# American Institute of Mathematical Sciences

February  2019, 13(1): 1-10. doi: 10.3934/amc.2019001

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

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

* Corresponding author

Received  March 2015 Published  December 2018

Fund Project: 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.

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.

Citation: Ryutaroh Matsumoto. Strongly secure quantum ramp secret sharing constructed from algebraic curves over finite fields. Advances in Mathematics of Communications, 2019, 13 (1) : 1-10. doi: 10.3934/amc.2019001
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