CAJ | 학술논문

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。
해문심입연구료Lai-Massey결구적위수궤특성。수선，증명료기우방사궤호정형치환?설계적3륜Lai-Massey모형병불구유위수궤특성，급출료Lai-Massey결구설계자소득결론적일개반례。기차，증명료쌍사?위임의정형치환시，지소3륜 Lai-Massey 결구재구유위수궤특성；증명료쌍사?위방사정형치환시，지소4륜적Lai-Massey결구재구유초위수궤특성。결론표명，위구조위수궤특성경호적Lai-Massey결구실례，쌍사?최호설계위비선성적정형치환혹궤호정형치환。
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.