다중 컴파트먼트 비밀공유 기법

초록

Secret sharing is a cryptographic technique that involves dividing a secret or a piece of sensitive information into multiple sharesor parts, which can significantly increase the confidentiality of a secret. There has been a lot of research on secret sharing for differentcontexts or situations. Tassa's conjunctive secret sharing method employs polynomial derivatives to facilitate hierarchical secret sharing. However, the use of derivatives introduces several limitations in hierarchical secret sharing. Firstly, only a single group of participantscan be created at each level due to the shares being generated from a sole derivative. Secondly, the method can only reconstruct asecret through conjunction, thereby restricting the specification of arbitrary secret reconstruction conditions. Thirdly, Birkhoff interpolationis required, adding complexity compared to the more accessible Lagrange interpolation used in polynomial-based secret sharing. Thispaper introduces the multi-compartment secret sharing method as a generalization of the conjunctive hierarchical secret sharing. Ourproposed method first encrypts a secret using external groups’ shares and then generates internal shares for each group by embeddingthe encrypted secret value in a polynomial. While the polynomial can be reconstructed with the internal shares, the polynomial just providesthe encrypted secret, requiring external shares for decryption. This approach enables the creation of multiple participant groups at asingle level. It supports the implementation of arbitrary secret reconstruction conditions, as well as conjunction. Furthermore, the useof polynomials allows the application of Lagrange interpolation.

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