Design Of Stream Cipher Based On FCSR Cascade Structure

With the rapid development of information society,while the Internet has brought people a convenient life,it also breeds many security risks.The use of cryptographic technology provides strong support for resisting these security risks.Among them,Sequence ciphers that can generate pseudo-random numbers have received great attention,and research on them is in full swing.As an emerging component of serial ciphers,the Feedback Carry Shift Register(FCSR)has become a research hotspot of stream ciphers due to its good pseudorandom characteristics similar to m-sequences.At the same time,cascading different cipher components as the source of randomness for stream ciphers has become the mainstream direction of stream cipher algorithm design,and has been highly valued by the majority of researchers.In view of this,this paper,two kinds of cascade structures based on FCSR are designed by studying the cascade structure of FCSR,and based on these two cascade structures new sequence cipher algorithms are proposed,and the pseudo-random property and security of its key stream generation are analyzed.The specific contents are as follows:On the one hand: due to the cascade of Galois structured LFSR and Galois structured FCSR,the sequence cipher algorithm can not effectively resist real-time attacks against Galois structured FCSR.We replaced the Galois structure LFSR in the above cascade structure with Galois structure FCSR for multi-level cascade,and constructed a sequence cipher algorithm based on this cascade structure.Specifically,first,by analyzing the period of the output sequence of the Galois FCSR cascade structure under the condition of different connection numbers,the parameter setting of the maximum period of the output sequence of the sequence cipher based on this cascade structure is given;It is subsequently proved that the sequence cipher algorithm obtained after self-shrinking or linear filtering of the output sequence based on this cascade structure can effectively avoid the initialization loopholes in the original cascade structure and effectively resist Real-time attack on the FCSR of the Galois structure;the final random number detection shows that the output sequence of the self-shrinking or filtering sequence cipher algorithm based on this new cascade structure can effectively pass all the pseudo-random tests of NIST and the National Secret.On the other hand: Due to the linear structure of the LFSR in the Grain family algorithm,it is vulnerable to algebraic attacks and related attacks.We use FCSR instead of LFSR and cascade the nonlinear feedback shift register(NFSR),and build based on this Grain-like structure sequence cipher algorithm of cascade structure.Specifically,Firstly,the pseudorandom nature of FCSR is analyzed and solved by referring to the Boolean network and semi-tensor product method for nonlinear feedback shift register(NFSR),and the Boolean network of FCSR,the state update matrix of FCSR,and all of FCSR are obtained.The possible state circles and the length of the corresponding periodic sequence are analyzed.The properties of FCSR and the output sequence of FCSR with periodic input are analyzed;then a Grain-like structure sequence cipher algorithm based on this cascade structure is constructed and analyzed The related properties of the output sequence of this new type of Grain-like structure sequence cipher algorithm.Analysis shows that the new type of Grainlike structure sequence cipher algorithm can effectively resist various attacks against Grainlike algorithms and real-time attacks against FCSR;finally,random number detection It shows that the output sequence of this new type of Grain-like structure sequence cipher algorithm can effectively pass all the pseudo-randomness tests of NIST and National Secrets.The two FCSR-based cascading structures designed in this paper are supplementary to the original algorithm.The structure is simple,easy to understand,and the security is improved.Applying the semi-tensor product to the FCSR provides a new idea for analyzing the state space of the FCSR and the period of the output sequence.