Results 1  10
of
1,733
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. ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
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
Relativized Worlds Without WorstCase to AverageCase Reductions for NP
, 2010
"... We prove that relative to an oracle, there is no worstcase to averagecase reduction for NP. We also handle classes that are somewhat larger than NP, as well as worstcase to errorlessaveragecase reductions. In fact, we prove that relative to an oracle, there is no worstcase. We also handle reduc ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We prove that relative to an oracle, there is no worstcase to averagecase reduction for NP. We also handle classes that are somewhat larger than NP, as well as worstcase to errorlessaveragecase reductions. In fact, we prove that relative to an oracle, there is no worstcase. We also handle
WorstCase to AverageCase Reductions Revisited
"... A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomialtime samplable distribution (e.g., the uniform distribution) and a language in NTIME(f(n)) for some polynomial function f, such that the language is hard on the average with respect to this dis ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
worstcase/averagecase connection. In other words, their techniques give a way to bypass the impossibility arguments. By taking a closer look at the proof of [GSTS05], we discover that the worstcase/averagecase connection is proven by a reduction that ”almost ” falls under the category ruled out
Worst case to Average Case Reductions for Polynomials
 the Proceedings of the 49th Annual Symposium on Foundations of Computer Science (FOCS
, 2008
"... A degreed polynomial p in n variables over a field F is equidistributed if it takes on each of its F  values close to equally often, and biased otherwise. We say that p has a low rank if it can be expressed as a bounded combination of polynomials of lower degree. Green and Tao [GT07] have shown t ..."
Abstract

Cited by 20 (9 self)
 Add to MetaCart
that bias imply low rank over large fields (i.e. for the case d < F). They have also conjectured that bias imply low rank over general fields. In this work we affirmatively answer their conjecture. Using this result we obtain a general worst case to average case reductions for polynomials. That is, we
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 ..."
Abstract

Cited by 131 (23 self)
 Add to MetaCart
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
Average case reductions for Subset Sum and Decoding of Linear Codes
, 1999
"... Average case reductions for Subset Sum and Decoding of Linear Codes Genevi`eve Arboit Master of Science Graduate Department of Computer Science University of Toronto 1999 In a 1996 paper, R. Impagliazzo and M. Naor show two average case reductions for the Subset Sum problem (SS). We use similar idea ..."
Abstract
 Add to MetaCart
Average case reductions for Subset Sum and Decoding of Linear Codes Genevi`eve Arboit Master of Science Graduate Department of Computer Science University of Toronto 1999 In a 1996 paper, R. Impagliazzo and M. Naor show two average case reductions for the Subset Sum problem (SS). We use similar
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 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
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
Average Case Complexity ∗
"... Abstract. We attempt to motivate, justify and survey the average case reduction theory. 1. ..."
Abstract
 Add to MetaCart
Abstract. We attempt to motivate, justify and survey the average case reduction theory. 1.
Results 1  10
of
1,733