Correction to "Secret Sharing Schemes With Bipartite Access Structure"

We point out some mistakes in Lemma 5.1 and Proposition 5.2 in our paper. Since we are supposing that a ≤ b, the first and the second statements of Lemma 5.1 are not symmetric. The second one must be corrected to: 2. y r = max{0, (t − aN 1)/b} and x r = (t − by r)/a. Besides, the proof of Lemma 5.1 can be more easily understood by beginning it with the proof of the third statement. Due to this mistake in Lemma 5.1, the statement and the proof of Proposition 5.2 are not correct. Proposition 5.2, which is a characterization of the ideal weighted threshold access structures with two weights, must be changed to: Proposition 5.2 A weighted threshold access structure with two weights Γ = W (a, b, t, N 1 , N 2) is ideal if and only if one of the following situations occurs: • x 1 + y 1 = x r + y r , where x 1 = 0 or y 1 = N 2 , that is, Γ = Ω 4 (n, n 1 , n 2) with n 1 = x r , n 2 = y 1 and n = x 1 + y 1. • r = 2 and x 1 = 0, that is, Γ = Ω 2 (n, n 1 , n 2), where n 1 = x 2 , n 2 = y 1 and n = x 2 + y 2. • r ≥ 3, x 1 = 0, x 2 = 2 and x 2 + y 2 = x r + y r , that is, Γ = Ω 2 (n, n 1 , n 2), where n 1 = x r , n 2 = y 1 and n = n 2 + 2.