IEEE Transactions on Information Theory最新文献

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Instance-Optimality in Optimal Value Estimation: Adaptivity via Variance-Reduced Q-Learning 最优值估计中的实例最优性:通过降低方差的 Q 学习实现适应性
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2024-04-09 DOI: 10.1109/TIT.2024.3386122
Eric Xia;Koulik Khamaru;Martin J. Wainwright;Michael I. Jordan
{"title":"Instance-Optimality in Optimal Value Estimation: Adaptivity via Variance-Reduced Q-Learning","authors":"Eric Xia;Koulik Khamaru;Martin J. Wainwright;Michael I. Jordan","doi":"10.1109/TIT.2024.3386122","DOIUrl":"10.1109/TIT.2024.3386122","url":null,"abstract":"Various algorithms in reinforcement learning exhibit dramatic variability in their convergence rates and ultimate accuracy as a function of the problem structure. Such instance-specific behavior is not captured by existing global minimax bounds, which are worst-case in nature. We analyze the problem of estimating optimal <inline-formula> <tex-math>$Q$ </tex-math></inline-formula>-state-action value functions for a discounted Markov decision process with discrete states and actions; our main result is to identify an instance-dependent functional that controls the difficulty of estimation in the <inline-formula> <tex-math>$ell _{infty } $ </tex-math></inline-formula>-norm. Using a local minimax framework, we show that this functional arises in lower bounds on the accuracy on any estimation procedure. We establish the sharpness of these lower bounds, up to factors logarithmic in the state and action spaces, by analyzing a variance-reduced version of <inline-formula> <tex-math>$Q$ </tex-math></inline-formula>-learning. Our theory provides a precise way of distinguishing “easy” problems from “hard” ones in the context of <inline-formula> <tex-math>$Q$ </tex-math></inline-formula>-learning, as illustrated by an ensemble with a continuum of difficulty.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5025-5039"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140595323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Enhanced Differential-Linear Cryptanalysis of Forró With MILP 用MILP增强Forró的微分-线性密码分析
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-21 DOI: 10.1109/TIT.2026.3695599
Zhengting Li;Lin Ding;Xinhai Wang;Honglei Wang;Jiang Wan;Fan Zhang
{"title":"Enhanced Differential-Linear Cryptanalysis of Forró With MILP","authors":"Zhengting Li;Lin Ding;Xinhai Wang;Honglei Wang;Jiang Wan;Fan Zhang","doi":"10.1109/TIT.2026.3695599","DOIUrl":"https://doi.org/10.1109/TIT.2026.3695599","url":null,"abstract":"ARX-based design is a major building block of modern cryptographic ciphers due to its efficiency in software. Forró is an ARX-based stream cipher proposed by Coutinho et al. at ASIACRYPT 2022, which was designed to provide higher security margin than the ChaCha stream cipher. In this paper, we propose a full automated MILP model called &lt;italic&gt;MinForró&lt;/i&gt;, to derive linear approximations for the Forró stream cipher. For the differential part, a two-stage strategy to search for single-bit differential trails with high differential correlations is presented, which helps us to find the first-ever 3-round differential trails for Forró. By combining the linear approximations obtained by &lt;italic&gt;MinForró&lt;/i&gt; and 3-round differential trail for Forró, we propose improved differential-linear distinguishers for 4-, 5-, 5.25-, 5.5-, 5.75-, 6-, 6.25- and 6.5-round Forró with complexities &lt;inline-formula&gt; &lt;tex-math&gt;$2^{32.44}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{46}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{50}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{64.32}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{87.12}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{117.92}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{174.92}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt; &lt;tex-math&gt;$2^{226.88}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, respectively. The proposed differential-linear distinguishers for 4-, 5-, 5.25- and 5.5-round Forró significantly improve the existing distinguishers by factors of &lt;inline-formula&gt; &lt;tex-math&gt;$2^{4.11}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{83.68}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{127.64}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt; &lt;tex-math&gt;$2^{178.20}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, respectively. To the best of our knowledge, this is the first differential-linear distinguisher for Forró that reaches 6.5 rounds, which is a significant advancement over the existing record of 5.5 rounds. We have implemented the differential-linear distinguishers for 4- and 5-round Forró on a common PC, and the experimental results confirm the correctness of these distinguishers. Furthermore, when combined with the &lt;italic&gt;Probabilistic Neutral Bits&lt;/i&gt; (PNB) technique, we obtain key recovery attacks on 5.5-, 6-, 6.5- and 6.75-round Forró with time complexities &lt;inline-formula&gt; &lt;tex-math&gt;$2^{149.20}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{151.84}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$2^{213.49}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt; &lt;tex-math&gt;$2^{251.97}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, respectively. The proposed key recovery attack on 5.5-round Forró significantly improves the time complexity of the existing attack by a factor of &lt;inline-formula&gt; &lt;tex-math&gt;$2^{75.84}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. To the best of our knowledge, this is the firs","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5237-5250"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normalized Maximum Likelihood Code-Length on Riemannian Data Spaces 黎曼数据空间的归一化最大似然码长
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-08 DOI: 10.1109/TIT.2026.3690992
Kota Fukuzawa;Atsushi Suzuki;Kenji Yamanishi
{"title":"Normalized Maximum Likelihood Code-Length on Riemannian Data Spaces","authors":"Kota Fukuzawa;Atsushi Suzuki;Kenji Yamanishi","doi":"10.1109/TIT.2026.3690992","DOIUrl":"https://doi.org/10.1109/TIT.2026.3690992","url":null,"abstract":"In recent years, with the large-scale expansion of graph data, there has been an increased focus on Riemannian data spaces other than Euclidean space. In particular, the development of hyperbolic spaces has been remarkable, and they have high expressive power for graph data with hierarchical structures. Normalized Maximum Likelihood (NML) is employed in regret minimization and model selection. However, existing formulations of NML have been developed primarily in Euclidean spaces and are inherently dependent on the choice of coordinate systems, making it non-trivial to extend NML to Riemannian manifolds. In this study, we define a new NML that reflects the geometric structure of Riemannian manifolds, called the Riemannian manifold NML (Rm-NML). This Rm-NML is invariant under coordinate transformations and coincides with the conventional NML under the natural parameterization in Euclidean space. We extend existing computational techniques for NML to the setting of Riemannian manifolds. Furthermore, we derive a method to simplify the computation of Rm-NML on Riemannian symmetric spaces, which encompass data spaces of growing interest such as hyperbolic spaces. To illustrate the practical application of our proposed method, we explicitly computed the Rm-NML for normal distributions on hyperbolic spaces.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5059-5076"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lower Bounds on Conversion Bandwidth for MDS Convertible Codes in Split Regime 分裂状态下MDS可转换码的转换带宽下界
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-13 DOI: 10.1109/TIT.2026.3692929
Lewen Wang;Sihuang Hu
{"title":"Lower Bounds on Conversion Bandwidth for MDS Convertible Codes in Split Regime","authors":"Lewen Wang;Sihuang Hu","doi":"10.1109/TIT.2026.3692929","DOIUrl":"https://doi.org/10.1109/TIT.2026.3692929","url":null,"abstract":"We propose several new lower bounds on the bandwidth cost of MDS convertible codes using a linear-algebraic framework. The derived bounds improve previous results in certain parameter regimes and match the bandwidth cost of the construction proposed by Maturana and Rashmi (2022 IEEE International Symposium on Information Theory) for <inline-formula> <tex-math>$r^{F}le r^{I}le k^{F}$ </tex-math></inline-formula>, implying that our bounds are tight in this case.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4850-4859"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient Decoding of Double-Circulant and Wozencraft Codes From Square-Root Errors 基于平方根误差的双循环码和Wozencraft码的高效解码
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-01 DOI: 10.1109/TIT.2026.3689757
Oren Dubin;Noam Oz;Noga Ron-Zewi
{"title":"Efficient Decoding of Double-Circulant and Wozencraft Codes From Square-Root Errors","authors":"Oren Dubin;Noam Oz;Noga Ron-Zewi","doi":"10.1109/TIT.2026.3689757","DOIUrl":"https://doi.org/10.1109/TIT.2026.3689757","url":null,"abstract":"We present efficient decoding algorithms from square-root errors for two known families of double-circulant codes: A construction based on Sidon sets (Bhargava, Taveres, and Shiva, <italic>IEEE IT 74</i>; Calderbank, <italic>IEEE IT 83</i>; Guruswami and Li, <italic>IEEE IT 2025</i>), and a construction based on cyclic codes (Chen, Peterson, and Weldon, <italic>Information and Control 1969</i>). We further observe that the work of Guruswami and Li implicitly gives a transformation from double-circulant codes of certain block lengths to Wozencraft codes which preserves that distance of the codes, and we show that this transformation also preserves efficiency of decoding. By instantiating this transformation with the first family of double-circulant codes based on Sidon sets, we obtain an explicit construction of a Wozencraft code that is efficiently decodable from square-root errors. We also discuss limitations on instantiating this transformation with the second family of double-circulant codes based on cyclic codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4710-4718"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analog Secure Distributed Matrix Multiplication 模拟安全分布式矩阵乘法
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-04 DOI: 10.1109/TIT.2026.3690055
Okko Makkonen;Camilla Hollanti
{"title":"Analog Secure Distributed Matrix Multiplication","authors":"Okko Makkonen;Camilla Hollanti","doi":"10.1109/TIT.2026.3690055","DOIUrl":"https://doi.org/10.1109/TIT.2026.3690055","url":null,"abstract":"In this paper, we present secure distributed matrix multiplication (SDMM) schemes over the complex numbers with good numerical stability and small mutual information leakage by utilizing polynomial interpolation with roots of unity. Furthermore, we give constructions utilizing the real numbers by first encoding the real matrices to smaller complex matrices using a technique we call <italic>complexification</i>. These schemes over the real numbers enjoy many of the benefits of the schemes over the complex numbers, including good numerical stability, but are computationally more efficient. To analyze the numerical stability and the mutual information leakage, we give some bounds on the condition numbers of Vandermonde matrices whose evaluation points are roots of unity.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4751-4765"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11505934","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Dimension and Bose Distance of Some BCH Codes of Length $frac{q^{m}-1}{lambda}$ 一些长度BCH码的维数和玻色距离 $frac{q^{m}-1}{lambda}$
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-04-13 DOI: 10.1109/TIT.2026.3683359
Run Zheng;Nung-Sing Sze;Zejun Huang
{"title":"The Dimension and Bose Distance of Some BCH Codes of Length $frac{q^{m}-1}{lambda}$","authors":"Run Zheng;Nung-Sing Sze;Zejun Huang","doi":"10.1109/TIT.2026.3683359","DOIUrl":"https://doi.org/10.1109/TIT.2026.3683359","url":null,"abstract":"BCH codes are important error correction codes, widely utilized due to their robust algebraic structure, multi-error correcting capability, and efficient decoding algorithms. Despite their practical importance and extensive study, their parameters, including dimension, minimum distance and Bose distance, remain largely unknown in general. This paper addresses this challenge by investigating the dimension and Bose distance of BCH codes of length <inline-formula> <tex-math>$(q^{m} - 1)/lambda $ </tex-math></inline-formula> over the finite field <inline-formula> <tex-math>$mathbb {F}_{q}$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$lambda $ </tex-math></inline-formula> is a positive divisor of <inline-formula> <tex-math>$q - 1$ </tex-math></inline-formula>. Specifically, for narrow-sense BCH codes of this length with <inline-formula> <tex-math>$m geq 4$ </tex-math></inline-formula>, we derive explicit formulas for their dimension for designed distances <inline-formula> <tex-math>$2 leq delta leq (q^{lfloor (2m - 1)/3 rfloor + 1} - 1)/{lambda } + 1$ </tex-math></inline-formula>. We also provide explicit formulas for their Bose distance in the range <inline-formula> <tex-math>$2 leq delta leq (q^{lfloor (2m - 1)/3 rfloor + 1} - 1)/{lambda }$ </tex-math></inline-formula>. These ranges for <inline-formula> <tex-math>$delta $ </tex-math></inline-formula> are notably larger than the previously known results for this class of BCH codes. Furthermore, we extend these findings to determine the dimension and Bose distance for certain non-narrow-sense BCH codes of the same length. Several optimal linear codes can be obtained from these BCH codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4766-4787"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(2,2)-GB Codes: Classification and Comparison With Weight-4 Surface Codes (2,2)-GB码:与Weight-4曲面码的分类与比较
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-07 DOI: 10.1109/TIT.2026.3691161
François Arnault;Philippe Gaborit;Nicolas Saussay
{"title":"(2,2)-GB Codes: Classification and Comparison With Weight-4 Surface Codes","authors":"François Arnault;Philippe Gaborit;Nicolas Saussay","doi":"10.1109/TIT.2026.3691161","DOIUrl":"https://doi.org/10.1109/TIT.2026.3691161","url":null,"abstract":"Generalized Bicycle (GB) codes offer a compelling alternative to surface codes for quantum error correction. This paper focuses on (2,2)-Generalized Bicycle codes, constructed from pairs of binary circulant matrices with two non-zero elements per row. Leveraging a lower bound on their minimum distance, we construct three novel infinite families of optimal (2,2)-GB codes with parameters <inline-formula> <tex-math>$ [[2n^{2}, 2, n]] $ </tex-math></inline-formula>, <inline-formula> <tex-math>$ [[4r^{2}, 2, 2r]] $ </tex-math></inline-formula>, and <inline-formula> <tex-math>$ [[(2t + 1)^{2} + 1, 2, 2t + 1]] $ </tex-math></inline-formula>. These families match the performance of Kitaev’s toric code and the best 2D weight-4 surface codes, reaching known theoretical limits. In particular, the second family breaks a long-held belief by providing optimal even-distance GB codes, previously deemed impossible. All are CSS codes derived from Cayley graphs. Recognizing that standard equivalence relations do not preserve their CSS structure, we introduce a CSS-preserving equivalence relation for rigorous comparison of Cayley graph-based CSS codes. Under this framework, the first two families are inequivalent to all previously known optimal weight-4 2D surface codes, while the third family is equivalent to the best-known odd-distance 2D surface code. Finally, we classify all extremal, non-equivalent <inline-formula> <tex-math>$(2,2)$ </tex-math></inline-formula>-GB codes with length below 200 and present a comparison table with existing notable 2D weight-4 surface codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5000-5024"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Function-Correcting Codes With Data Protection 功能-纠错码与数据保护
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-12 DOI: 10.1109/TIT.2026.3692458
Charul Rajput;B. Sundar Rajan;Ragnar Freij-Hollanti;Camilla Hollanti
{"title":"Function-Correcting Codes With Data Protection","authors":"Charul Rajput;B. Sundar Rajan;Ragnar Freij-Hollanti;Camilla Hollanti","doi":"10.1109/TIT.2026.3692458","DOIUrl":"https://doi.org/10.1109/TIT.2026.3692458","url":null,"abstract":"Function-correcting codes (FCCs) are designed to provide error protection for the value of a function computed on the data. Existing work typically focuses solely on protecting the function value and not the underlying data. In this work, we propose a general framework that offers protection for both the data and the function values. Since protecting the data inherently contributes to protecting the function value, we focus on scenarios where the function value requires stronger protection than the data itself. A two-step construction procedure for such codes is proposed, and bounds on the optimal redundancy of general FCCs with data protection are reported. Using these results, we exhibit examples that show that data protection can be added to existing FCCs without increasing redundancy. Using our two-step construction procedure, we present explicit constructions of FCCs with data protection for specific families of functions, such as locally bounded functions and the Hamming weight function. We associate a graph called <italic>minimum-distance graph</i> to a code and use it to show that perfect codes and maximum distance separable (MDS) codes cannot provide additional protection to function values over and above the amount of protection for data for any function. Then we focus on linear FCCs and provide some results for linear functions, leveraging their inherent structural properties. While FCCs for linear functions have been considered earlier in the literature, to the best of our knowledge, the linearity of the FCC itself has not been studied before. Finally, we generalize the Plotkin and Hamming bounds well known in classical error-correcting coding theory to FCCs with data protection.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4860-4880"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11516282","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Unified Key Recovery Framework for Impossible Boomerang Attacks: Applications to Full-Round-ARADI and SKINNYe v2 不可能回旋镖攻击的统一密钥恢复框架:全轮aradi和SKINNYe v2的应用
IF 2.6 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-03-14 DOI: 10.1109/TIT.2026.3693296
Lin Jiao;Xichao Hu;Dengguo Feng;Yongqiang Li;Senpeng Wang;Yonglin Hao;Xinxin Gong
{"title":"A Unified Key Recovery Framework for Impossible Boomerang Attacks: Applications to Full-Round-ARADI and SKINNYe v2","authors":"Lin Jiao;Xichao Hu;Dengguo Feng;Yongqiang Li;Senpeng Wang;Yonglin Hao;Xinxin Gong","doi":"10.1109/TIT.2026.3693296","DOIUrl":"https://doi.org/10.1109/TIT.2026.3693296","url":null,"abstract":"The impossible boomerang attack is a powerful cryptanalytic technique, but existing key recovery methods face several limitations that restrict its applicability. Specifically, the key pre-guessing is coarse-grained, S-box details are ignored in the differential propagation, the complexity estimation and the key guessing order determination remain rudimentary. To overcome these issues, we introduce three key improvement measures. First, we propose a flexible partial key and difference pre-guessing technique based on directed graphs, enabling selective identification of required keys and differences for generating partial pairs and quartets. Second, we propose a pre-sieving technique to early eliminate invalid quartets by exploiting cipher-specific details. Third, we introduce an automatic key-guessing strategy based on the same directed graphs to efficiently determine valid guessing orders. We integrate these techniques to develop a unified key recovery framework for impossible boomerang attacks, accompanied by a formal and precise characterization of the overall complexity. This is the first framework to support flexible key and difference pre-guessing while incorporating block cipher details during key recovery for impossible boomerang attacks. Crucially, it enables the automatic generation of detailed recovery steps, a capability missing in prior work. As applications, under the four related-key/tweakey setting, we apply the framework to <monospace>ARADI</monospace>, a low-latency cipher proposed by the National Security Agency (NSA), and <monospace>SKINNYev2</monospace>, a threshold-implementation-friendly cipher proposed at EUROCRYPT 2020. For <monospace>ARADI</monospace>, we achieve the first full-round attack with <inline-formula> <tex-math>$2^{130}$ </tex-math></inline-formula> data, <inline-formula> <tex-math>$2^{253.78}$ </tex-math></inline-formula> time, and <inline-formula> <tex-math>$2^{235.75}$ </tex-math></inline-formula> memory complexity. For <monospace>SKINNYev2</monospace>, we present the first 34-round impossible boomerang attack with <inline-formula> <tex-math>$2^{66}$ </tex-math></inline-formula> data, <inline-formula> <tex-math>$2^{253.75}$ </tex-math></inline-formula> time, and <inline-formula> <tex-math>$2^{239.75}$ </tex-math></inline-formula> memory complexity. These results demonstrate the framework’s significance and its substantial improvement in advancing the impossible boomerang attack.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5183-5206"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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