Fox密码的多维零相关线性分析

Multidimensional Zero-Correlation Linear Attacks on Fox Block Cipher

Fox密码算法是由欧洲学者Junod和Vaudenay是基于Mediacrypt公司的实际需求而设计的系列分组密码.由于在各种平台上的性能表现良好,该算法在许多安全产品中取代了IDEA算法,成为欧洲应用最普遍的密码算法之一.本文首先关注了Fox密码的零相关线性逼近问题,构造出一些关于Fox密码的4轮零相关线性逼近;然后利用合适的线性逼近,结合部分和技术,分析了减缩轮Fox密码针对多维零相关分析技术的安全性,并且成功地恢复部分轮子密钥信息.结果显示:攻击对5轮Fox-64的计算复杂度大约是260.9次5轮Fox加密,对6轮Fox-64分析大约需要2119.4次6轮Fox加密.额外添加1轮并穷举轮子密钥,结果显示零相关分析方法对7轮Fox密码轮子密钥恢复依然有效.本文是第一个关于Fox密码零相关线性分析的结果.

Block cipher Fox was designed by Junod and Vaudenay based on the actual requirements of the Mediacrypt company. Because of its high performances on various platforms, Fox has replaced the IDEA in many security products, and has become one of the most popular ciphers used in Europe. In this paper, we first introduce some 4 round linear approximations of Fox with zero-correlation, then present some key-recovery attacks on reduced round Fox using the Partial-sum technique. It is shown that the key-recovery attack on 5 round Fox-64 needs about 260.9 encryptions and the attack on 6 round Fox-64 requires about 2119.4 encryptions. It can be extended to 7 rounds by adding one round in the end using the key exhaustive search. This paper is the first attempt of zero-correlation linear cryptanalysis on the cipher Fox.