Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations

• URL: http://arxiv.org/abs/2505.00894v2
• Date: Wed, 16 Jul 2025 11:37:23 GMT
• Title: Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations
• Authors: Itai Dinur, Nathan Keller, Avichai Marmor,
• Abstract summary: We show that adaptivity provides a significant extra power in cryptanalytic time-space tradeoffs with (possibly unlimited) preprocessing time.<n>We present a new model that allows analyzing non-adaptive preprocessing algorithms for a wide array of search and decision problems.
• Score: 10.282294365033785
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The power of adaptivity in algorithms has been intensively studied in diverse areas of theoretical computer science. In this paper, we obtain a number of sharp lower bound results which show that adaptivity provides a significant extra power in cryptanalytic time-space tradeoffs with (possibly unlimited) preprocessing time. Most notably, we consider the discrete logarithm (DLOG) problem in a generic group of $N$ elements. The classical `baby-step giant-step' algorithm for the problem has time complexity $T=O(\sqrt{N})$, uses $O(\sqrt{N})$ bits of space (up to logarithmic factors in $N$) and achieves constant success probability. We examine a generalized setting where an algorithm obtains an advice string of $S$ bits and is allowed to make $T$ arbitrary non-adaptive queries that depend on the advice string (but not on the challenge group element). We show that in this setting, the $T=O(\sqrt{N})$ online time complexity of the baby-step giant-step algorithm cannot be improved, unless the advice string is more than $\Omega(\sqrt{N})$ bits long. This lies in stark contrast with the classical adaptive Pollard's rho algorithm for DLOG, which can exploit preprocessing to obtain the tradeoff curve $ST^2=O(N)$. We obtain similar sharp lower bounds for several other cryptanalytic problems. To obtain our results, we present a new model that allows analyzing non-adaptive preprocessing algorithms for a wide array of search and decision problems in a unified way. Since previous proof techniques inherently cannot distinguish between adaptive and non-adaptive algorithms for the problems in our model, they cannot be used to obtain our results. Consequently, our proof uses a variant of Shearer's lemma for this setting, due to Barthe, Cordero-Erausquin, Ledoux, and Maurey (2011). This seems to be the first time a variant of Shearer's lemma for permutations is used in an algorithmic context.

Related papers

• Near-Optimal Quantum Algorithms for Bounded Edit Distance and Lempel-Ziv Factorization [2.684542790908823]
  We present a quantum $tildeO(sqrtnk+k2)$-time algorithm that uses $tildeO(sqrtnz)$ queries, where $tildeO(cdot)$ hides polylogarithmic factors. Our second main contribution is a quantum algorithm that achieves the optimal time complexity of $tildeO(sqrtnz)$.
  arXiv  Detail & Related papers  (2023-11-03T09:09:23Z)
• Robust Approximation Algorithms for Non-monotone $k$-Submodular Maximization under a Knapsack Constraint [0.0]
  Two deterministic approximation algorithms are presented for the problem of non-monotone $k$-submodular complexity under a knapsack constraint. Our algorithms provide constant approximation ratios within only $O(nk)$ query complexity for the non-monotone objective.
  arXiv  Detail & Related papers  (2023-09-21T12:42:52Z)
• Efficiently Learning One-Hidden-Layer ReLU Networks via Schur Polynomials [50.90125395570797]
  We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $mathbbRd$ with respect to the square loss. Our main result is an efficient algorithm for this learning task with sample and computational complexity $(dk/epsilon)O(k)$, whereepsilon>0$ is the target accuracy.
  arXiv  Detail & Related papers  (2023-07-24T14:37:22Z)
• Deterministic Nonsmooth Nonconvex Optimization [82.39694252205011]
  We show that randomization is necessary to obtain a dimension-free dimension-free algorithm.<n>Our algorithm yields the first deterministic dimension-free algorithm for optimizing ReLU networks.
  arXiv  Detail & Related papers  (2023-02-16T13:57:19Z)
• Pseudonorm Approachability and Applications to Regret Minimization [73.54127663296906]
  We convert high-dimensional $ell_infty$-approachability problems to low-dimensional pseudonorm approachability problems. We develop an algorithmic theory of pseudonorm approachability, analogous to previous work on approachability for $ell$ and other norms.
  arXiv  Detail & Related papers  (2023-02-03T03:19:14Z)
• Gaussian Process Bandit Optimization with Few Batches [49.896920704012395]
  We introduce a batch algorithm inspired by finite-arm bandit algorithms. We show that it achieves the cumulative regret upper bound $Oast(sqrtTgamma_T)$ using $O(loglog T)$ batches within time horizon $T$. In addition, we propose a modified version of our algorithm, and characterize how the regret is impacted by the number of batches.
  arXiv  Detail & Related papers  (2021-10-15T00:54:04Z)
• Choosing the Right Algorithm With Hints From Complexity Theory [16.33500498939925]
  We show that the Metropolis algorithm is clearly the best of all algorithms regarded for reasonable problem sizes. An artificial algorithm of this type having an $O(n log n)$ runtime leads to the result that the significance-based compact genetic algorithm (sig-cGA) can solve the DLB problem in time $O(n log n)$ with high probability.
  arXiv  Detail & Related papers  (2021-09-14T11:12:32Z)
• Online Sub-Sampling for Reinforcement Learning with General Function Approximation [111.01990889581243]
  In this paper, we establish an efficient online sub-sampling framework that measures the information gain of data points collected by an RL algorithm. For a value-based method with complexity-bounded function class, we show that the policy only needs to be updated for $proptooperatornamepolylog(K)$ times. In contrast to existing approaches that update the policy for at least $Omega(K)$ times, our approach drastically reduces the number of optimization calls in solving for a policy.
  arXiv  Detail & Related papers  (2021-06-14T07:36:25Z)
• Practical and Parallelizable Algorithms for Non-Monotone Submodular Maximization with Size Constraint [20.104148319012854]
  We present and parallelizable for a submodular function, not necessarily a monotone, with respect to a size constraint. We improve the best approximation factor achieved by an algorithm that has optimal adaptivity and nearly optimal complexity query to $0.193 - varepsilon$.
  arXiv  Detail & Related papers  (2020-09-03T22:43:55Z)
• Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint [75.85952446237599]
  We show that a modified greedy algorithm can achieve an approximation factor of $0.305$. We derive a data-dependent upper bound on the optimum. It can also be used to significantly improve the efficiency of such algorithms as branch and bound.
  arXiv  Detail & Related papers  (2020-08-12T15:40:21Z)
• The $(1+(\lambda,\lambda))$ Genetic Algorithm for Permutations [0.0]
  We show that the $(lambda,lambda)$ genetic algorithm finds the optimum in $O(n2)$ fitness queries. We also present the first analysis of this algorithm on a permutation-based problem called Ham.
  arXiv  Detail & Related papers  (2020-04-18T17:04:57Z)
• Model Selection in Contextual Stochastic Bandit Problems [51.94632035240787]
  We develop a meta-algorithm that selects between base algorithms. We show through a lower bound that even when one of the base algorithms has $O(sqrtT)$ regret, in general it is impossible to get better than $Omega(sqrtT)$ regret.
  arXiv  Detail & Related papers  (2020-03-03T18:46:34Z)
• Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives [10.291482850329892]
  Mixed integer programming (MIP) can be used to solve (to optimality) $ell_0$-regularized regression problems. We propose two classes of scalable algorithms: an exact algorithm that can handlepapprox 50,000$ features in a few minutes, and approximate algorithms that can address instances with $papprox6$. In addition, we present new estimation error bounds for $ell$-regularizeds.
  arXiv  Detail & Related papers  (2020-01-17T18:47:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.