Unique shortest vector problem (uSVP) plays an important role in lattice based cryptography. Many cryptographic schemes based their security on it. For the cofidence of those applications, it is essential to cl
Any non-zero ideal in a number field can be factored into a product of prime ideals. In this paper we report a surprising connection between the complexity of the shortest vector problem (SVP) of prime ideals in number fields and their decomposition groups. When applying the result to number...
Computational complexity Lattices Shortest vector problem Approximation algorithms Hardness of approximation View PDFReferences [1] D. Aharonov, O. Regev, Lattice problems in NP ∩ coNP, in: Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004, pp. 362–371. Google Schol...
Also the robust linear binary programming problem with binary uncertainty sets has been shown to be in the same complexity class [15]. Examples where the complexity of multi-stage robust problems has been studied include shortest path [11], spanning tree [25], or selection problems [20], [...
Complexity in Decision-Making: Streamlining decision-making processes by leveraging quantum computing to rapidly assess complex scenarios, optimize solutions, and facilitate precise decision-making in real-time. Security Concerns: Mitigating security risks through the implementation of quantum cryptography, ensu...
The hardness of the shortest vector problem for lattices is a fundamental assumption underpinning the security of many lattice-based cryptosystems, and therefore, it is important to evaluate its difficulty. Here, recent advances in studying the hardness of problems in large-scale lattice computing have...
Link-based algorithms implemented in cppRouting are, in increasing order of complexity : Method of Successive Average (msa) : is defined as with the actual number of iteration. Frank-Wolfe (fw) : is computed by minimizing the Beckmann function with bisection method. Conjugate Frank-Wolfe (cfw)...
However, their disadvantage lies in the complexity of mathematical models and computational processes required, which can lead to increased computational costs and challenges in interpretation and precise quantification. We recommend these advanced estimators for future applications and highlight the ongoing ...
We statistically infer the entropy of each language model as an index of what we call average prediction complexity. We compare complexity rankings across corpora and show that a language that tends to be more complex than another language in one corpus also tends to be more complex in another...
Summary: In 2009, Bl枚mer and Naewe proposed the Generalized Shortest Vector Problem $(ext {GSVP})$. We initiate the study of the promise problem ($ext {GAPSAM}$) for $ext {GSVP}$. It is a promise problem associated with estimating the subspace avoiding minimum. We show $ext {GAP...