On secret sharing from extended norm-trace curves
This work addresses the need for secure secret sharing schemes in cryptography, but it is incremental as it builds on and clarifies existing methods.
The paper tackles the problem of designing ramp secret sharing schemes with good parameters and an additional security layer, using codes from extended norm-trace curves, and demonstrates that a prior method for estimating weights is a clever application of an existing bound rather than a competing approach.
In [4] Camps-Moreno et al. treated (relative) generalized Hamming weights of codes from extended norm-trace curves and they gave examples of resulting good asymmetric quantum error-correcting codes employing information on the relative distances. In the present paper we study ramp secret sharing schemes which are objects that require an analysis of higher relative weights and we show that not only do schemes defined from one-point algebraic geometric codes from extended norm-trace curves have good parameters, they also posses a second layer of security along the lines of [11]. It is left undecided in [4, page 2889] if the ``footprint-like approach'' as employed by Camps-Moreno herein is strictly better for codes related to extended norm-trace codes than the general approach for treating one-point algebraic geometric codes and their likes as presented in [12]. We demonstrate that the method used in [4] to estimate (relative) generalized Hamming weights of codes from extended norm-trace curves can be viewed as a clever application of the enhanced Goppa bound in [12] rather than a competing approach.