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Maximum Quadratic Assignment Problem: Reduction from Maximum Label Cover and LPbased Approximation Algorithm
"... Abstract. We show that for every positive ε> 0, unless N P ⊂ RP, it is impossible to approximate the maximum quadratic assignment problem within a factor better than 2 log1−ε n by a reduction from the maximum label cover problem. Then, we present an O ( √ n)approximation algorithm for the problem ..."
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Abstract. We show that for every positive ε> 0, unless N P ⊂ RP, it is impossible to approximate the maximum quadratic assignment problem within a factor better than 2 log1−ε n by a reduction from the maximum label cover problem. Then, we present an O ( √ n)approximation algorithm for the problem based on rounding of the linear programming relaxation often used in the state of the art exact algorithms. 1
TTS: Rank Attacks in TameLike Multivariate PKCs
, 2004
"... We herein discuss two modes of attack on multivariate publickey cryptosystems. A 2000 GoubinCourtois article applied these techniques against a special class of multivariate PKC’s called “TriangularPlusMinus ” (TPM), and may explain in part the present dearth of research on “true ” multivariates ..."
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We herein discuss two modes of attack on multivariate publickey cryptosystems. A 2000 GoubinCourtois article applied these techniques against a special class of multivariate PKC’s called “TriangularPlusMinus ” (TPM), and may explain in part the present dearth of research on “true ” multivariates – multivariate PKC’s in which the middle map is not really taken in a much larger field. These attacks operate by finding linear combinations of matrices with a given rank. Indeed, we can describe the two attacks very aptly as “highrank ” and “lowrank”. However, TPM was not general enough to cover all pertinent true multivariate PKC’s. Tamelike PKC’s, multivariates with relatively few terms per equation in the central map and an easy inverse, is a superset of TPM that can enjoy both fast private maps and short setup times. However, inattention can still let rank attacks succeed in tamelike PKCs. The TTS (Tame Transformation Signatures) family of digital signature schemes lies at this cusp of contention. Previous TTS instances (proposed at ICISC ’03) claim good resistance to other known attacks. But we show how careless construction in current TTS instances (TTS/4 and TTS / ) exacerbates the security concern of rank, and show two different cryptanalysis in under AES units. TTS is not the only tamelike PKC with these liabilities – they are shared by a few other misconstructed schemes. A suitable equilibrium between speed and security must be struck. We suggest a generic way to craft tamelike PKC’s more resistant to rank attacks. A demonstrative TTS variant with similar dimensions is built for which rank attack takes AES units, while remaining very fast and as resistant to other attacks. The proposed TTS variants can scale up. In short: We show that rank attacks apply to the wider class of tamelike PKC’s, sometimes even better than previously described. However, this is relativized by the realization that we can build adequately resistant tamelike multivariate PKC’s, so the general theme still seem viable compared to more traditional or largefield multivariate alternatives. 1
16741056/2008/17(02)/041504 Chinese Physics B and IOP Publishing Ltd
, 2007
"... Multiproxy quantum group signature scheme with threshold shared verification ∗ ..."
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Multiproxy quantum group signature scheme with threshold shared verification ∗
Partially supported by a grant from the Israel Science Foundation
"... The equation u t = \Deltau + ¯jruj, ¯ 2 R, is studied in R n and in the periodic case. It is shown that the equation is wellposed in L 1 and possesses regularizing properties. For nonnegative initial data and ¯ ! 0 the solution decays in L 1 (R n ) as t ! 1. In the periodic case it tends un ..."
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The equation u t = \Deltau + ¯jruj, ¯ 2 R, is studied in R n and in the periodic case. It is shown that the equation is wellposed in L 1 and possesses regularizing properties. For nonnegative initial data and ¯ ! 0 the solution decays in L 1 (R n ) as t ! 1. In the periodic case it tends uniformly to a limit. A consistent difference scheme is presented and proved to be stable and convergent. AMS Classifications: 35K15, 35K55 1. Introduction In this paper we consider the Cauchy problem for the semilinear parabolic equation (1.1) u t = \Deltau + ¯jruj; 0 6= ¯ 2 R; u(x; 0) = u 0 (x); in R n as well as in the periodic case. Throughout the paper we denote by ru the gradient with respect to the x coordinates. We treat the questions of existence, uniqueness, regularity and long time decay for initial conditions in L 1 . In the case of R n and very smooth initial condition, say u 0 2 C 4 0 (R n ) (i.e. four times continuously differentiable with compact support), the glob...
unknown title
, 901
"... Preprint typeset in JHEP style HYPER VERSION Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions ..."
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Preprint typeset in JHEP style HYPER VERSION Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions