There are many schemes to detect and identify cheaters when the number of participants is exactly equal to t in secret sharing schemes. However, most of them need dealers or redundant information to detect the dishonest participants when participants are greater than threshold t. Harn et al. proposed a dynamic threshold secret reconstruction scheme, which the threshold can be improved to k during reconstruction. Less than k - 1 participants cannot recover the shared secret. Their scheme uses the symmetric polynomial to resist the external adversary. However, each participant needs to hold a polynomial. Thus, the complexity of storage of the scheme is high. Furthermore, the scheme cannot detect and identify the cheaters who present falsified information during secret reconstruction. In this paper, we propose a secret sharing scheme with dynamic threshold k that can identify up to k - 1 dishonest participants who have no legal share information. The scheme does not need the help of the dealer to detect cheaters. The dealer uses the traditional polynomial to distribute a secret to each participant. In the secret reconstruction phase, the share information of each participant is transformed and then presents to other participants who verify it using the public key of the sender. If the presented information is falsified, it will fail the verification and the related participant is identified as a cheater. Otherwise, the secret can be correctly reconstructed. Meanwhile, our scheme ensures that the external adversary who eavesdrops the reconstruction messages cannot recover the secret. The trade-off is that our scheme has additional computation overhead.
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