arXiv subjects

Nikolaj I. Schwartzbach

Publications and source records attributed to Nikolaj I. Schwartzbach.

11 recordsLinked to original sources

arXiv2026

Collision Resistance of Single-Layer Neural Nets

We initiate the study of the algorithmic complexity of finding collisions in single-layer binary neural networks. Given a random matrix $\mathbf{A} \in \mathbb{R}^{m\times n}$, an input $\mathbf{x} \in \{-1,1\}^n$ is mapped to a binary output vector $φ(\mathbf{A}\mathbf{x})\in \{-1,1\}^m$, where $φ$ is an activation function with constant behavior on $[κ, \infty)$ for some threshold $κ\geq 0$. We identify the threshold scale $κ=Θ(1/\sqrtα)$, where $α=m/n$, as separating two complementary phenomena. When $κ\ll 1/\sqrtα$, we give a simple online algorithm that efficiently produces extensive collisions. When $κ\gg 1/\sqrtα$, for a natural \emph{randomized} non-periodic activation and suitable oscillation complexity, we prove that the extensive-collision space exhibits an overlap gap property (OGP), yielding an exponential lower bound against online algorithms. Ours is the first work to use the overlap gap property as a rigorous criterion for collision resistance. The key difference between collision finding and average-case search is that collision finding has a new ``worst-case'' aspect: the collision finder has full control over the choice of colliding pairs. Our lower bound is proved in the online model; extending such guarantees to broader classes of algorithms, including spectral, algebraic, lattice-based, or quantum methods, remains an open direction.

cs.CR↗

arXiv2025

Overlap Gap and Computational Thresholds in the Square Wave Perceptron

Square Wave Perceptrons (SWPs) form a class of neural network models with oscillating activation function that exhibit intriguing ``hardness'' properties in the high-dimensional limit at a fixed constraint density $α= O(1)$. In this work, we examine two key aspects of these models. The first is related to the so-called \emph{overlap-gap property}, that is a disconnectivity feature of the geometry of the solution space of combinatorial optimization problems proven to cause the failure of a large family of solvers, and conjectured to be a symptom of algorithmic hardness. We identify, both in the storage and in the teacher-student settings, the emergence of an overlap gap at a threshold $α_{\mathrm{OGP}}(δ)$, which can be made arbitrarily small by suitably increasing the frequency of oscillations $1/δ$ of the activation. This suggests that in this small-$δ$ regime, typical instances of the problem are hard to solve even for small values of $α$. Second, in the teacher-student setup, we show that the recovery threshold of the planted signal for message-passing algorithms can be made arbitrarily large by reducing $δ$. These properties make SWPs both a challenging benchmark for algorithms and an interesting candidate for cryptographic applications.

cond-mat.dis-nn↗

arXiv2025

Are Neural Networks Collision Resistant?

When neural networks are trained to classify a dataset, one finds a set of weights from which the network produces a label for each data point. We study the algorithmic complexity of finding a collision in a single-layer neural net, where a collision is defined as two distinct sets of weights that assign the same labels to all data. For binary perceptrons with oscillating activation functions, we establish the emergence of an overlap gap property in the space of collisions. This is a topological property believed to be a barrier to the performance of efficient algorithms. The hardness is supported by numerical experiments using approximate message passing algorithms, for which the algorithms stop working well below the value predicted by our analysis. Neural networks provide a new category of candidate collision resistant functions, which for some parameter setting depart from constructions based on lattices. Beyond relevance to cryptography, our work uncovers new forms of computational hardness emerging in large neural networks which may be of independent interest.

cond-mat.dis-nn↗

arXiv2024

Optimal MEV Extraction Using Absolute Commitments

We propose a new, more potent attack on decentralized exchanges. This attack leverages absolute commitments, which are commitments that can condition on the strategies made by other agents. This attack allows an adversary to charge monopoly prices by committing to undercut those other miners that refuse to charge an even higher fee. This allows the miner to extract the maximum possible price from the user, potentially through side channels that evade the inefficiencies and fees usually incurred. This is considerably more efficient than the prevailing strategy of `sandwich attacks', wherein the adversary induces and profits from fluctuations in the market price to the detriment of users. The attack we propose can, in principle, be realized by the irrevocable and self-executing nature of smart contracts, which are readily available on many major blockchains. Thus, the attack could potentially be used against a decentralized exchange and could drastically reduce the utility of the affected exchange.

cs.GT↗

arXiv2024

Which Games are Unaffected by Absolute Commitments?

We identify a subtle security issue that impacts mechanism design in scenarios in which agents can absolutely commit to strategies. Absolute commitments allow the strategy of an agent to depend on the commitments made by the other agents. This changes fundamental game-theoretic assumptions by inducing a meta-game in which agents choose which strategies they commit to. We say that a game that is unaffected by such commitments is Stackelberg resilient and show that computing it is intractible in general, although it can be computed efficiently for two-player games of perfect information. We show the intuitive, but technically non-trivial result, that, if a game is resilient when some number of players have the capacity to make commitments, it is also resilient when these commitments are available to fewer players. We demonstrate the non-triviality of Stackelberg resilience by analyzing two escrow mechanisms from the literature. These mechanisms have the same intended functionality, but we show that only one is Stackelberg resilient. Our model is particularly relevant in Web3 scenarios, where these absolute commitments can be realized by the automated and irrevocable nature of smart contracts. Our work highlights an important issue in ensuring the secure design of Web3. In particular, our work suggests that smart contracts already deployed on major blockchains may be susceptible to these attacks.

cs.GT↗

arXiv2023

$k$-SUM in the Sparse Regime

In the average-case $k$-SUM problem, given $r$ integers chosen uniformly at random from $\{0,\dots,M-1\}$, the objective is to find a ``solution'' set of $k$ numbers that sum to $0$ modulo $M$. In the dense regime of $M \leq r^k$, where solutions exist with high probability, the complexity of these problems is well understood. Much less is known in the sparse regime of $M\gg r^k$, where solutions are unlikely to exist. In this work, we initiate the study of the sparse regime for $k$-SUM and its variant $k$-XOR, especially their planted versions, where a random solution is planted in a randomly generated instance and has to be recovered. We provide evidence for the hardness of these problems and suggest new applications to cryptography. Complexity. First we study the complexity of these problems in the sparse regime and show: - Conditional Lower Bounds. Assuming established conjectures about the hardness of average-case (non-planted) $k$-SUM/$k$-XOR when $M = r^k$, we provide non-trivial lower bounds on the running time of algorithms for planted $k$-SUM when $r^k\leq M\leq r^{2k}$. - Hardness Amplification. We show that for any $M \geq r^k$, if an algorithm running in time $T$ solves planted $k$-SUM/$k$-XOR with success probability $Ω(1/\text{polylog}(r))$, then there is an algorithm running in time $\tilde{O}(T)$ that solves it with probability $(1-o(1))$. - New Reductions and Algorithms. We provide reductions for $k$-SUM/$k$-XOR from search to decision, as well as worst-case and average-case reductions to the Subset Sum problem from $k$-SUM, as well as a new algorithm for average-case $k$-XOR at low densities. Cryptography. We show that by additionally assuming mild hardness of $k$-XOR, we can construct Public Key Encryption (PKE) from a weaker variant of the Learning Parity with Noise (LPN) problem than was known before.

cs.CC↗

arXiv2023

Side Contract Commitment Attacks on Blockchains

We identify a subtle security issue that impacts the design of smart contracts, because agents may themselves deploy smart contracts (side contracts). Typically, equilibria of games are analyzed in vitro, under the assumption that players cannot arbitrarily commit to strategies. However, equilibria thus obtained do not hold in general in vivo, when games are deployed on a blockchain. Being able to deploy side contracts changes fundamental game-theoretic assumptions by inducing a meta-game wherein agents strategize to deploy the best contracts. Not taking side contracts into account thus fails to capture an important aspect of deploying smart contracts in practice. A game that remains secure when the players can deploy side contracts is said to be side contract resilient. We demonstrate the non-triviality of side contract resilience by analyzing two smart contracts for decentralized commerce. These contracts have the same intended functionality, but we show that only one is side contract resilient. We then demonstrate a side contract attack on first-price auctions, which are the transaction mechanisms used by most major blockchains. We show that an agent may deploy a contract ensuring their transaction is included in the next block at almost zero cost while forcing most other agents to enter into a lottery for the remaining block space. This benefits all the users, but is detrimental to the miners. This might be cause for re-evaluation of the use of auctions in transaction fee mechanisms. We show that the attack works under certain conditions that hold with high probability from natural distributions. The attack also works against the transaction mechanism EIP-1559. Our work highlights an issue that is necessary to address to ensure the secure deployment of smart contracts and suggests that other contracts already deployed on major blockchains may be susceptible to these attacks.

cs.GT↗

arXiv2023

Stackelberg Attacks on Auctions and Blockchain Transaction Fee Mechanisms

We study an auction with $m$ identical items in a context where $n$ agents can arbitrarily commit to strategies. In general, such commitments non-trivially change the equilibria by inducing a metagame of choosing which strategies to commit to. In this model, we demonstrate a strategy that an attacker may commit to that ensures they receive one such item for free, while forcing the remaining agents to enter into a lottery for the remaining items (albeit for free). The attack is thus detrimental to the auctioneer who loses most of their revenue. For various types of auctions that are not too congested, we show that the strategy works as long as the agents have valuations that are somewhat concentrated. In this case, all agents will voluntarily cooperate with the attacker to enter into the lottery, because doing so gives them a chance of receiving a free item that would have otherwise cost an amount commensurate with their valuation. The attack is robust to a large constant fraction of the agents being either oblivious to the attack or having exceptionally high valuations (thus reluctant to enter into the lottery). For these agents, the attacker may coerce them into cooperating by promising them a free item rather than entering in to the lottery. We show that the conditions for the attack to work hold with high probability when (1) the auction is not too congested, and (2) the valuations are sampled i.i.d. from either a uniform distribution or a Pareto distribution. The attack works for first-price auctions, second-price auctions and the transaction fee mechanism EIP-1559 used by the Ethereum blockchain.

cs.GT↗

arXiv2023

Outsourcing Adjudication to Strategic Jurors

We study a scenario where an adjudication task (e.g., the resolution of a binary dispute) is outsourced to a set of agents who are appointed as jurors. This scenario is particularly relevant in a Web3 environment, where no verification of the adjudication outcome is possible, and the appointed agents are, in principle, indifferent to the final verdict. We consider simple adjudication mechanisms that use (1) majority voting to decide the final verdict and (2) a payment function to reward the agents with the majority vote and possibly punish the ones in the minority. Agents interact with such a mechanism strategically: they exert some effort to understand how to properly judge the dispute and cast a yes/no vote that depends on this understanding and on information they have about the rest of the votes. Eventually, they vote so that their utility (i.e., their payment from the mechanism minus the cost due to their effort) is maximized. Under reasonable assumptions about how an agent's effort is related to her understanding of the dispute, we show that appropriate payment functions can be used to recover the correct adjudication outcome with high probability. Our findings follow from a detailed analysis of the induced strategic game and make use of both theoretical arguments and simulation experiments.

cs.GT↗

arXiv2022

Payment Schemes from Limited Information with Applications in Distributed Computing

We propose a generic mechanism for incentivizing behavior in an arbitrary finite game using payments. Doing so is trivial if the mechanism is allowed to observe all actions taken in the game, as this allows it to simply punish those agents who deviate from the intended strategy. Instead, we consider an abstraction where the mechanism probabilistically infers information about what happened in the game. We show that payment schemes can be used to implement any set of utilities if and only if the mechanism can essentially infer completely what happened. We show that finding an optimal payment scheme for games of perfect information is \textsf{P}-complete, and conjecture it to be \textsf{PPAD}-hard for games of imperfect information. We prove a lower bound on the size of the payments, showing that the payments must be linear in the intended level of security. We demonstrate the applicability of our model to concrete problems in distributed computing, namely decentralized commerce and secure multiparty computation, for which the payments match the lower bound asymptotically.

cs.GT↗

arXiv2021

Game theory on the blockchain: a model for games with smart contracts

We propose a model for games in which the players have shared access to a blockchain that allows them to deploy smart contracts to act on their behalf. This changes fundamental game-theoretic assumptions about rationality since a contract can commit a player to act irrationally in specific subgames, making credible otherwise non-credible threats. This is further complicated by considering the interaction between multiple contracts which can reason about each other. This changes the nature of the game in a nontrivial way as choosing which contract to play can itself be considered a move in the game. Our model generalizes known notions of equilibria, with a single contract being equivalent to a Stackelberg equilibrium, and two contracts being equivalent to a reverse Stackelberg equilibrium. We prove a number of bounds on the complexity of computing SPE in such games with smart contracts. We show that computing an SPE is $\textsf{PSPACE}$-hard in the general case. Specifically, in games with $k$ contracts, we show that computing an SPE is $Σ_k^\textsf{P}$-hard for games of imperfect information. We show that computing an SPE remains $\textsf{PSPACE}$-hard in games of perfect information if we allow for an unbounded number of contracts. We give an algorithm for computing an SPE in two-contract games of perfect information that runs in time $O(m\ell)$ where $m$ is the size of the game tree and $\ell$ is the number of terminal nodes. Finally, we conjecture the problem to be $\textsf{NP}$-complete for three contracts.

cs.GT↗