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95
Implementing Tate Pairing
 IN ALGORITHMIC NUMBER THEORY SYMPOSIUM
, 2002
"... The Weil and Tate pairings have found several new applications in cryptography. To efficiently implement these cryptosystems it is necessary to optimise the computation time for the Tate pairing. This paper provides methods to achieve fast computation of the Tate pairing. We also give divisionfre ..."
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Cited by 171 (5 self)
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The Weil and Tate pairings have found several new applications in cryptography. To efficiently implement these cryptosystems it is necessary to optimise the computation time for the Tate pairing. This paper provides methods to achieve fast computation of the Tate pairing. We also give divisionfree
Five, Six, and SevenTerm KaratsubaLike Formulae
"... Abstract—The KaratsubaOfman algorithm starts with a way to multiply two 2term (i.e., linear) polynomials using three scalar multiplications. There is also a way to multiply two 3term (i.e., quadratic) polynomials using six scalar multiplications. These are used within recursive constructions to m ..."
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Cited by 1 (0 self)
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to multiply two higherdegree polynomials in subquadratic time. We present divisionfree formulae which multiply two 5term polynomials with 13 scalar multiplications, two 6term polynomials with 17 scalar multiplications, and two 7term polynomials with 22 scalar multiplications. These formulae may be mixed
LEARNING ARITHMETIC READONCE FORMULAS*
"... Abstract. A formula is readonce if each variable appears at most once in it. An arithmetic readonce formula is one in which the operators are addition, subtraction, multiplication, and division. We present polynomial time algorithms for exact learning of arithmetic readonce formulas over a field. ..."
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+ 5 elements (where n is the number of variables) and over infinite fields. We also show the existence of nonuniform deterministic membership query algorithms for arbitrary readonce formulas over fields of characteristic 0, and divisionfree readonce formulas over fields that have at least 2n
kdivisible random variables in free probability
, 2012
"... We introduce and study the notion of kdivisible elements in a noncommutative probability space. A kdivisible element is a (noncommutative) random variable whose nth moment vanishes whenever n is not a multiple of k. First, we consider the combinatorial convolution ∗ in the lattices NC of noncr ..."
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Cited by 2 (0 self)
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crossing partitions and NCk of kdivisible noncrossing partitions and show that convolving k times with the zetafunction in NC is equivalent to convolving once with the zetafunction in NCk. Furthermore, when x is kdivisible, we derive a formula for the free cumulants of xk in terms of the free cumulants of x
Product of free random variables and kdivisible noncrossing partitions
 Elec. Comm. Probab
, 2012
"... We derive a formula for the moments and the free cumulants of the multiplication of k free random variables in terms of kequal and kdivisible noncrossing partitions. This leads to a new simple proof for the bounds of the rightedge of the support of the free multiplicative convolution µk, given b ..."
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Cited by 2 (2 self)
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We derive a formula for the moments and the free cumulants of the multiplication of k free random variables in terms of kequal and kdivisible noncrossing partitions. This leads to a new simple proof for the bounds of the rightedge of the support of the free multiplicative convolution µk, given
DAMTP/0569 hepth/0508031 Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory
, 2005
"... A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations are found. These include generalisations of those found by ..."
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by Flato and Fronsdal for SO(3, 2). In even dimensions the products for free representations split into two types depending on whether the dimension is divisible by four or not.
2IREENA, Ecole Polytechnique de l’Université de Nantes
"... Abstract—This paper considers a minimum meansquared error (MMSE) single user adaptive receiver for the asynchronous directsequence codedivision multipleaccess (DSCDMA) system, based on the leastmeansquare (LMS) algorithm. It is known that in this context the adaptive algorithm can be iterated ..."
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the receiver coefficients, saving significant time processing. Secondly, in order to further increase the convergence rate, a divisionfree version of the gradient adaptive lattice (GAL) algorithm is proposed. Since the lattice predictor orthogonalizes the input signals, this algorithm achieves a faster
SK1 of graded division algebras
"... Abstract. The reduced Whitehead group SK1 of a graded division algebra graded by a torsionfree abelian group is studied. It is observed that the computations here are much more straightforward than in the nongraded setting. Bridges to the ungraded case are then established by the following two the ..."
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Cited by 7 (7 self)
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Abstract. The reduced Whitehead group SK1 of a graded division algebra graded by a torsionfree abelian group is studied. It is observed that the computations here are much more straightforward than in the nongraded setting. Bridges to the ungraded case are then established by the following two
An efficient regular matrix inversion circuit architecture for mimo processing
 in Proc. IEEE Int. Symp. Circuits Systems
, 2006
"... AbstractA novel circuit architecture and algorithm is pre There is some evidence that methods which involve resented for the efficient implementation of a matrix inversion currence, such as ShermanMorrison, iterative methods, and unit. The divisionfree algorithm yields a scaled version of the v. ..."
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Cited by 4 (0 self)
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AbstractA novel circuit architecture and algorithm is pre There is some evidence that methods which involve resented for the efficient implementation of a matrix inversion currence, such as ShermanMorrison, iterative methods, and unit. The divisionfree algorithm yields a scaled version of the v
Tight bounds on the capacity of binary input random CDMA systems
 IEEE TRANS. INFORM. THEORY
, 2008
"... We consider multiple access communication on a binary input additive white Gaussian noise channel using randomly spread code division. For a general class of symmetric distributions for spreading coefficients, in the limit of a large number of users, we prove an upper bound on the capacity, which ma ..."
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Cited by 15 (4 self)
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matches a formula that Tanaka obtained by using the replica method. We also show concentration of various relevant quantities including mutual information, capacity and free energy. The mathematical methods are quite general and allow us to discuss extensions to other multiuser scenarios.
Results 1  10
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