Optimal Threshold Changeable Secret Sharing with New Threshold Change Range

摘要

Motivated by the need of catering for changes of security policy during the deployment of distribution of trust, threshold changeable secret sharing studies the construction of secret sharing schemes that have a built-in mechanism that, when activated, transforms the scheme into one with different access structures. By combining the two main techniques frequently used in previous constructions: packing and folding, we construct optimal threshold changeable ramp schemes that cover the full threshold change range, while known constructions either achieve only reconstruction threshold change or change both privacy and reconstruction thresholds but require the two thresholds to change proportionally. We justify the claim that the full threshold change range for which optimal schemes are possible is completely covered by proving a completeness result information-theoretically. The share size of these threshold changeable ramp schemes are much bigger than the lower bounds for plain ramp schemes (without requiring threshold changeability). This suggests the natural open question of understanding the share size lower and upper bounds for ramp schemes with built-in structures.