Generalised cheater detection and identification

Cheater detection and identification are important issues in the process of secret reconstruction. To detect and identify cheaters most of the algorithms need the dealer to generate and distribute additional information to shareholders. Recently, algorithms have been proposed to detect and identify cheaters. If more than t (i.e. the threshold) shares, for example j (i.e. t <; j) shares in the secret reconstruction, then redundancy of shares can be used to detect and identify cheaters. The detectability and identifiability of cheaters are proportional to the number of redundant shares. However, the number of redundant shares, j - t is fixed if original shares are used in the secret reconstruction. So, a threshold changeable verifiable secret sharing (TCVSS) has been developed, which allows shareholders working together to change the threshold t into a new threshold t´ (i.e. t´ <; j) and generate new shares; whereas at the same time, maintain the original secret. The verifiability of the proposed TCVSS enables shareholders to verify that their new shares have been properly generated. The number of redundant shares can be changed to j - t´ if new shares are used in the secret reconstruction. Discussion on how to determine the new threshold t´ in order to detect and identify cheaters successfully has also been included.