BBB security for 5-round even-Mansour-based key-alternating Feistel ciphers

Abstract

In this paper, we study the security of the Key-Alternating Feistel (KAF) ciphers, a class of key alternating ciphers with the Feistel structure, where each round of the cipher is instantiated with n-bit public round permutation Pi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_i$$\\end{document}, namely the i-th round of the cipher maps (XL,XR)↦(XR,Pi(XR⊕Ki)⊕Ki⊕XL).\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} (X_L, X_R) \\mapsto (X_R, P_i(X_R \\oplus K_i) \\oplus K_i \\oplus X_L). \\end{aligned}$$\\end{document}We have shown that our 5 round construction with independent round permutations and independent round keys achieves 2n/3-bit security in the random permutation model, i.e., the setting where the adversary is allowed to make forward and inverse queries to the round permutations in a black box way.