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Uniform Random Number Generation and Secret Key Agreement for General Sources by Using Sparse Matrices

  • Jun MuramatsuEmail author
  • Shigeki Miyake
Chapter
Part of the Mathematics for Industry book series (MFI, volume 29)

Abstract

In this paper, we investigate the problems of uniform random number generation, independent uniform random number generation, and secret key agreement, which provide the information theoretic security. We consider the strong uniformity and strong independence, where it has been unclear whether or not sparse matrices can be applied to these problems for general (correlated) sources with respect to these criteria. To prove the theorems, we first introduce the notion of the balanced-coloring property and the collision-resistance property. We next apply these properties to the problems. Since an ensemble of sparse matrices (with logarithmic column weight) over a finite field satisfies these properties, we can construct a code achieving the fundamental limits by using sparse matrices.

Keywords

Information theory Information theoretic security Uniform random number generation Independent uniform random number gneneration Secret key agreement Ensemble of sparse matrices over a finite field 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.NTT Communication Science LaboratoriesNTT CorporationKyotoJapan
  2. 2.NTT Network Innovation LaboratoriesNTT CorporationKanagawaJapan

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