Construction of Arithmetic Secret Sharing Schemes by Using Torsion Limits

Seher Tutdere, Osmanbey Uzunkol
2019 Hacettepe Journal of Mathematics and Statistics  
In 2014, Cascudo, Cramer, and Xing [I. Cascudo, R. Cramer, and C. 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
more » ... ction fields over finite fields. Mathematics Subject Classification (2010). 94A62, 11R58, 11T71
doi:10.15672/hujms.460348 fatcat:ikqzpatkvjenvfaemqyb2z5gxy