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Analytic Analysis of Algorithms
, 1992
"... . The average case analysis of algorithms can avail itself of the development of synthetic methods in combinatorial enumerations and in asymptotic analysis. Symbolic methods in combinatorial analysis permit to express directly the counting generating functions of wide classes of combinatorial struct ..."
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Cited by 331 (13 self)
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structures. Asymptotic methods based on complex analysis permit to extract directly coefficients of structurally complicated generating functions without a need for explicit coefficient expansions. Three major groups of problems relative to algebraic equations, differential equations, and iteration
On the Complexity of the BKW Algorithm on LWE
"... Abstract. In this paper we present a study of the complexity of the BlumKalaiWasserman (BKW) algorithm when applied to the Learning with Errors (LWE) problem, by providing refined estimates for the data and computational effort requirements for solving concrete instances of the LWE problem. We app ..."
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Cited by 3 (0 self)
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Abstract. In this paper we present a study of the complexity of the BlumKalaiWasserman (BKW) algorithm when applied to the Learning with Errors (LWE) problem, by providing refined estimates for the data and computational effort requirements for solving concrete instances of the LWE problem. We
Better Algorithms for LWE and LWR
"... Abstract. The Learning With Error problem (LWE) is becoming more and more used in cryptography, for instance, in the design of some fully homomorphic encryption schemes. It is thus of primordial importance to find the best algorithms that might solve this problem so that concrete parameters can be p ..."
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Cited by 2 (0 self)
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Abstract. The Learning With Error problem (LWE) is becoming more and more used in cryptography, for instance, in the design of some fully homomorphic encryption schemes. It is thus of primordial importance to find the best algorithms that might solve this problem so that concrete parameters can
On the Combinatorial and Algebraic Complexity of Quantifier Elimination
, 1996
"... In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields is given. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this date. A new feature of this algorithm is that the role of th ..."
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Cited by 230 (29 self)
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In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields is given. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this date. A new feature of this algorithm is that the role
P.: An improved BKW algorithm for LWE with applications to cryptography and lattices
 In: CRYPTO
, 2015
"... Abstract. In this paper, we study the Learning With Errors problem and its binary variant, where secrets and errors are binary or taken in a small interval. We introduce a new variant of the Blum, Kalai and Wasserman algorithm, relying on a quantization step that generalizes and finetunes modulus s ..."
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Cited by 3 (0 self)
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to solve these variants in subexponential time. Moreover, we also show how the previous algorithm can be used to solve the BinaryLWE problem with n samples in subexponential time 2(ln 2/2+o(1))n / log logn. This analysis does not require any heuristic assumption, contrary to other algebraic approaches
RingLWE in polynomial rings
 In Public Key Cryptography
, 2012
"... Abstract. The RingLWE problem, introduced by Lyubashevsky, Peikert, and Regev (Eurocrypt 2010), has been steadily finding many uses in numerous cryptographic applications. Still, the RingLWE problem defined in [LPR10] involves the fractional ideal R ∨ , the dual of the ring R, which is the source ..."
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Cited by 6 (0 self)
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Abstract. The RingLWE problem, introduced by Lyubashevsky, Peikert, and Regev (Eurocrypt 2010), has been steadily finding many uses in numerous cryptographic applications. Still, the RingLWE problem defined in [LPR10] involves the fractional ideal R ∨ , the dual of the ring R, which is the source
Benchmarking GPUs to tune dense linear algebra
, 2008
"... We present performance results for dense linear algebra using recent NVIDIA GPUs. Our matrixmatrix multiply routine (GEMM) runs up to 60 % faster than the vendor’s implementation and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80–90 % of the pe ..."
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Cited by 242 (2 self)
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We present performance results for dense linear algebra using recent NVIDIA GPUs. Our matrixmatrix multiply routine (GEMM) runs up to 60 % faster than the vendor’s implementation and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80
On the Asymptotic Complexity of Solving LWE
"... Abstract. We provide for the first time an asymptotic comparison of all known algorithms for the search version of the Learning with Errors (LWE) problem. This includes an analysis of several latticebased approaches as well as the combinatorial BKW algorithm. Our analysis of the latticebased appr ..."
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Abstract. We provide for the first time an asymptotic comparison of all known algorithms for the search version of the Learning with Errors (LWE) problem. This includes an analysis of several latticebased approaches as well as the combinatorial BKW algorithm. Our analysis of the lattice
On the 'Piano Movers' Problem II. General Techniques for Computing Topological Properties of Real Algebraic Manifolds
, 1982
"... This paper continues the discussion, begun in [SS], of the following problem, which arises in robotics: Given a collection of bodies B, which may be hinged, i.e. may allow internal motion around various joints, and given a region bounded by a collection of polyhedral or other simple walls, decide ..."
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Cited by 228 (9 self)
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whether or not there exists a continuous motion connecting two given positions and orientations of the whole collection of bodies. We show that this problem can be handled by appropriate refinements of methods introduced by Tarski and Collins, which lead to algorithms for this problem which are polynomial
Mahabir Prasad JhanwarDefinition LWE problem Hardness of LWE Cryptographic Applications
, 2012
"... Fix a size parameter n ≥ 1, a modulus q ≥ 2, and an “error " probability distribution χ: Zq → R + on Zq. For a s ∈R Z n q, let As,χ be a probability distribution on Z n q × Zq obtained by choosing a vector a ∈R Z n q, choosing e ∈χ Zq and outputting the pair (a, 〈a, s 〉 + e mod q) We say that a ..."
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that an algorithm solves LWEq,χ if, for any s ∈ Z n q, given an arbitrary number of independent samples from As,χ it outputs s with high probability.
Results 11  20
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