2Communication Complexity of the Equality Problem Recall the equality function EQ(x;y) from the last section which checked whether or not the inputs x;yto Alice and Bob are equal. �ؐ�̋me���uta_H`�X�}x|~��{�IeY�ϻ@�*��"��"ʓ,x���7O:+�~�Z�8 ���]%Y8uuU�����c��#��V����ɂub�"R��4�����n����C����P�;�����Z%yd�Th�L�GW�S�V�P�_�e`��@���o����$D r�8.#�+6�� Is Catrina and de Hoogh the most computationally efficient constant-round protocol currently out there that does a secure equals-zero test of a secret value to generate a secret result? Can Costs #1 and #3 also be moved to a pre-processing phase? We prove that the probabilistic communication complexity of this problem is equal to O(N); the computational complexity of the proposed protocol is polynomial in the size of inputs.Our protocol improves the result achieved in 1991 by Feder et al. By SPDZ-like environment I mean each secret number $a$ is represented by each party having a 'share' of that number $a_i$, such that $\sum a_i = a (\mod p)$ for some large prime (or exponent of a prime) $p$. Communication Complexity of Equality comparison (Catrina and de Hoogh) Ask Question Asked 3 years, 11 months ago. There are two players with unlimited computational power, each of whom holds ann bit input, say x and y. Does this mean the total communication complexity is something like $O(kn^2)$? Once again, we can 1Before the rst round of communication, pick a pairwise independent h : U 7! Can Costs #1 and #3 also be moved to a pre-processing phase? Over the last three decades, communication complexity [51] has proved itself to be among the most useful of abstractions in computer science. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy, 2020 Stack Exchange, Inc. user contributions under cc by-sa, https://crypto.stackexchange.com/questions/42052/communication-complexity-of-equality-comparison-catrina-and-de-hoogh/42141#42141, Communication Complexity of Equality comparison (Catrina and de Hoogh). Does it mean $O(n^2)$ data complexity? Having a diverse, inclusive workforce means that an organisation can offer a wide range of ideas, skills, resources and energies to give it a competitive edge. One application is to the communication complexity of Equality. The problem is usually stated as follows: … Multiparty Computation for Interval, Equality, and Comparison without Bit-Decomposition Protocol Takashi Nishide1,2 and Kazuo Ohta1 1 Department of Information and Communication Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka Chofu-shi, Tokyo 182-8585 Japan This question comes from what I asked in a comment here, although I realized that I don't actually care about which input is less than the other, if they're different. Is Catrina and de Hoogh the most computationally efficient constant-round protocol currently out there that does a secure equals-zero test of a secret value to generate a secret result? There are clear benefits to having a more diverse workforce. The Communication Complexity of Set Intersection and Multiple Equality Testing. Neither knows the other’s input, and they wish to collaboratively compute f(x,y) where functionf: {0,1}n×{0,1}n →{0,1} is known to both. 1.1 The communication complexity of equality Consider the function Equality : f0;1gn f 0;1gn!f0;1g, Equality(x;y) = 1 ,x= y. Trivially, Equality can be computed with communication n+ 1: Asends her input to B; B then communicates the value of Equality. Generate a secret product of two secret numbers. Our protocol improves the result achieved in 1995(Feder, Kushilevitz, Naor, Nisan). communication complexity, there exists a way of obtaining measure-ment statistics that violate some Bell inequality. the randomized communication complexity of any r-round protocol for EqualityTesting that errs with probability p err, and 9Eq(k;r;p err) the correspond-ing complexity of ExistsEqual. The deterministic communication complexity of Equality is D(EQ) n. Proof. Suppose Alice and … Active 3 years, 11 months ago. >> 08/30/2019 ∙ by Dawei Huang, et al. The EQUALITY problem is usually one’s first encounter with communication complexity and is one of the most fundamental problems in the field. J.J.M. The SPDZ protocol, shows that the multiplication of secret values to generate a secret value (Cost #4) can be moved to a pre-processing phase by generating Mulitplicative Triples. Some version We will discuss di erent measures of complexity for the basic model, The Communication Complexity of Set Intersection and Multiple Equality Testing By Dawei Huang, Seth Pettie, Yixiang Zhang and Zhijun Zhang Get PDF (532 KB) We develop a new lower bound method for analysing the complexity of the Equality function (EQ) in the Simultaneous Message Passing (SMP) model of communication complexity.The new technique gives tight lower bounds of \(\varOmega {\left( \sqrt{n}\right) }\) for both EQ and its negation NE in the non-deterministic version of quantum-classical SMP, where Merlin is … Alice and Bob each hold an n-bit string, x For proving communication complexity lower bounds, we analyze the combinatorial structure imposed by protocols. The paper shows a way to do equality-to-zero testing in a constant number of rounds. 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