Adaptively secure, splittable, and robust threshold unsigncryption

Abstract As a variant of the signcryption scheme, threshold unsigncryption operates among multiple receiver members through a (t, n) threshold process during the unsigncryption phase to improve security and robustness, and has been widely deployed in various applications such as cloud computing, blockchain, and electronic auctions. However, existing schemes only consider security under a limited static corruption model, where the adversary selects which parties to corrupt before the protocol begins. As a result, these schemes lack the flexibility to address more complex attack forms posed by real-world adversaries. To solve this issue, it is worth investigating threshold unsigncryption schemes with adaptive security. In this paper, we propose the first provably secure (t, n) threshold unsigncryption scheme in the standard model against adaptive corruption adversaries who can corrupt parties at any time during protocol execution. The main contributions include: First, we provide the formal syntactic definition and security model of threshold unsigncryption schemes under the adaptive corruption model. Second, we employ the dual system technique to formally prove that the proposed scheme can achieve adaptive security in the standard model. Notably, our scheme is equipped with valuable properties such as non-interactivity, robustness, public verifiability, and splittable unsigncryption, significantly enhancing usability and functional completeness. Besides, we implement the proposed scheme on two types of elliptic curve groups with different security levels and evaluate its practical performance under different thresholds. Experiments demonstrate that on a composite order group with 80-bit security, a single receiver only takes 16.61 s to perform the threshold unsigncryption phase when the number of receivers n is 20 and the threshold t reaches up to 18. As a pioneering adaptively secure threshold unsigncryption scheme, our work not only establishes a benchmark for future proposals but also broadens its application in scenarios requiring high-security levels and flexible key management, such as electronic voting.