- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 2
- Construction of arithmetic secret sharing schemes by using torsion limits
Construction of arithmetic secret sharing schemes by using torsion limits
Authors : Seher Tutdere, Osmanbey Uzunkol
Pages : 638-647
Doi:10.15672/hujms.460348
View : 11 | Download : 4
Publication Date : 2020-04-02
Article Type : Research
Abstract :Cascudo, Cramer, and Xing [Torsion limits and Riemann-Roch systems for function fields and applications, IEEE Trans. Inf. Theory, 2014] gave a construction of arithmetic secret sharing schemes by using the torsion limits of algebraic function fields and Riemann-Roch systems. In this work, we give some new conditions for the construction of arithmetic secret sharing schemes. Furthermore, we give new bounds on the torsion limits of certain towers of function fields over finite fields.Keywords : Algebraic function fields, torsion limits, Arithmetic secret sharing schemes