SVP Is NP-Hard for Some Rank-2 Cyclotomic Modules
本文证明了在特定环上,二维全秩自由子模中的最短向量问题(SVP)是NP完全的,并通过多项式时间归约克服了环作用带来的障碍。
本文证明了在特定环上,二维全秩自由子模中的最短向量问题(SVP)是NP完全的,并通过多项式时间归约克服了环作用带来的障碍。
本文证明了在特定环的理想格上,精确最短向量问题(CVP)是NP完全的,并通过从X3C问题归约的方法解决了这一问题。
This study addresses the failure of classical source coding theorems caused by distributional uncertainty in complex networks. Leveraging nonlinear expectation theory and the law of large numbers under sublinear expectations, this work establishes an axiomatic framework and introduces the concept of nonlinear information entropy. On this basis, a source coding theorem under distributional uncertainty is formulated to characterize achievable rate bounds. Specifically, it is proven that nonlinear information entropy serves as the upper bound on coding rates under the maximum error criterion and as a cluster point under the minimum error criterion. These findings overcome the limitations of traditional frameworks and significantly advance the theoretical understanding of encoding mechanisms for sources with uncertain distributions.
This work addresses the significant performance degradation of conventional detection methods—designed under deterministic channel models—when the noise distribution exhibits uncertainty in its mean and variance. For the first time, nonlinear expectation theory is introduced into communication detection to tackle this challenge. The authors develop robust optimal detectors with explicit analytical forms for two distinct scenarios: variance-only uncertainty and joint mean–variance uncertainty. Theoretical analysis reveals that mean uncertainty profoundly alters the detector structure. The proposed framework consistently outperforms classical approaches across a range of distributional uncertainties, as demonstrated by extensive simulations that confirm both its superiority and practical applicability.
This work conducts a third-party cryptanalysis of Gleeok-128, a low-latency multi-branch pseudorandom function (PRF), focusing on deficiencies in linear security evaluation under its multi-branch structure and the feasibility of key recovery. We propose a two-stage Mixed-Integer Linear Programming (MILP) modeling framework that unifies differential-linear and integral distinguisher construction while tightening algebraic degree bounds. Our analysis reveals, for the first time, a full linear distinguishability vulnerability in Branch 3; leveraging this, we optimize the linear layer parameters to enhance resistance. Experimentally, we achieve a 7-round integral distinguisher for the full PRF and an 8-round key-recovery attack, improving distinguisher rounds for individual branches by 3 and 2, respectively, with a data complexity of only $2^{48}$. These results significantly surpass prior security bounds and advance automated analysis frameworks for multi-branch primitives.
本文证明了在特定环上,二维全秩自由子模中的最短向量问题(SVP)是NP完全的,并通过多项式时间归约克服了环作用带来的障碍。
本文证明了在特定环的理想格上,精确最短向量问题(CVP)是NP完全的,并通过从X3C问题归约的方法解决了这一问题。
This study addresses the failure of classical source coding theorems caused by distributional uncertainty in complex networks. Leveraging nonlinear expectation theory and the law of large numbers under sublinear expectations, this work establishes an axiomatic framework and introduces the concept of nonlinear information entropy. On this basis, a source coding theorem under distributional uncertainty is formulated to characterize achievable rate bounds. Specifically, it is proven that nonlinear information entropy serves as the upper bound on coding rates under the maximum error criterion and as a cluster point under the minimum error criterion. These findings overcome the limitations of traditional frameworks and significantly advance the theoretical understanding of encoding mechanisms for sources with uncertain distributions.
This work addresses the significant performance degradation of conventional detection methods—designed under deterministic channel models—when the noise distribution exhibits uncertainty in its mean and variance. For the first time, nonlinear expectation theory is introduced into communication detection to tackle this challenge. The authors develop robust optimal detectors with explicit analytical forms for two distinct scenarios: variance-only uncertainty and joint mean–variance uncertainty. Theoretical analysis reveals that mean uncertainty profoundly alters the detector structure. The proposed framework consistently outperforms classical approaches across a range of distributional uncertainties, as demonstrated by extensive simulations that confirm both its superiority and practical applicability.
This work conducts a third-party cryptanalysis of Gleeok-128, a low-latency multi-branch pseudorandom function (PRF), focusing on deficiencies in linear security evaluation under its multi-branch structure and the feasibility of key recovery. We propose a two-stage Mixed-Integer Linear Programming (MILP) modeling framework that unifies differential-linear and integral distinguisher construction while tightening algebraic degree bounds. Our analysis reveals, for the first time, a full linear distinguishability vulnerability in Branch 3; leveraging this, we optimize the linear layer parameters to enhance resistance. Experimentally, we achieve a 7-round integral distinguisher for the full PRF and an 8-round key-recovery attack, improving distinguisher rounds for individual branches by 3 and 2, respectively, with a data complexity of only $2^{48}$. These results significantly surpass prior security bounds and advance automated analysis frameworks for multi-branch primitives.