# A Novel Hybrid Elementary Cellular Automata and Its Application in a Stream Cipher
## 1 Introduction  
The stream cipher belongs to the symmetric cryptosystem in modern cryptography. It is close to the \"one-time pad\" (OTP) cryptosystem. In theory, [PERSON] proved that the OTP is absolutely secure in 1949 [1]. However, a keystream with the same length as the plaintext should be transmitted through a secure channel in the OTP. It is unpractical and wasteful in general. Moreover, the key management of the OTP is difficult. Hence, the stream cipher has gradually been used as a substitute for the OTP [2]. The core of a stream cipher is the keystream generator. A secret key with an acceptable length is employed as the input of the keystream generator to generate a keystream. Meanwhile, the keystream generated by a qualified stream cipher is difficult to be distinguished from a real random sequence. It means that the keystream should be provided with good pseudo-randomness, including long period, high linear complexity, uniform statistical property, etc. [3] Accordingly, the stream cipher possesses many advantages, such as offering good security and being lightweight and efficient. It is widely used in secret communication, especially in the military, government, etc. [4]. Thus, it is meaningful to design a qualified stream cipher. The traditional stream cipher is based on the linear feedback shift register (LFSR). The sequence with the longest period generated by the LFSR is the m-sequence, which possesses good statistical properties [5]. However, the period of the m-sequence is limited by the series and taps of the LFSR. Meanwhile, the state values and structure of the LFSR are easily recovered by the Berlekamp-Massey (B-M) synthesis. Hence, the security of the stream cipher based on the LFSR is weak. It cannot be used in building a stream cipher directly. Subsequently, many improvement schemes consisting of the driving part (LFSR) and the nonlinear part were proposed [6]. The keystream generators of the stream cipher based on this structure can be divided into three kinds according to the nonlinear part: nonlinear-combiner generator [7], such as E0 used in Bluetooth [8]; nonlinear-filter generator [9], for example, ISO/IEC international standard stream cipher SNOW 2.0 [10]; clock-controlled generator [11], for instance, the stream cipher A5/1 [12]. The above schemes utilize the nonlinear part to break or cover up the linearity of the LFSR. Accordingly, the resistance of these improved stream ciphers for the linear analysis is enhanced, especially the analysis based on the B-M synthesis. Nevertheless, cryptanalysis is also developed with the improvement of the stream cipher. [PERSON] et al. proposed a novel cryptanalysis based on binary particle swarm optimization (BPSO) and the divide-and-conquer approach. It reduces the number of exhaust searches significantly. They also successfully acquired the initial states of the LFSR in the Geffe generator based on the nonlinear combiner [13]. As for the nonlinear-filter generator, the generalized filter state guessing attacks (GFSGAs) were designed by [PERSON] [14]. This method can recover the secret states in the filter and LFSR effectively. [PERSON] et al. proposed a straightforward guess-and-determine attack (SGDA) based on a genetic algorithm. This method can reduce the time consumption of attacks to the small-scale SNOW2.0 [15]. Moreover, the guess-and-determine analysis [16] and algebraic attack [17] also apply to the stream cipher based on the clock-controlled generator. Thus, although the stream ciphers based on the LFSR and nonlinear part are easily implemented, and possess good statistical properties, lots of cryptanalyses are proposed to recover the internal states in the LFSR because the LFSR is a mature technology that can be regarded as the Boolean function. Meanwhile, the Boolean function's correlation and algebraic immunity were proposed to estimate the resistance of the stream cipher for the correlation and algebraic attack [18].