulation of the “hash combiner” is to build what we call random oracle (RO) combiners, utilizing stronger assumptions for stronger constructions. Indeed, we circumvent the previous lower bounds for collision resistance by constructing a simple length-preserving RO combiner C˜h1,h2Z1,Z2(M)=h1(M,Z1)⊕h2(M,Z2),where Z1,Z2 are random salts of appropriate length. We show that this extra randomness is necessary for RO combiners, and indeed our construction is somewhat tight with this lower bound. On the negative side, we show that one cannot generically apply the composition theorem to further replace “monolithic” hash functions h1 and h2 by some simpler indifferentiable construction (such as the Merkle-Damgård transformation) from smaller components, such as fixed-length compression functions. Finally, despite this issue, we directly prove collision resistance of the Merkle-Damgård variant of our combiner, where h1 and h2 are replaced by iterative Merkle-Damgård hashes applied to a fixed-length compression function. Thus, we can still subvert the concatenation barrier for collision-resistance combiners while utilizing practically small fixed-length components underneath.}, author = {Dodis, Yevgeniy and Ferguson, Niels and Goldin, Eli and Hall, Peter and Pietrzak, Krzysztof Z}, booktitle = {43rd Annual International Cryptology Conference}, isbn = {9783031385445}, issn = {1611-3349}, location = {Santa Barbara, CA, United States}, pages = {514--546}, publisher = {Springer Nature}, title = {{Random oracle combiners: Breaking the concatenation barrier for collision-resistance}}, doi = {10.1007/978-3-031-38545-2_17}, volume = {14082}, year = {2023}, } @inproceedings{14457, abstract = {Threshold secret sharing allows a dealer to split a secret s into n shares, such that any t shares allow for reconstructing s, but no t-1 shares reveal any information about s. Leakage-resilient secret sharing requires that the secret remains hidden, even when an adversary additionally obtains a limited amount of leakage from every share. Benhamouda et al. (CRYPTO’18) proved that Shamir’s secret sharing scheme is one bit leakage-resilient for reconstruction threshold t≥0.85n and conjectured that the same holds for t = c.n for any constant 0≤c≤1. Nielsen and Simkin (EUROCRYPT’20) showed that this is the best one can hope for by proving that Shamir’s scheme is not secure against one-bit leakage when t0c.n/log(n). In this work, we strengthen the lower bound of Nielsen and Simkin. We consider noisy leakage-resilience, where a random subset of leakages is replaced by uniformly random noise. We prove a lower bound for Shamir’s secret sharing, similar to that of Nielsen and Simkin, which holds even when a constant fraction of leakages is replaced by random noise. To this end, we first prove a lower bound on the share size of any noisy-leakage-resilient sharing scheme. We then use this lower bound to show that there exist universal constants c1, c2, such that for sufficiently large n it holds that Shamir’s secret sharing scheme is not noisy-leakage-resilient for t≤c1.n/log(n), even when a c2 fraction of leakages are replaced by random noise. }, author = {Hoffmann, Charlotte and Simkin, Mark}, booktitle = {8th International Conference on Cryptology and Information Security in Latin America}, isbn = {9783031444685}, issn = {1611-3349}, location = {Quito, Ecuador}, pages = {215--228}, publisher = {Springer Nature}, title = {{Stronger lower bounds for leakage-resilient secret sharing}}, doi = {10.1007/978-3-031-44469-2_11}, volume = {14168}, year = {2023}, } @inproceedings{14691, abstract = {Continuous Group-Key Agreement (CGKA) allows a group of users to maintain a shared key. It is the fundamental cryptographic primitive underlying group messaging schemes and related protocols, most notably TreeKEM, the underlying key agreement protocol of the Messaging Layer Security (MLS) protocol, a standard for group messaging by the IETF. CKGA works in an asynchronous setting where parties only occasionally must come online, and their messages are relayed by an untrusted server. The most expensive operation provided by CKGA is that which allows for a user to refresh their key material in order to achieve forward secrecy (old messages are secure when a user is compromised) and post-compromise security (users can heal from compromise). One caveat of early CGKA protocols is that these update operations had to be performed sequentially, with any user wanting to update their key material having had to receive and process all previous updates. Late versions of TreeKEM do allow for concurrent updates at the cost of a communication overhead per update message that is linear in the number of updating parties. This was shown to be indeed necessary when achieving PCS in just two rounds of communication by [Bienstock et al. TCC’20]. The recently proposed protocol CoCoA [Alwen et al. Eurocrypt’22], however, shows that this overhead can be reduced if PCS requirements are relaxed, and only a logarithmic number of rounds is required. The natural question, thus, is whether CoCoA is optimal in this setting. In this work we answer this question, providing a lower bound on the cost (concretely, the amount of data to be uploaded to the server) for CGKA protocols that heal in an arbitrary k number of rounds, that shows that CoCoA is very close to optimal. Additionally, we extend CoCoA to heal in an arbitrary number of rounds, and propose a modification of it, with a reduced communication cost for certain k. We prove our bound in a combinatorial setting where the state of the protocol progresses in rounds, and the state of the protocol in each round is captured by a set system, each set specifying a set of users who share a secret key. We show this combinatorial model is equivalent to a symbolic model capturing building blocks including PRFs and public-key encryption, related to the one used by Bienstock et al. Our lower bound is of order k•n1+1/(k-1)/log(k), where 2≤k≤log(n) is the number of updates per user the protocol requires to heal. This generalizes the n2 bound for k=2 from Bienstock et al.. This bound almost matches the k⋅n1+2/(k-1) or k2⋅n1+1/(k-1) efficiency we get for the variants of the CoCoA protocol also introduced in this paper.}, author = {Auerbach, Benedikt and Cueto Noval, Miguel and Pascual Perez, Guillermo and Pietrzak, Krzysztof Z}, booktitle = {21st International Conference on Theory of Cryptography}, isbn = {9783031486203}, issn = {1611-3349}, location = {Taipei, Taiwan}, pages = {271--300}, publisher = {Springer Nature}, title = {{On the cost of post-compromise security in concurrent Continuous Group-Key Agreement}}, doi = {10.1007/978-3-031-48621-0_10}, volume = {14371}, year = {2023}, } @inproceedings{14692, abstract = {The generic-group model (GGM) aims to capture algorithms working over groups of prime order that only rely on the group operation, but do not exploit any additional structure given by the concrete implementation of the group. In it, it is possible to prove information-theoretic lower bounds on the hardness of problems like the discrete logarithm (DL) or computational Diffie-Hellman (CDH). Thus, since its introduction, it has served as a valuable tool to assess the concrete security provided by cryptographic schemes based on such problems. A work on the related algebraic-group model (AGM) introduced a method, used by many subsequent works, to adapt GGM lower bounds for one problem to another, by means of conceptually simple reductions. In this work, we propose an alternative approach to extend GGM bounds from one problem to another. Following an idea by Yun [EC15], we show that, in the GGM, the security of a large class of problems can be reduced to that of geometric search-problems. By reducing the security of the resulting geometric-search problems to variants of the search-by-hypersurface problem, for which information theoretic lower bounds exist, we give alternative proofs of several results that used the AGM approach. The main advantage of our approach is that our reduction from geometric search-problems works, as well, for the GGM with preprocessing (more precisely the bit-fixing GGM introduced by Coretti, Dodis and Guo [Crypto18]). As a consequence, this opens up the possibility of transferring preprocessing GGM bounds from one problem to another, also by means of simple reductions. Concretely, we prove novel preprocessing bounds on the hardness of the d-strong discrete logarithm, the d-strong Diffie-Hellman inversion, and multi-instance CDH problems, as well as a large class of Uber assumptions. Additionally, our approach applies to Shoup’s GGM without additional restrictions on the query behavior of the adversary, while the recent works of Zhang, Zhou, and Katz [AC22] and Zhandry [Crypto22] highlight that this is not the case for the AGM approach.}, author = {Auerbach, Benedikt and Hoffmann, Charlotte and Pascual Perez, Guillermo}, booktitle = {21st International Conference on Theory of Cryptography}, isbn = {9783031486203}, issn = {1611-3349}, pages = {301--330}, publisher = {Springer Nature}, title = {{Generic-group lower bounds via reductions between geometric-search problems: With and without preprocessing}}, doi = {10.1007/978-3-031-48621-0_11}, volume = {14371}, year = {2023}, } @inproceedings{14693, abstract = {Lucas sequences are constant-recursive integer sequences with a long history of applications in cryptography, both in the design of cryptographic schemes and cryptanalysis. In this work, we study the sequential hardness of computing Lucas sequences over an RSA modulus. First, we show that modular Lucas sequences are at least as sequentially hard as the classical delay function given by iterated modular squaring proposed by Rivest, Shamir, and Wagner (MIT Tech. Rep. 1996) in the context of time-lock puzzles. Moreover, there is no obvious reduction in the other direction, which suggests that the assumption of sequential hardness of modular Lucas sequences is strictly weaker than that of iterated modular squaring. In other words, the sequential hardness of modular Lucas sequences might hold even in the case of an algorithmic improvement violating the sequential hardness of iterated modular squaring. Second, we demonstrate the feasibility of constructing practically-efficient verifiable delay functions based on the sequential hardness of modular Lucas sequences. Our construction builds on the work of Pietrzak (ITCS 2019) by leveraging the intrinsic connection between the problem of computing modular Lucas sequences and exponentiation in an appropriate extension field.}, author = {Hoffmann, Charlotte and Hubáček, Pavel and Kamath, Chethan and Krňák, Tomáš}, booktitle = {21st International Conference on Theory of Cryptography}, isbn = {9783031486234}, issn = {1611-3349}, location = {Taipei, Taiwan}, pages = {336--362}, publisher = {Springer Nature}, title = {{(Verifiable) delay functions from Lucas sequences}}, doi = {10.1007/978-3-031-48624-1_13}, volume = {14372}, year = {2023}, } @inproceedings{14736, abstract = {Payment channel networks (PCNs) are a promising technology to improve the scalability of cryptocurrencies. PCNs, however, face the challenge that the frequent usage of certain routes may deplete channels in one direction, and hence prevent further transactions. In order to reap the full potential of PCNs, recharging and rebalancing mechanisms are required to provision channels, as well as an admission control logic to decide which transactions to reject in case capacity is insufficient. This paper presents a formal model of this optimisation problem. In particular, we consider an online algorithms perspective, where transactions arrive over time in an unpredictable manner. Our main contributions are competitive online algorithms which come with provable guarantees over time. We empirically evaluate our algorithms on randomly generated transactions to compare the average performance of our algorithms to our theoretical bounds. We also show how this model and approach differs from related problems in classic communication networks.}, author = {Bastankhah, Mahsa and Chatterjee, Krishnendu and Maddah-Ali, Mohammad Ali and Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, booktitle = {27th International Conference on Financial Cryptography and Data Security}, isbn = {9783031477539}, issn = {1611-3349}, location = {Bol, Brac, Croatia}, pages = {309--325}, publisher = {Springer Nature}, title = {{R2: Boosting liquidity in payment channel networks with online admission control}}, doi = {10.1007/978-3-031-47754-6_18}, volume = {13950}, year = {2023}, } @inproceedings{19985, abstract = {We consider a natural problem dealing with weighted packet selection across a rechargeable link, which e.g., finds applications in cryptocurrency networks. The capacity of a link (u, v) is determined by how much nodes u and v allocate for this link. Specifically, the input is a finite ordered sequence of packets that arrive in both directions along a link. Given (u, v) and a packet of weight x going from u to v, node u can either accept or reject the packet. If u accepts the packet, the capacity on link (u, v) decreases by x. Correspondingly, v’s capacity on (u, v) increases by x. If a node rejects the packet, this will entail a cost affinely linear in the weight of the packet. A link is “rechargeable” in the sense that the total capacity of the link has to remain constant, but the allocation of capacity at the ends of the link can depend arbitrarily on the nodes’ decisions. The goal is to minimise the sum of the capacity injected into the link and the cost of rejecting packets. We show that the problem is NP-hard, but can be approximated efficiently with a ratio of (1 + E) . (1 + square3) for some arbitrary E>0.}, author = {Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, booktitle = {30th International Colloquium on Structural Information and Communication Complexity}, isbn = {9783031327322}, issn = {1611-3349}, location = {Alcalá de Henares, Spain}, pages = {576--594}, publisher = {Springer Nature}, title = {{Weighted acket selection for rechargeable links in cryptocurrency networks: Complexity and approximation}}, doi = {10.1007/978-3-031-32733-9_26}, volume = {13892}, year = {2023}, } @inproceedings{13143, abstract = {GIMPS and PrimeGrid are large-scale distributed projects dedicated to searching giant prime numbers, usually of special forms like Mersenne and Proth primes. The numbers in the current search-space are millions of digits large and the participating volunteers need to run resource-consuming primality tests. Once a candidate prime N has been found, the only way for another party to independently verify the primality of N used to be by repeating the expensive primality test. To avoid the need for second recomputation of each primality test, these projects have recently adopted certifying mechanisms that enable efficient verification of performed tests. However, the mechanisms presently in place only detect benign errors and there is no guarantee against adversarial behavior: a malicious volunteer can mislead the project to reject a giant prime as being non-prime. In this paper, we propose a practical, cryptographically-sound mechanism for certifying the non-primality of Proth numbers. That is, a volunteer can – parallel to running the primality test for N – generate an efficiently verifiable proof at a little extra cost certifying that N is not prime. The interactive protocol has statistical soundness and can be made non-interactive using the Fiat-Shamir heuristic. Our approach is based on a cryptographic primitive called Proof of Exponentiation (PoE) which, for a group G, certifies that a tuple (x,y,T)∈G2×N satisfies x2T=y (Pietrzak, ITCS 2019 and Wesolowski, J. Cryptol. 2020). In particular, we show how to adapt Pietrzak’s PoE at a moderate additional cost to make it a cryptographically-sound certificate of non-primality.}, author = {Hoffmann, Charlotte and Hubáček, Pavel and Kamath, Chethan and Pietrzak, Krzysztof Z}, booktitle = {Public-Key Cryptography - PKC 2023}, isbn = {9783031313677}, issn = {1611-3349}, location = {Atlanta, GA, United States}, pages = {530--553}, publisher = {Springer Nature}, title = {{Certifying giant nonprimes}}, doi = {10.1007/978-3-031-31368-4_19}, volume = {13940}, year = {2023}, } @phdthesis{14506, abstract = {Payment channel networks are a promising approach to improve the scalability bottleneck of cryptocurrencies. Two design principles behind payment channel networks are efficiency and privacy. Payment channel networks improve efficiency by allowing users to transact in a peer-to-peer fashion along multi-hop routes in the network, avoiding the lengthy process of consensus on the blockchain. Transacting over payment channel networks also improves privacy as these transactions are not broadcast to the blockchain. Despite the influx of recent protocols built on top of payment channel networks and their analysis, a common shortcoming of many of these protocols is that they typically focus only on either improving efficiency or privacy, but not both. Another limitation on the efficiency front is that the models used to model actions, costs and utilities of users are limited or come with unrealistic assumptions. This thesis aims to address some of the shortcomings of recent protocols and algorithms on payment channel networks, particularly in their privacy and efficiency aspects. We first present a payment route discovery protocol based on hub labelling and private information retrieval that hides the route query and is also efficient. We then present a rebalancing protocol that formulates the rebalancing problem as a linear program and solves the linear program using multiparty computation so as to hide the channel balances. The rebalancing solution as output by our protocol is also globally optimal. We go on to develop more realistic models of the action space, costs, and utilities of both existing and new users that want to join the network. In each of these settings, we also develop algorithms to optimise the utility of these users with good guarantees on the approximation and competitive ratios.}, author = {Yeo, Michelle X}, issn = {2663-337X}, pages = {162}, publisher = {Institute of Science and Technology Austria}, title = {{Advances in efficiency and privacy in payment channel network analysis}}, doi = {10.15479/14506}, year = {2023}, } @inproceedings{14490, abstract = {Payment channel networks (PCNs) are a promising solution to the scalability problem of cryptocurrencies. Any two users connected by a payment channel in the network can theoretically send an unbounded number of instant, costless transactions between them. Users who are not directly connected can also transact with each other in a multi-hop fashion. In this work, we study the incentive structure behind the creation of payment channel networks, particularly from the point of view of a single user that wants to join the network. We define a utility function for a new user in terms of expected revenue, expected fees, and the cost of creating channels, and then provide constant factor approximation algorithms that optimise the utility function given a certain budget. Additionally, we take a step back from a single user to the whole network and examine the parameter spaces under which simple graph topologies form a Nash equilibrium.}, author = {Avarikioti, Zeta and Lizurej, Tomasz and Michalak, Tomasz and Yeo, Michelle X}, booktitle = {43rd International Conference on Distributed Computing Systems}, isbn = {9798350339864}, issn = {2575-8411}, location = {Hong Kong, China}, pages = {603--613}, publisher = {IEEE}, title = {{Lightning creation games}}, doi = {10.1109/ICDCS57875.2023.00037}, volume = {2023}, year = {2023}, }