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The sum of PRPs is a secure PRF

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2000) 1807 470-484
DOI: 10.1007/3-540-45539-6_34
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Abstract

Given d independent pseudorandom permutations (PRPs) πi, . . ., πd over {0, 1}n, it appears natural to define a pseudorandom function (PRF) by adding (or XORing) the permutation results: SUMd(x) = π1(x) ⊕ . . . ⊕ πd(x). This paper investigates the security of SUMd and also considers a variant that only uses one single PRP over {0, 1}n.

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Lucks, S. (2000). The sum of PRPs is a secure PRF. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1807, pp. 470–484). Springer Verlag. https://doi.org/10.1007/3-540-45539-6_34

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