Lai-Massey结构伪随机特性研究

该文深入研究了Lai-Massey结构的伪随机特性。首先，证明了基于仿射几乎正形置换设计的3轮Lai- Massey模型并不具有伪随机特性，给出了Lai-Massey结构设计者所得结论的一个反例。其次，证明了双射为任意正形置换时，至少3轮Lai-Massey结构才具有伪随机特性；证明了双射为仿射正形置换时，至少4轮的Lai-Massey结构才具有超伪随机特性。结论表明，为构造伪随机特性更好的Lai-Massey结构实例，双射最好设计为非线性的正形置换或几乎正形置换。

On the Pseudorandomness of the Lai-Massey Scheme

The pseudoranness of the Lai-Massey schme is studied in this paper. First, itis proved that if is an affine almost orthomorphism, 3-round Lai-Massey scheme can not reach the pseudorandomness, which is a counterexample of the Lai-Massey scheme designer's result. Then, it is proved that at least 3-round Lai-Massey scheme is need for the property of pseudorandomness when the bijective is an arbitrary orthomorphism, and at least 4-round Lai-Massey scheme is need for the property of super pseudorandomness when the bijective is an orthomorphism. From the above results, it is preferable to design a bijective which is nonlinear orthomorphism or almost orthomorphism to construct the Lai-Massey scheme with better pseudorandomness.