The Grain-like Cipher And Its Security Analysis

The WG keystream generator consists of linear feedback shift register (LFSR) over GF(2n) and a WG transformation. There are many theories to proof the randomness of WG cipher, while there are few theories to proof the Grain cipher. In order to combine advantages of the Grain cipher and the WG cipher, we propose the Grain-like cipher. When we analyse the algebraic attack and correlation attack in Grain cipher, quantitative results have not been mentioned. We can get quantitative results about simplified models, which give the criteria of the Grain-like cipher in some degree.Engineering and implementation are simple and efficient over GF(2). Owing to the relationships between GF(qn) and GF(q), an improved method of generating m-sequences over GF(q") from m-sequences over GF(q) is proposed to facilitate the implementation of the Grain-like cipher. Then we apply it to replace the LFSR over GF(2n). Moreover, we can put it into the application of WG1 and WG8 over GF(2), then demonstrate the low complexity of implementing the WG cipher when compared to the complexity of calculation of WG7, WG8cipher over GF(27) and GF(28). Finally, we verify that the improved method is reasonable and meaningful.The output stream bits of the Grain-like cipher can reserve the previous randomness properties and can have high and exact linear complexity. In this paper, we analyse the model of the simplified Grain-like cipher Ⅰ, and then give the result of the Grain-like cipher I.This can reflect the security of the Grain-like cipher in algebraic attack. Moreover, the Grain-like cipher can demonstrate higher level of security in the context of algebraic attack when it compared to the Grain cipher. Correlation attack is a traditional way. A hypothesis that seven outputs from NLFSR can be received by attacker is given at first. We gain some detailed results by giving a hypothesis and analyse the simplified Grain-like cipher Ⅱ and the modified WG8 cipher. Thus it is meaningful that this paper does research for these results.