scholarly journals Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation

2005 ◽  
pp. 79-99 ◽  
Author(s):  
Martin Hirt ◽  
Jesper Buus Nielsen
Keyword(s):  
Communication Complexity ◽  
Upper Bounds ◽  
Multiparty Computation

scholarly journals The hardest halfspace

2021 ◽  
Vol 30 (2) ◽  
Author(s):  
Alexander A. Sherstov
Keyword(s):  
Lower Bounds ◽  
Rational Approximation ◽  
Communication Complexity ◽  
Rational Functions ◽  
Explicit Construction ◽  
Upper Bounds ◽  
Infinity Norm ◽  
Communication Problem

AbstractWe study the approximation of halfspaces $$h:\{0,1\}^n\to\{0,1\}$$ h : { 0 , 1 } n → { 0 , 1 } in the infinity norm by polynomials and rational functions of any given degree. Our main result is an explicit construction of the “hardest” halfspace, for which we prove polynomial and rational approximation lower bounds that match the trivial upper bounds achievable for all halfspaces. This completes a lengthy line of work started by Myhill and Kautz (1961). As an application, we construct a communication problem that achieves essentially the largest possible separation, of O(n) versus $$2^{-\Omega(n)}$$ 2 - Ω ( n ) , between the sign-rank and discrepancy. Equivalently, our problem exhibits a gap of log n versus $$\Omega(n)$$ Ω ( n ) between the communication complexity with unbounded versus weakly unbounded error, improving quadratically on previous constructions and completing a line of work started by Babai, Frankl, and Simon (FOCS 1986). Our results further generalize to the k-party number-on-the-forehead model, where we obtain an explicit separation of log n versus $$\Omega(n/4^{n})$$ Ω ( n / 4 n ) for communication with unbounded versus weakly unbounded error.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Secure multiparty computation solutions of collection member decision

2013 ◽  
Vol 33 (12) ◽  
pp. 3527-3530
Author(s):  
Yongli DOU ◽  
Haichun WANG ◽  
Jian KANG
Keyword(s):  
Secure Multiparty Computation ◽  
Multiparty Computation
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