Properties(const) Lemma 3: Even if there is only one honest participant and the remaining n-1 participants form a coalition in order to deceive him,their probability of cheating successfully is only 1-(1-[1/(q-1)]) n-k+1 ≦ (n-k+1)/(q-1) Lemma 4: The secret information given to each participant consists of k+2(n-1) elements of the finite field GF(q).
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