Sum of Permutations Sample Clauses

Sum of Permutations. The sum of two independent n-bit permutations P1, P2, SoPP1 ,P2 (x) = P1(x) ⊕ P2(x) , (1) was first introduced by Bellare et al. [7]. Closely following this introduction, Lucks [46] proved around 22n/3 security and Bellare and Xxxxxxxxxxx [5] around 2n/n security. An intensive line of research of Patarin [56–58] yielded around optimal 2n security, up to constant, following the mirror theory. Xxx et al. [22] proved around 2n security using their rather compact and elegant chi-squared method. The two independent permutations can be simulated using a single one through domain separation [5, 46]:
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