Choice of parameters Sample Clauses

Choice of parameters. | | | | The parameters t = I , n = x and k need to be chosen correctly to ensure the security of the AS scheme. The scheme is proved IND-CPA secure in [3, Theorem 3] for t = µ · k whenever the (xj, |k/2∫, t, r)-SPR assumption holds. The vector xj ∈ Fn−1 is derived from x by removing a coordinate. Two lower bounds for (n − 1)/k are stated in [3]: n − 1 k (2µ 1)r+1 ≥ − and n − 1 k (r + 1)µ − r . ≥ The first one is derived from a bound in [10] that describes the current state- of-the-art probabilistic polynomial time algorithm to solve the SPRP. The al- gorithm succeeds with probability 1 − O(nO(r)/|F|) whenever t > k( n )1/(r+1) k + k + 1. (1) This entails an exponential growth on the ciphertext size in terms of the number of encryptions if multiplication needs to be supported. Since we only need to support addition, we set µ = 0 and omit ctr from the ciphertexts. We also want to choose the smallest t possible due to (1). To allow unique decryption it is necessary that t > k and we set t = k + 1. This means that (1) is not satisfied for any choice of n and k.
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