Construction of Arithmetic Secret Sharing Schemes by Using Torsion Limits

TL;DR

This paper improves the construction of arithmetic secret sharing schemes by applying new bounds on torsion limits of algebraic function fields, enhancing their efficiency and security.

Contribution

It introduces novel bounds on torsion limits of algebraic function fields and towers, advancing the theoretical foundation for secret sharing schemes.

Findings

Improved bounds on torsion limits for algebraic function fields.

Enhanced construction methods for arithmetic secret sharing schemes.

New theoretical insights into towers of function fields.

Abstract

Recent results of Cascudo, Cramer, and Xing on the construction of arithmetic secret sharing schemes are improved by using some new bounds on the torsion limits of algebraic function fields. Furthermore, new bounds on the torsion limits of certain towers of function fields are given.