Strongly Secure Quantum Ramp Secret Sharing Constructed from Algebraic Curves over Finite Fields

TL;DR

This paper introduces a new quantum ramp secret sharing scheme using algebraic curves over finite fields, allowing the number of shares to grow independently of the share dimension, improving flexibility over previous methods.

Contribution

It presents a novel construction of strongly secure quantum ramp secret sharing schemes leveraging algebraic curves, overcoming previous limitations on share dimension and share number.

Findings

Allows arbitrarily large number of shares for fixed share dimension

Ensures strong security in quantum ramp secret sharing

Uses algebraic curves over finite fields for construction

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.