Feistel Networks

Constructions built from the Feistel round structure, and how many rounds are needed for indifferentiability or indistinguishability from a random permutation.

Status	Statement	Tags
	Constant-round Luby–Rackoff, quantum Resolved for r=7. Carolan (Compressed Permutation Oracles, ePrint 2025/1734, STOC 2026) proves seven-round Luby-Rackoff with truly random round functions is indistinguishable from a random invertible permutation against Omega(N^{1/12}) bidirectional quantum queries (his Theorem 6.5), exactly this page’s conjecture with r=7 – and states, without full proof here, that the result lifts to pseudorandom round functions (the strong qPRP form) by a standard hybrid argument. The paper’s own abstract calls this ‘resolving an open question of (Zhandry, 2012).’	Feistel Networks Pseudorandom Permutations Quantum Query Complexityotherequivalenceresearch-solved
	6-round Feistel indifferentiability Whether 6-round Feistel is fully indifferentiable from a random permutation is open, bridging the proven r=5 attack and the proven r>=8 construction. 2 open	Feistel Networks Indifferentiability Pseudorandom Permutationsothertight-bound