Breaking the FF3 Format Preserving Encryption

The NIST standard FF3 scheme (also known as BPS scheme) is a tweakable block cipher based on a 8-round Feistel Network. We break it with a practical attack. Our attack exploits the bad domain separation in FF3 design. The attack works with chosen plaintexts and tweaks when the message domain is small. Our FF3 attack requires $O(N^{\frac{11}{6}})$ chosen plaintexts with time complexity $N^{5}$, where $N^2$ is domain size to the Feistel Network. Due to the bad domain separation in 8-round FF3, we reduced the FF3 attack to an attack on 4-round Feistel Networks. In our generic attack, we reconstruct the entire codebook of 4-round Feistel Network with $N^{\frac{3}{2}} \left( \frac{N}{2} \right)^{\frac{1}{6}}$ known plaintexts and time complexity $N^{4}$

Generic Round-Function-Recovery Attacks for Feistel Networks over Small Domains

Feistel Networks (FN) are now being used massively to encrypt credit card numbers through format-preserving encryption. In our work, we focus on FN with two branches, entirely unknown round functions, modular additions (or other group operations), and when the domain size of a branch (called $N$) is small. We investigate round-function-recovery attacks. The best known attack so far is an improvement of Meet-In-The-Middle (MITM) attack by Isobe and Shibutani from ASIACRYPT~2013 with optimal data complexity $q=r \frac{N}{2}$ and time complexity $N^{ \frac{r-4}{2}N + o(N)}$, where $r$ is the round number in FN. We construct an algorithm with a surprisingly better complexity when $r$ is too low, based on partial exhaustive search. When the data complexity varies from the optimal to the one of a codebook attack $q=N^2$, our time complexity can reach $N^{O \left( N^{1-\frac{1}{r-2}} \right) }$. It crosses the complexity of the improved MITM for $q\sim N\frac{\mathrm{e}^3}{r}2^{r-3}$. We also estimate the lowest secure number of rounds depending on $N$ and the security goal. We show that the format-preserving-encryption schemes FF1 and FF3 standardized by NIST and ANSI cannot offer 128-bit security (as they are supposed to) for $N\leq11$ and $N\leq17$, respectively (the NIST standard only requires $N \geq 10$), and we improve the results by Durak and Vaudenay from CRYPTO~2017