Strongly Secure Quantum Ramp Secret Sharing Constructed from Algebraic Curves over Finite Fields
This addresses a specific problem in quantum cryptography for secure data sharing, though it appears incremental as it builds on prior work to remove a constraint.
The paper tackled the limitation in quantum ramp secret sharing where share dimension had to exceed the number of shares, and the result was a new construction using algebraic curves over finite fields that allows arbitrarily large share numbers for fixed share dimensions.
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.