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WorstCase to AverageCase Reductions for Module Lattices
"... Abstract. Most latticebased cryptographic schemes are built upon the assumed hardness of the Short Integer Solution (SIS) and Learning With Errors (LWE) problems. Their efficiencies can be drastically improved by switching the hardness assumptions to the more compact RingSIS and RingLWE problems. ..."
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Cited by 7 (1 self)
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lattices (which themselves generalize arbitrary and ideal lattices). As these new problems enlarge the toolbox of the latticebased cryptographer, they could prove useful for designing new schemes. Importantly, the worstcase to averagecase reductions for the module problems are (qualitatively) sharp
Worstcase to averagecase reductions based on Gaussian measures
 SIAM J. on Computing
, 2004
"... We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the dimension of the lattice. The lattice problems we consider are the shortest vector problem, the shortest indepe ..."
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Cited by 128 (23 self)
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We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost linear in the dimension of the lattice. The lattice problems we consider are the shortest vector problem, the shortest
Structural lattice reduction: Generalized worstcase to averagecase reductions. Eprint report 2014/283
, 2014
"... In lattice cryptography, worstcase to averagecase reductions rely on two problems: Ajtai’s SIS and Regev’s LWE, which refer to a very small class of random lattices related to the group G = Znq. We generalize worstcase to averagecase reductions to (almost) all integer lattices, by allowing G to ..."
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Cited by 1 (1 self)
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In lattice cryptography, worstcase to averagecase reductions rely on two problems: Ajtai’s SIS and Regev’s LWE, which refer to a very small class of random lattices related to the group G = Znq. We generalize worstcase to averagecase reductions to (almost) all integer lattices, by allowing G
A WorstCase to AverageCase Connection for CVP
"... We prove a connection of the worstcase complexity and the averagecase complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least with ..."
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We prove a connection of the worstcase complexity and the averagecase complexity for the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP for lattices under a certain natural distribution, at least
Lattices that admit logarithmic worstcase to averagecase connection factors
, 2006
"... We demonstrate an averagecase problem which is as hard as finding γ(n)approximate shortest vectors in certain ndimensional lattices in the worst case, where γ(n) = O( log n). The previously best known factor for any class of lattices was γ(n) = Õ(n). To obtain our results, we focus on families ..."
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Cited by 23 (11 self)
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We demonstrate an averagecase problem which is as hard as finding γ(n)approximate shortest vectors in certain ndimensional lattices in the worst case, where γ(n) = O( log n). The previously best known factor for any class of lattices was γ(n) = Õ(n). To obtain our results, we focus
An Improved WorstCase to AverageCase Connection for Lattice Problems (extended abstract)
 In FOCS
, 1997
"... We improve a connection of the worstcase complexity and the averagecase complexity of some wellknown lattice problems. This fascinating connection was first discovered by Ajtai [1] in 1996. We improve the exponent of this connection from 8 to 3:5 + ffl. Department of Computer Science, State Unive ..."
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Cited by 57 (10 self)
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We improve a connection of the worstcase complexity and the averagecase complexity of some wellknown lattice problems. This fascinating connection was first discovered by Ajtai [1] in 1996. We improve the exponent of this connection from 8 to 3:5 + ffl. Department of Computer Science, State
On WorstCase to AverageCase Reductions for NP Problems
 IN PROCEEDINGS OF THE 44TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2003
"... We show that if an NPcomplete problem has a nonadaptive selfcorrector with respect to a samplable distribution then coNP is contained in AM/poly and the polynomial hierarchy collapses to the third level. Feigenbaum and Fortnow show the same conclusion under the stronger assumption that an NPcompl ..."
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Cited by 61 (6 self)
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complete problem has a nonadaptive random selfreduction. Our result
LatticeBased Access Control Models
, 1993
"... The objective of this article is to give a tutorial on latticebased access control models for computer security. The paper begins with a review of Denning's axioms for information flow policies, which provide a theoretical foundation for these models. The structure of security labels in the ..."
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Cited by 1485 (56 self)
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The objective of this article is to give a tutorial on latticebased access control models for computer security. The paper begins with a review of Denning's axioms for information flow policies, which provide a theoretical foundation for these models. The structure of security labels
The stretchlength tradeoff in geometric networks: Worstcase and averagecase study
 In preparation
, 2010
"... ar ..."
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