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

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 circle plus Ki)circle plus Ki circle plus 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.