Abstract
We propose a verifiable [Formula: see text]-threshold secret sharing scheme using Lagrange interpolation and secure cryptographic hash functions. This scheme is an improvement of Shao’s scheme [Inform. Sci. 278 (2014) 104–109]. In our variant, verification of shares is achieved through computation of their multiplicative inverses in conjunction with a secure hash function such as SHA-3. This idea results in a significant size reduction, in comparison with Shao’s scheme, to the shares assigned to each participant. Applications of the proposed scheme include sharing of cryptographic keys, access codes, etc. Furthermore, we improve our construction to present a method for secret sharing with adjustable access structure. This can further be extended to a secret sharing scheme with essential participants, where any authorized set of participants must meet a threshold in the number of essential participants it contains. While our proposal has smaller share sizes compared to Shao’s scheme, it also adds the capabilities of changeable parameters and essential participants.
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