Hardware Optimization And Variable Structure Design Of FCSR

Stream ciphers are widely used in various fields of cryptography.Feedback shift register(FSR)is a basic component widely used in stream ciphers.Among them,linear feedback shift register(LFSR)has the advantages of fast running speed,large period and good statistical characteristics.However,the linear characteristics of its structure make it possible to face the threat of algebraic attacks.The Shift Register with Carry Feedback(FCSR)not only has the excellent statistical characteristics of LFSR,but also provides output sequences with high linear complexity and higher security.Therefore,it has been applied in many stream cipher structures.Such as F-FCSR-H v3,F-FCSR-16 v3,etc.In this paper,by studying the characteristics of the transfer matrix of FCSR,the corresponding relationship between the changes in the FCSR internal feedback and the transfer matrix of FCSR is discussed,and the shift theorem of FCSR is proposed.In addition,a Ternary FCSR with low diffusion delay is constructed,and the resulting FCSR is constructed.According to the shift theorem,the shift transformation is carried out.The completed work is as follows:On the one hand: the existing construction method of FCSR is mainly to search for the number of connections that meet the conditions first,and then construct the transition matrix through the algorithm.In this process,searching for the number of qualified connections has a high algorithm complexity,and only a fixed structure FCSR can be obtained by constructing the algorithm.This paper proves FCSR's shift transformation theorem(EL theorem and ER theorem),and expounds the correspondence between the connection number and the variable structure of FCSR.In addition,the optimization effect of this structural change on common circuit indicators in the hardware implementation part is analyzed.In the process of structural transformation,the critical path can be reduced,the internal fan-out can be reduced,the modularity of the system can be improved,and the layout and wiring of the circuit can be optimized.Based on this theorem,it is proposed to construct a variable structure Ring FCSR with a given number of connections.It is analyzed that this method can reduce the workload of searching for the number of connections,thereby simplifying the process of constructing FCSR.Applying this shift theorem to FCSR-based F-FCSR-H v3 and F-FCSR-16 v3,the variable number of structures is obtained.On the other hand: Ternary FCSR is an FCSR structure with more feedback types.The construction method of Ternary FCSR is based on four construction criteria.The construction process can be roughly described as: first express the number of connections that meet the requirements in its non-connected form;then place feedback in other locations according to the matrix determinant operation relationship and related theorems until the total number is half of the order of the matrix.The analysis found that the construction process did not consider the diffusion delay,so a Ternary FCSR construction algorithm with low diffusion delay was proposed.In the construction process,the pre-construction process of the Ring FCSR construction algorithm with low diffusion delay was first extracted and combined with construction algorithm of Ternary FCSR to construct a Ternary FCSR with lower diffusion delay and good other hardware characteristics.Applying the Ternary FCSR constructed by the construction algorithm to the F-FCSR-H v3 and F-FCSR-16 v3 structures,it can be found that the structure obtained by the new construction algorithm still has good critical path length and fan-out,although compared with the original algorithm,the cost is slightly increased,but the diffusion delay has been greatly optimized.The optimization of diffusion delay speeds up the initialization process of the key and improves the system's resistance to attacks in the initialization phase.Finally,the shift transform theorem of FCSR is applied to the constructed structure,and the variable structure quantity of the structure is given.