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175
Fully homomorphic encryption using ideal lattices
 In Proc. STOC
, 2009
"... We propose a fully homomorphic encryption scheme – i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result – that, to construct an encryption scheme that permits evaluation of arbitra ..."
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Cited by 663 (17 self)
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that is almost bootstrappable. Latticebased cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a publickey ideal in a polynomial ring
Algebraic Algorithms for Sampling from Conditional Distributions
 Annals of Statistics
, 1995
"... We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so a ..."
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Cited by 268 (20 self)
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We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so
Involutive Bases of Polynomial Ideals
, 1999
"... In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a monomial set. Such a division provides for each monomial the ..."
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Cited by 55 (13 self)
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In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a monomial set. Such a division provides for each monomial
Improving DISPGB Algorithm Using the Discriminant Ideal
, 2004
"... In 1992, V. Weispfenning proved the existence of Comprehensive Gröbner Bases (CGB) and gave an algorithm to compute one. That algorithm was not very efficient and not canonical. Using his suggestions, A. Montes obtained in 2002 a more efficient algorithm (DISPGB) for Discussing Parametric Gröbner Ba ..."
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Cited by 20 (4 self)
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Bases. Inspired in its philosophy, V. Weispfenning defined, in 2002, how to obtain a Canonical Comprehensive Gröbner Basis (CCGB) for parametric polynomial ideals, and provided a constructive method. In this paper we use Weispfenning’s CCGB ideas to make substantial improvements on Montes DISPGB
The Complexity of McKay's Canonical Labeling Algorithm
, 1996
"... We study the time complexity of McKay's algorithm to compute canonical forms and automorphism groups of graphs. The algorithm is based on a type of backtrack search, and it performs pruning by discovered automorphisms and by hashing partial information of vertex labelings. In practice, the algo ..."
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Cited by 51 (1 self)
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We study the time complexity of McKay's algorithm to compute canonical forms and automorphism groups of graphs. The algorithm is based on a type of backtrack search, and it performs pruning by discovered automorphisms and by hashing partial information of vertex labelings. In practice
Canonical Bases for Subalgebras on Two Generators in the
"... Abstract. In this paper we examine subalgebras on two generators in the univariate polynomial ring. A set, S, of polynomials in a subalgebra of a polynomial ring is called a canonical basis (also referred to as SAGBI basis) for the subalgebra if all lead monomials in the subalgebra are products of l ..."
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for subalgebras When studying subalgebras of the polynomial ring it is important to construct convenient bases which can be used for example to determine whether a given element is in the subalgebra. Given a finite set of generators for an ideal it is algorithmic to construct a socalled
COMPUTING CANONICAL REPRESENTATIVES OF REGULAR DIFFERENTIAL IDEALS
"... In this paper, we give three theoretical and practical contributions for solving polynomial ODE or PDE systems. The first one is practical: an algorithm which improves the purely algebraic part of Rosenfeld–Gröbner (the polynomial ODE or PDE systems simplifier which is the core of the Maple 5.5 di ..."
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is theoretical as well as practical: an algorithm to compute canonical representatives of differential polynomials modulo regular differential ideals without any use of Gröbner bases. This algorithm simplifies the theory (somehow a “pedagogic ” contribution) but permits us also to perform easily linear algebra
Ideal bases for graded polynomial rings and applications to interpolation
 MONOGRAFÍAS DE LA ACADEMIA DE CIENCIAS DE ZARAGOZA. 20: 97–110, (2002)
, 2002
"... Based on a generalized algorithm for the division with remainder of polynomials in several variables, a method for the construction of standard bases for polynomial ideals with respect to arbitrary grading structures is derived. In the case of ideals with finite codimension, which can be viewed upon ..."
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Cited by 5 (2 self)
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Based on a generalized algorithm for the division with remainder of polynomials in several variables, a method for the construction of standard bases for polynomial ideals with respect to arbitrary grading structures is derived. In the case of ideals with finite codimension, which can be viewed
About the canonical discussion of polynomial systems with parameters
, 2006
"... Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Gröbner bases depending on the values of the parameters. An improvement using a discriminant ideal to rewrite the tree wa ..."
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Cited by 3 (2 self)
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Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Gröbner bases depending on the values of the parameters. An improvement using a discriminant ideal to rewrite the tree
Rational simplification modulo a polynomial ideal
 IN ISSAC ’06
, 2006
"... We present two algorithms for simplifying rational expressions modulo an ideal of the polynomial ring k[x1,...,xn]. The first method generates the set of equivalent expressions as a module over k[x1,...,xn] and computes a reduced Gröbner basis. From this we obtain a canonical form for the expression ..."
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Cited by 7 (0 self)
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We present two algorithms for simplifying rational expressions modulo an ideal of the polynomial ring k[x1,...,xn]. The first method generates the set of equivalent expressions as a module over k[x1,...,xn] and computes a reduced Gröbner basis. From this we obtain a canonical form
Results 1  10
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175