Stream ciphers based on nonlinear feedback shift register are used in information security of hardware restricted devices such as smart cards

radio frequency identification (RFID) and wireless sensor network. Typical examples of these ciphers are Trivium

Grain v1 and Mickey. Previous algorithms of full diffusion have disadvantages such as few analyzing rounds and indistinct dependent relationship. This paper proposes an algorithm for full diffusion of stream cipher based on nonlinear feedback shift register. The internal states of cipher are represented as linear sets and nonlinear sets. Then round functions of stream cipher are converted to operations of sets. So we can estimate the lower bound of rounds which a stream cipher needs to reach full nonlinear diffusion. Using this algorithm

this paper presents an improved one bit differential distinguisher of Trivium and a real-time attack on full rounds of Trivium-B. Moreover

this method can provide certain theory basis for the design of this kind of stream cipher.