Efficient t ‐cheater identifiable ( k , n ) secret‐sharing scheme for t ≤ ⌊(( k − 2)/2)⌋

In Eurocrypt 2011, Obana proposed a ( k , n ) secret‐sharing scheme that can identify up to ⌊(( k − 2)/2)⌋ cheaters. The number of cheaters that this scheme can identify meets its upper bound. When the number of cheaters t satisfies t ≤ ⌊(( k − 1)/3)⌋, this scheme is extremely efficient since the size of share | i | can be written as | i | = ||/ɛ, which almost meets its lower bound, where || denotes the size of secret and ε denotes the successful cheating probability; when the number of cheaters t is close to ⌊(( k − 2)/2)⌋, the size of share is upper bounded by | i | = ( n ·( t + 1) · 2 3 t − 1 ||)/ɛ. A new ( k , n ) secret‐sharing scheme capable of identifying ⌊(( k − 2)/2)⌋ cheaters is presented in this study. Considering the general case that k shareholders are involved in secret reconstruction, the size of share of the proposed scheme is | i | = (2 k − 1 ||)/ɛ, which is independent of the parameters t and n . On the other hand, the size of share in Obana's scheme can be rewritten as | i | = (n · ( t + 1) · 2 k − 1 ||)/ɛ under the same condition. With respect to the size of share, the proposed scheme is more efficient than previous one when the number of cheaters t is close to ⌊(( k − 2)/2)⌋.