Strongly secure quantum ramp secret sharing constructed from algebraic curves over finite fields

Ryutaroh Matsumoto

doi:10.3934/amc.2019001

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2019, Volume 13, Issue 1: 1-10. Doi: 10.3934/amc.2019001

This issue Previous Article Next Article The secrecy capacity of the arbitrarily varying wiretap channel under list decoding

Strongly secure quantum ramp secret sharing constructed from algebraic curves over finite fields

Ryutaroh Matsumoto^1,2, ,

1.
Department of Information and Communication Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan
2.
Department of Mathematical Sciences, Aalborg University, Denmark

* Corresponding author
* Corresponding author

Received: February 28, 2015

Published: December 2018

This research is partly supported by the National Institute of Information and Communications Technology, Japan, and by the Japan Society for the Promotion of Science Grant Nos. 23246071 and 26289116, and the Villum Foundation through their VELUX Visiting Professor Programme 2013-2014.

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Abstract

The first construction of strongly secure quantum ramp secret sharing by Zhang and Matsumoto had an undesirable feature that the dimension of quantum shares must be larger than the number of shares. By using algebraic curves over finite fields, we propose a new construction in which the number of shares can become arbitrarily large for fixed dimension of shares.

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Mathematics Subject Classification: Primary: 81P94; Secondary: 94A62, 94B27.

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References

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