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Communication Preserving Protocols for Secure Function Evaluation
 In Proc. of 33rd STOC
, 2001
"... A secure function evaluation protocol allows two parties to jointly compute a function f(x; y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: "any function f that can be computed using polynomial resources can be computed securely usin ..."
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Cited by 58 (5 self)
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A secure function evaluation protocol allows two parties to jointly compute a function f(x; y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: "any function f that can be computed using polynomial resources can be computed securely using polynomial resources" (where `resources' refers to communication and computation). This result follows by a general transformation from any circuit for f to a secure protocol that evaluates f . Although the resources used by protocols resulting from this transformation are polynomial in the circuit size, they are much higher (in general) than those required for an insecure computation of f . We propose a new methodology for designing secure protocols, utilizing the communication complexity tree (or branching program) representation of f . We start with an efficient (insecure) protocol for f and transform it into a secure protocol. In other words, "any function f that can be computed using communication complexity c can be can be computed securely using communication complexity that is polynomial in c and a security parameter". We show several simple applications of this new methodology resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the "millionaires problem ", where two participants want to compare their values but reveal no other information. Our protocol is more efficient than previously known ones in either communication or computation. 1.
Communication Complexity and Secure Function Evaluation
, 2001
"... A secure function evaluation protocol allows two parties to jointly compute a function f(x; y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: "any function f that can be computed using polynomial resources can be computed securely u ..."
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Cited by 14 (1 self)
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A secure function evaluation protocol allows two parties to jointly compute a function f(x; y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: "any function f that can be computed using polynomial resources can be computed securely using polynomial resources" (where `resources' refers to communication and computation). This result follows by a general transformation from any circuit for f to a secure protocol that evaluates f . Although the resources used by protocols resulting from this transformation are polynomial in the circuit size, they are much higher (in general) than those required for an insecure computation of f . For the design of efficient secure protocols we suggest two new methodologies, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching program) representation of f . We start with an efficient (insecure) protocol for f and transform it into a secure protocol. In other words, "any function f that can be computed using communication complexity c can be can be computed securely using communication complexity that is polynomial in c and a security parameter". The second methodology uses the circuit computing f , enhanced with lookup tables as its underlying computational model. It is possible to simulate any RAM machine in this model with polylogarithmic blowup. Hence it is possible to start with a computation of f on a RAM machine and transform it into a secure protocol. We show many applications of these new methodologies resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the "millionaires problem", where two partici...
Streaming Computation of Combinatorial Objects
 In Proceedings of the Seventeenth Annual IEEE Conference on Computational Complexity
, 2002
"... We prove (mostly tight) space lower bounds for "streaming " (or "online") computations of four fundamental combinatorial objects: errorcorrecting codes, universal hash functions, extractors, and dispersers. Streaming computations for these objects are motivated algorithmically ..."
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Cited by 7 (2 self)
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We prove (mostly tight) space lower bounds for "streaming " (or "online") computations of four fundamental combinatorial objects: errorcorrecting codes, universal hash functions, extractors, and dispersers. Streaming computations for these objects are motivated algorithmically by massive data set applications and complexitytheoretically by pseudorandomness and derandomization for spacebounded probabilistic algorithms.
Quantum and Classical CommunicationSpace Tradeoffs from Rectangle Bounds
"... We derive bounds on the product of the communication C and space S for communicating circuits. The first bound applies to quantum circuits and follows from a "bipartite product" result for the discrepancy of communication problems. If for any problem f : XY the multicolor discrepancy ..."
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Cited by 6 (2 self)
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We derive bounds on the product of the communication C and space S for communicating circuits. The first bound applies to quantum circuits and follows from a "bipartite product" result for the discrepancy of communication problems. If for any problem f : XY the multicolor discrepancy of the communication matrix of f is 1/2 then the problem in which Alice receives some l inputs, Bob r inputs, and their task is to compute f(x i , y j ) for the l r pairs of inputs (x i , y j ), has a quantum communicationspace tradeo# CS (lrd log Z).
Communication vs. computation
 Proc. 31st International Colloquium of Automata, Languages and Programming (ICALP
, 2004
"... We initiate a study of tradeoffs between communication and computation in wellknown communication models and in other related models. The fundamental question we investigate is the following: Is there a computational task that exhibits a strong tradeoff behavior between the amount of communication ..."
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Cited by 1 (1 self)
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We initiate a study of tradeoffs between communication and computation in wellknown communication models and in other related models. The fundamental question we investigate is the following: Is there a computational task that exhibits a strong tradeoff behavior between the amount of communication and the amount of time needed for local computation? Under various standard assumptions, we exhibit boolean functions that show strong tradeoffs in the following computation models: (1) twoparty randomized communication complexity; (2) query complexity; (3) property testing. For the model of deterministic communication complexity, we show a similar result relative to a random oracle. Finally, we study a timedegree tradeoff problem that arises in arithmetization of boolean functions, and relate it to timecommunication tradeoff questions in multiparty communication complexity and in cryptography.
Aspekty Komunikacyjne Oblicze N Systemw Automatw Sko Nczonych
, 1999
"... port I would never be able to finish this thesis. I also thank my parents; they were always enthusiastic about my work. Contents 1 Introduction 1 1.1 Modes of Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Complexity Issues for Multiautomata Systems . . . . . . . ..."
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port I would never be able to finish this thesis. I also thank my parents; they were always enthusiastic about my work. Contents 1 Introduction 1 1.1 Modes of Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Complexity Issues for Multiautomata Systems . . . . . . . . . . . . . . . . . . 2 1.3 Notions and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 Multiautomata and Multiprocessors Systems . . . . . . . . . . . . . . . 4 1.3.2 Alternative Notion: Multihead and Multiprocessor Finite Automata. . 5 1.3.3 Communication Complexity . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.4 Communication Measure for Multiautomata Systems . . . . . . . . . . 6 1.3.5 Kolmogorov Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.6 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Previous Results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Abstract
, 2001
"... We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by Raz [30] to the quantum case. Applying this ..."
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We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by Raz [30] to the quantum case. Applying this method we give an exponential separation between bounded error quantum communication complexity and nondeterministic quantum communication complexity. We develop several other Fourier based lower bound methods, notably showing that ¯s(f) / log n, for the average sensitivity ¯s(f) of a function f, yields a lower bound on the bounded error quantum communication complexity of f(x ∧ y ⊕ z), where x is a Boolean word held by Alice and y, z are Boolean words held by Bob. We then prove the first large lower bounds on the bounded error quantum communication complexity of functions, for which a polynomial quantum speedup is possible. For all the functions we investigate, the only previously applied general lower bound method based on discrepancy yields bounds that are O(log n). 1
computational complexity COMMUNICATION VS. COMPUTATION
"... Abstract. We initiate a study of tradeoffs between communication and computation in wellknown communication models and in other related models. The fundamental question we investigate is the following: Is there a computational task that exhibits a strong tradeoff behavior between the amount of comm ..."
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Abstract. We initiate a study of tradeoffs between communication and computation in wellknown communication models and in other related models. The fundamental question we investigate is the following: Is there a computational task that exhibits a strong tradeoff behavior between the amount of communication and the amount of time needed for local computation? Under various standard assumptions, we exhibit Boolean functions that show strong tradeoffs between communication and time complexity in the following scenarios: Twoparty communication complexity. We exhibit a polynomialtime computable Boolean function that has a low randomized communication complexity, while any communicationefficient (randomized) protocol for this function requires a superpolynomial amount of local computation. In the case of deterministic twoparty protocols, we show a similar result relative to a random oracle. Query complexity. We exhibit a polynomialtime computable Boolean function that can be computed by querying a few bits of its input, but where any such queryefficient scheme requires a superpolynomial amount of computation. Property testing. We exhibit a polynomialtime decidable property that can be tested (i.e., strings which have the property can be distinguished from ones that are far from the property) by querying a few bits of the input, but where any such queryefficient tester requires a superpolynomial amount of computation. Finally, we study a timedegree tradeoff problem that arises in arithmetization of Boolean functions, and relate it to timecommunication tradeoff questions in multiparty communication complexity and cryptography.