Length Doublers Sample Clauses

Length Doublers. ‌ For arbitrary finite key space K and n ∈ N, a length doubler is a function E : K × {0, 1}[n,2n−1] → {0, 1}[n,2n−1] such that for every fixed key K ∈ K, EK(·) = E (K,·) is a length preserving invertible function on {0, 1}[n,2n−1]. We denote its inverse for fixed key K by E−1(·) = E−1(K,·). Note that E should behave like a random permutation for every length input in [n, 2n − 1]. Denote by VPerm([n, 2n − 1]) the set of all length-preserving and invertible functions on {0, 1}[n,2n−1]. The security of E is measured by considering a distinguisher D that has two-sided query access to either EK for a randomly drawn key K ←− K, or a random length-preserving permutation ρ ←−$ VPerm([n, 2n− 1]), and its goal is to try to distinguish the real construction from the ideal one: Advvsprp(D)= Pr K ←−$ K : DEK± = 1 − Pr ρ ←−$ VPerm([n, 2n − 1]) : Dρ± = 1 . As in Sect. 2.1, the key space corresponds to the source of randomness of the construction K±. It may take various shapes, but it will always be clear from the context.