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

F. Betül Durak and Serge Vaudenay

##### Abstract

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.

Available format(s)
Publication info
Published elsewhere. MINOR revision.ACNS 2018
Keywords
Feisten Networkgeneric attacks
Contact author(s)
durakfbetul @ gmail com
History
2018-04-18: revised
See all versions
Short URL
https://ia.cr/2018/108

CC BY

BibTeX

@misc{cryptoeprint:2018/108,
author = {F.  Betül  Durak and Serge Vaudenay},
title = {Generic Round-Function-Recovery Attacks for Feistel Networks over Small Domains},
howpublished = {Cryptology ePrint Archive, Paper 2018/108},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/108}},
url = {https://eprint.iacr.org/2018/108}
}

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