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Diagonal Circuit Identity Testing and Lower
, 2007
"... In this paper we give the first deterministic polynomial time algorithm for testing whether a diagonal depth3 circuit C(x1,..., xn) (i.e. C is a sum of powers of linear functions) is zero. We also prove an exponential lower bound showing that such a circuit will compute determinant or permanent onl ..."
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In this paper we give the first deterministic polynomial time algorithm for testing whether a diagonal depth3 circuit C(x1,..., xn) (i.e. C is a sum of powers of linear functions) is zero. We also prove an exponential lower bound showing that such a circuit will compute determinant or permanent
Lower Bounds for the Sum of Graph–driven Read–Once Parity Branching Programs
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 68
, 2003
"... We prove the first lower bound for restricted read–once parity branching programs with unlimited parity nondeterminism where for each input the variables may be tested according to several orderings. Proving a superpolynomial lower bound for read–once parity branching programs is still a challengin ..."
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We prove the first lower bound for restricted read–once parity branching programs with unlimited parity nondeterminism where for each input the variables may be tested according to several orderings. Proving a superpolynomial lower bound for read–once parity branching programs is still a
Efficient, Oblivious Data Structures for MPC
"... Abstract. We present oblivious implementations of several data structures for secure multiparty computation (MPC) such as arrays, dictionaries, and priority queues. The resulting oblivious data structures have only polylogarithmic overhead compared with their classical counterparts. To achieve this ..."
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Cited by 1 (1 self)
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Abstract. We present oblivious implementations of several data structures for secure multiparty computation (MPC) such as arrays, dictionaries, and priority queues. The resulting oblivious data structures have only polylogarithmic overhead compared with their classical counterparts. To achieve
Identity Testing, multilinearity testing, and monomials in ReadOnce/Twice Formulas and Branching Programs ⋆
"... Abstract. We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero (ACIT). We give a deterministic polynomial time algorithm for this problem when the inputs are readtwice formulas. This algorithm also computes the MLIN predicate, testing if the input ..."
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Cited by 2 (1 self)
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Abstract. We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero (ACIT). We give a deterministic polynomial time algorithm for this problem when the inputs are readtwice formulas. This algorithm also computes the MLIN predicate, testing if the input
Deterministic polynomial identity testing in non commutative models
 Computational Complexity
, 2004
"... We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: 1. Non Commutative Arithmetic Formulas: The algorithm gets as an input an arithmetic formula in the noncommuting variables x1,..., xn and determines whether or not the output of the formula ..."
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Cited by 54 (10 self)
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expression). One application is a deterministic polynomial time identity testing for setmultilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for noncommutative algebraic branching programs as defined by Nisan. Finally, we observe an exponential
Oblivious Polynomial Evaluation and Secure SetIntersection from Algebraic PRFs
"... In this paper we study the two fundamental functionalities oblivious polynomial evaluation in the exponent and setintersection, and introduce a new technique for designing efficient secure protocols for these problems (and others). Our starting point is the [BGV11] technique (CRYPTO 2011) for verif ..."
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Cited by 2 (0 self)
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) for verifiable delegation of polynomial evaluations, using algebraic PRFs. We use this tool, that is useful to achieve verifiability in the outsourced setting, in order to achieve privacy in the standard twoparty setting. Our results imply new simple and efficient oblivious polynomial evaluation (OPE) protocols
Implementing a segmentationbased oblivious
, 2014
"... Part of the Computer Sciences Commons This Thesis is brought to you for free and open access by the Graduate College at Digital Repository @ Iowa State University. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Digital Repository @ Iowa Stat ..."
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Part of the Computer Sciences Commons This Thesis is brought to you for free and open access by the Graduate College at Digital Repository @ Iowa State University. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Digital Repository @ Iowa State University. For more information, please contact
More on Noncommutative Polynomial Identity Testing
"... We continue the study of noncommutative polynomial identity testing initiated by Raz and Shpilka and present efficient algorithms for the following problems in the noncommutative model: Polynomial identity testing: The algorithm gets as an input an arithmetic circuit with the promise that the polyno ..."
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Cited by 10 (0 self)
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sided error) and evaluates the circuit over the ring of matrices. In addition, we present query complexity lower bounds for identity testing and explore the possibility of derandomizing our algorithm. The analysis of our algorithm uses a noncommutative variant of the SchwartzZippel test. Minimizing algebraic
Pseudorandomness for Linear Length Branching Programs and Stack Machines
"... Abstract. We show the existence of an explicit pseudorandom generator G of linear stretch such that for every constant k, the output of G is pseudorandom against: – Oblivious branching programs over alphabet {0, 1} of length kn and size 2O(n / logn) on inputs of size n. – Nonoblivious branching pr ..."
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Abstract. We show the existence of an explicit pseudorandom generator G of linear stretch such that for every constant k, the output of G is pseudorandom against: – Oblivious branching programs over alphabet {0, 1} of length kn and size 2O(n / logn) on inputs of size n. – Nonoblivious branching
Results 1  10
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