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Optimal Reductions of Some Decisional Problems to the Rank Problem [chapter]

Jorge Luis Villar
2012 Lecture Notes in Computer Science  
Motivation Positive Results Negative Results Further Results Applications: Key Dependent Messages Security Attack model: the adversary asks for encryption of (affine) functions of the secret key  ...  Villar Reductions to the Rank Problem g y , g xy +s )] = Motivation Positive Results Negative Results Further Results π 1,j j≤i Jorge L. Villar Reductions to the Rank Problem  ...  Villar Reductions to the Rank Problem 2r m0 Motivation Positive Results Negative Results Further Results Jorge L.  ... 
doi:10.1007/978-3-642-34961-4_7 fatcat:b5bfswtlfrgwfhtg3dyzgnlo5e

A New Reduction from Search SVP to Optimization SVP [article]

Gengran Hu, Yanbin Pan
2012 arXiv   pre-print
In this paper, a new rank-preserving reduction is presented with only one call to the optimization SVP oracle.  ...  However, the former reduction from search SVP to optimization SVP by Kannan needs polynomial times calls to the oracle that solves the optimization SVP.  ...  The former reduction from decisional CVP to optimization CVP needs one call to the optimization CVP oracle, but it needs polynomial times calls to the decisional CVP oracle to reduce search CVP to decisional  ... 
arXiv:1204.2040v1 fatcat:q5mm2u3kqfdf5hx7l2h4zbqdpm

The Kernel Matrix Diffie-Hellman Assumption [chapter]

Paz Morillo, Carla Ràfols, Jorge L. Villar
2016 Lecture Notes in Computer Science  
This requires ruling out the existence of some black-box reductions between flexible problems (i.e., computational problems with a non unique solution).  ...  Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find "in the exponent" a nonzero vector in the kernel of A .  ...  As usually, the proposed generic model reduces the analysis of the hardness of some problems to solving a merely algebraic problem related to polynomials.  ... 
doi:10.1007/978-3-662-53887-6_27 fatcat:filvfwfzefhs5fyjx5phkbf6uu

Optimal collective dichotomous choice under partial order constraints

Ruth Ben-Yashar, Samir Khuller, Sarit Kraus
2001 Mathematical Social Sciences  
We show that this type renders the choice problem to be NP-complete by reduction from the problem of Vertex Cover. Applicability of the generalization to information filtering is discussed.  ...  This type reduces the choice problem to the tractable (solvable in polynomial time) problem of finding a maximum weight closed subset of a directed acyclic graph.  ...  The authors thank the referees for providing detailed suggestions and comments.  ... 
doi:10.1016/s0165-4896(00)00069-x fatcat:npsfavtx5bhdfixglertl3vgge

Reducing myopic behavior in FMS control: A semi-heterarchical simulation–optimization approach

Gabriel Zambrano Rey, Thérèse Bonte, Vittaldas Prabhu, Damien Trentesaux
2014 Simulation modelling practice and theory  
The purpose of this particularization is to accept configurations in which myopic behavior for some sub-problems is reduced while for other sub-problems is accepted.  ...  Figure V -6 shows some of these machines. Decisional entities This section describes the technological implementation of each decisional entity.  ...  Optimization Techniques for the Global Decisional Entity Appendix H.  ... 
doi:10.1016/j.simpat.2014.01.005 fatcat:7bqsmoebm5c7fh6xvu7xre2r7e

Efficient Encryption from Random Quasi-Cyclic Codes [article]

Carlos Aguilar, Olivier Blazy, Jean-Christophe Deneuville, Philippe Gaborit, Gilles Zémor
2016 arXiv   pre-print
We give a security proof, which reduces the IND-CPA security of our systems to a decisional version of the well known problem of decoding random families of quasi-cyclic codes for the Hamming and rank  ...  metrics (the respective QCSD and RQCSD problems).  ...  Hence even if the reduction is not optimal, it nevertheless shows the hardness of the problem.  ... 
arXiv:1612.05572v1 fatcat:up7iubangna3db2gd77tfi3ywe

Multi-Criteria Analysis and Decision-Support for Water Management at the Catchment Scale: An Application to Diffuse Pollution Control in the Venice Lagoon

Carlo Giupponi, Paolo Rosato
2002 Social Science Research Network  
The decisional context of the present study was determined by a given amount of public funds made available by the regional administration, to be used in an optimal way by choosing what to do (within a  ...  A multi-stage multi-criteria evaluation approach was developed, which subdivided the decisional problem into two operational phases.  ...  Obviously, the reduction of nutrient releases is considered, along with the reduction of flood risk, the most important parameters for the ranking of alternative projects.  ... 
doi:10.2139/ssrn.313585 fatcat:kpeqol6bkffhzkhkh2j6auzbwi

Lattice Decoding Attacks on Binary LWE [chapter]

Shi Bai, Steven D. Galbraith
2014 Lecture Notes in Computer Science  
problem using a re-scaling of the lattice.  ...  We consider the binary-LWE problem, which is the learning with errors problem when the entries of the secret vector are chosen from {0, 1} or {−1, 0, 1} (and the error vector is sampled from a discrete  ...  The authors wish to acknowledge NeSI (New Zealand eScience Infrastructure) and the Centre for eResearch at the University of Auckland for providing CPU hours and support.  ... 
doi:10.1007/978-3-319-08344-5_21 fatcat:2nx3d6xzojfl3ga26mej4a2zxm

Learning Modulo Theories for preference elicitation in hybrid domains [article]

Paolo Campigotto, Roberto Battiti, Andrea Passerini
2015 arXiv   pre-print
The refinement step is implemented as learning to rank, and a sparsifying norm is used to favour the selection of few informative features in the combinatorial space of candidate decisional features.  ...  The elicitation step leverages a Max-SMT solver to return optimal hybrid solutions according to the current utility model.  ...  Acknowledgments This research was partially supported by grant PRIN 2009LNP494 (Statistical Relational Learning: Algorithms and Applications) from Italian Ministry of University and Research.  ... 
arXiv:1508.04261v3 fatcat:zagrnbte3zfmljfbzq4ub3t4ru

Learning with Errors in the Exponent [chapter]

Özgür Dagdelen, Sebastian Gajek, Florian Göpfert
2016 Lecture Notes in Computer Science  
We initiate the study of a novel class of group-theoretic intractability problems.  ...  In fact, LWEE's duality is due to the reducibility to two seemingly unrelated assumptions: learning with errors and the representation problem [Brands, Crypto'93] in finite groups.  ...  Acknowledgements The authors would like to thank Steven Galbraith and Dan Bernstein to point to a bug in a previous version of the paper, and the attendees of the Cryptography Workshop in Oberwolfach for  ... 
doi:10.1007/978-3-319-30840-1_5 fatcat:7i25r2bn6bdgphr3lzqj64zmxq

On String Attractors

Nicola Prezza
2018 Italian Conference on Theoretical Computer Science  
In this brief communication we summarize possible future developments and open problems related to the subject.  ...  Complexity and Approximability The first open problem that we discuss is the complexity of 2-attractor: Problem 1. Is the (decisional version of) 2-attractor solvable in polynomial-time?  ...  Verification and approximation, on the other hand, are much easier problems: we can decide whether Γ is a proper k-attractor in optimal O(n) time and space [4] and, with a simple reduction to set-cover  ... 
dblp:conf/ictcs/Prezza18 fatcat:d6ictv57uff3fiw5dngmtsjpsy

Methodological Proposal for Optimal Location of Emergency Operation Centers through Multi-Criteria Approach

Umberto Di Matteo, Priscilla Pezzimenti, Davide Astiaso Garcia
2016 Sustainability  
Because of its stability and ease of use, this method is adopted for the selection problems considering the lowest performance rating with respect to a specified criterion [6] .  ...  Mulliner et al. [1] elaborated on a comparative analysis of different MCDM methods, comparing the rankings of the alternatives and their tolerance to change in criterion weights amongst the following MCDM  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/su8010050 fatcat:rplxgmts2fchdnl6dnjv24cmku

The Hidden Lattice Problem [article]

Luca Notarnicola, Gabor Wiese
2021 arXiv   pre-print
We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer – the Hidden Lattice Problem.  ...  Finally, we study variations of the problem and highlight its relevance to cryptanalysis.  ...  The Decisional Hidden Lattice Problem (DHLP) is the task to decide from the knowledge of µ, N and a basis of M, whether there exists a µ-small lattice L ⊆ Z m of rank 1 ≤ n ≤ m such that M ⊆ L (mod N )  ... 
arXiv:2111.05436v1 fatcat:wf7ex7gaznasbgd23bqebdip2y

Equivalences and Black-Box Separations of Matrix Diffie-Hellman Problems [chapter]

Jorge L. Villar
2017 Lecture Notes in Computer Science  
In this paper we give some positive and negative partial results about equivalence, in particular solving the open problem of whether the Linear and the Cascade MDDH problems are reducible to each other  ...  Then, we show that MDDH problems described with a different number of parameters are also separated (meaning that a successful reduction cannot decrease the amount of randomness used in the problem instance  ...  In fact, the core of this paper were developed during a fruiful stage at HGI Bochum. He is also thankful to some of the anonymous referees for their valuable remarks.  ... 
doi:10.1007/978-3-662-54365-8_18 fatcat:nimp42tqbrgjfebng3cetudm5y

The Hardness of LPN over Any Integer Ring and Field for PCG Applications [article]

Hanlin Liu, Xiao Wang, Kang Yang, Yu Yu
2022 IACR Cryptology ePrint Archive  
between its search and decisional versions; 2) an efficient reduction from LPN over F 2 to LPN over Z 2 λ ; and 3) generalization of our results to any integer ring. • For LPN over finite fields, we found  ...  In this paper, we thoroughly studied the concrete security of LPN problems in these settings and how it affects the protocol design. • We are the first to study the security of LPN over a ring Z 2 λ .  ...  We first analyze the cost of solving a decisional (HW, F)-LPN(k, N, t) problem against statistical decoding attacks in the case that |F| ≥ (2 + c)t for some constant c > 0.  ... 
dblp:journals/iacr/LiuWYY22 fatcat:eegcvgbgerhhfnvtbg4itdjv5m
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