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Some Improved Complexity Results for GapSVP and uSVP
, 2013
"... In this paper, first, it is proved that finding the approximate shortest vector with 1 n(n+log length in [λ1, γλ1] could be Karpreduced to GapSVP˜γ where γ = γ 2 (γn))(n−1) Second, it is proved that shortest vector problem itself could be reduced to GapSVP with a quite small gap. Third, we improve ..."
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the complexity results of uSVP, proving uSVP could be reduced from SVP (our results are better than any known result). What’s more, we prove that the search version of uSVP could be reduced to decisional version of uSVP with almost the same gap. 1
Some Complexity Results and Bit Unpredictable for Short Vector Problem
"... In this paper, we prove that finding the approximate shortest vector with length in [λ1, γλ1] could be reduced to GapSVP. We also prove that shortest vector problem could also be reduced to GapSVP with a small gap. As the complexity of uSVP is not very clear, we improve crurrent complexity results[1 ..."
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In this paper, we prove that finding the approximate shortest vector with length in [λ1, γλ1] could be reduced to GapSVP. We also prove that shortest vector problem could also be reduced to GapSVP with a small gap. As the complexity of uSVP is not very clear, we improve crurrent complexity results
Fully homomorphic encryption without modulus switching from classical GapSVP
 In Advances in Cryptology  Crypto 2012, volume 7417 of Lecture
"... We present a new tensoring technique for LWEbased fully homomorphic encryption. While in all previous works, the ciphertext noise grows quadratically (B → B 2 · poly(n)) with every multiplication (before “refreshing”), our noise only grows linearly (B → B · poly(n)). We use this technique to constr ..."
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Cited by 70 (5 self)
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process (no need for “modulus switching”), and this modulus can take arbitrary form. In addition, security can be classically reduced from the worstcase hardness of the GapSVP problem (with quasipolynomial approximation factor), whereas previous constructions could only exhibit a quantum reduction from
Accurate Unlexicalized Parsing
 IN PROCEEDINGS OF THE 41ST ANNUAL MEETING OF THE ASSOCIATION FOR COMPUTATIONAL LINGUISTICS
, 2003
"... We demonstrate that an unlexicalized PCFG can parse much more accurately than previously shown, by making use of simple, linguistically motivated state splits, which break down false independence assumptions latent in a vanilla treebank grammar. Indeed, its ..."
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Cited by 1026 (70 self)
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We demonstrate that an unlexicalized PCFG can parse much more accurately than previously shown, by making use of simple, linguistically motivated state splits, which break down false independence assumptions latent in a vanilla treebank grammar. Indeed, its
Executive Compensation
, 1999
"... This paper summarizes the empirical and theoretical research on executive compensation and provides a comprehensive and uptodate description of pay practices (and trends in pay practices) for chief executive officers (CEOs). Topics discussed include the level and structure of CEO pay (including de ..."
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Cited by 603 (19 self)
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This paper summarizes the empirical and theoretical research on executive compensation and provides a comprehensive and uptodate description of pay practices (and trends in pay practices) for chief executive officers (CEOs). Topics discussed include the level and structure of CEO pay (including detailed analyses of annual bonus plans, executive stock options, and option valuation), international pay differences, the paysetting process, the relation between CEO pay and firm performance (“payperformance sensitivities”), the relation between sensitivities and subsequent firm performance, relative performance evaluation, executive turnover, and the politics of CEO pay.
On Bounded Distance Decoding, Unique Shortest Vectors, and the Minimum Distance Problem
, 2009
"... We prove the equivalence, up to a small polynomial approximation factor p n / log n, of the lattice problems uSVP (unique Shortest Vector Problem), BDD (Bounded Distance Decoding) and GapSVP (the decision version of the Shortest Vector Problem). This resolves a longstanding open problem about the r ..."
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Cited by 25 (5 self)
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We prove the equivalence, up to a small polynomial approximation factor p n / log n, of the lattice problems uSVP (unique Shortest Vector Problem), BDD (Bounded Distance Decoding) and GapSVP (the decision version of the Shortest Vector Problem). This resolves a longstanding open problem about
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
 In STOC
, 2005
"... Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear co ..."
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Cited by 366 (6 self)
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Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear
The n cUnique Shortest Vector Problem is Hard
"... The unique Shortest Vector Problem (uSVP) gained prominence because it was the problem upon which the first provablysecure latticebased cryptosystems were built. But it was an open problem as to whether uSVP was as hard as the standard, more general, version of the shortest vector problem. We show ..."
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show that there is a reduction from the approximate decision version of the shortest vector problem (GapSVP) to the unique shortest vector problem. In particular, we show that for any γ> 6 √ n, there is a reduction from GapSVPγ to γ 6 √ nuSVP. This implies that the AjtaiDwork and the Regev
On the Efficacy of Solving LWE by Reduction to UniqueSVP
"... Abstract. We present a study of the concrete complexity of solving instances of the unique shortest vector problem (uSVP). In particular, we study the complexity of solving the Learning with Errors (LWE) problem by reducing the BoundedDistance Decoding (BDD) problem to uSVP and attempting to solve ..."
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Cited by 5 (1 self)
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Abstract. We present a study of the concrete complexity of solving instances of the unique shortest vector problem (uSVP). In particular, we study the complexity of solving the Learning with Errors (LWE) problem by reducing the BoundedDistance Decoding (BDD) problem to uSVP and attempting to solve
Results 1  10
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