A verifiable threshold multi-secret sharing scheme based on elliptic curve cryptography

A multi-secret sharing (MSS) scheme enables distribution of several secrets among a set of participants, such that only well-defined subsets of participants are authorized to recover the secrets. A multi-secret sharing scheme is verifiable (VMSS) if cheating detection and cheater identification are achievable in the process. Cheating detection ensures the correctness of shares and reconstructed secrets, while cheater identification reveals dishonest entities. These may include (1) the dealer distributing incorrect shares, (2) participants submitting fake shares during recovery, or (3) a malicious combiner impersonating the genuine one to collect shares and reconstruct secrets. Most existing VMSS schemes assume the dealer and participants can act dishonestly, whereas the combiner is considered fully trusted. However, an adversary could impersonate the combiner, send fraudulent requests to participants, and gather sufficient shares to recover the secrets. To the best of our knowledge, few studies have examined verification of the combiner. This paper proposes a verifiable threshold multi-secret sharing scheme that achieves cheating detection, cheater identification, and verification of both participants and the combiner, while also preventing dealer misbehavior. The scheme allows secure use of public channels and relies on elliptic curve cryptography (ECC) and the hardness of the elliptic curve discrete logarithm problem (ECDLP).