Construction of Quantum Anamorphic Evolving Dynamic Threshold Secret-Sharing Schemes

We propose the concept of Quantum Anamorphic Evolving Secret-Sharing(QAESS), combining two different cryptographic primitives in this paper. In QAESS, we have the anamorphic property, allowing alternate secrets to be embedded within the primary secret-sharing framework, accessible only under specific constraints, and the evolving property of secret-sharing (ESS) where the scheme can dynamically adapt by accommodating potentially an infinite number of new parties without reinitialization. To achieve this, the major hurdles we encounter are 1) the large dimensions of shares and the requirement of huge quantum memory, and 2) the system breakdown by inserting a spy. In our first construction, we present a QAESS scheme, and in the second construction, we use secret redistribution to mitigate the above challenges. Our constructions extensively use quantum trap codes, random permutations, and data structure techniques. We analyze the schemes’ efficiency, scalability, and robustness through theoretical proofs and complexity estimates. This integration of quantum anamorphism and evolving properties finds potential application in several Internet of Things (IoT) and other practical scenarios. We close the paper by discussing several advantages of our constructions and some interesting problems for further study.