Method and system for generating linear recursive sequence

Abstract

The invention relates to a method and a system for generating a linear recursive sequence. The method comprises the following steps of: selecting a parameters e and n, wherein both e and n are positive integers more than or equal to 2; the parameter e is used for determining a value range of elements in a register; and n is the total length of the register; determining the number k of feedback positions in the register, wherein k is more than or equal to 2 and less than or equal to n; determining the a feedback position set {i1, i2,..., ik-1, ik} according to the number k of the feedback positions, wherein ik is equal to n-1, i1 is more than or equal to 0 and less than i2, while i2 is more than i1 and less than the number behind i2, and the rest can be done in the same manner till ik-1 is less than or equal to n-2; selecting a state transfer matrix of the register; selecting a nonsingular original state vector of the register; and performing recursive computation on the original state vector according to the state transfer matrix to obtain the state vector sequence S of the register, wherein S=(S0, S1,...)=(St)t which is more than or equal to 0=((s0, t, s1, t,..., sn-1, t))t which is more than or equal to 0.

Description

technical field [0001] The invention relates to the technical field of information security, in particular to a ring Z / (2 e -1) A method and system for generating linear recursive sequences with complex characteristic polynomials. Background technique [0002] Sequence cipher is one of the important branches of cryptography, which plays an extremely important role in the field of military, diplomatic, government and commercial communication security. The core of serial cipher design is how to quickly generate a secure key stream. [0003] Before 2000, the main idea of ​​sequence cipher design was to combine linear sequence source with nonlinear transformation, such as nonlinear combination, nonlinear filtering and clock control. After 2000, the European NESSIE program and eSTREAM program have played an active role in promoting the development of sequence ciphers. In particular, driven by the eSTREAM project, a major breakthrough has been made in the overall design of sequ...

AI Technical Summary

Problems solved by technology

[0039] From the analysis of the above two points, we can see that the ring Z / (2 e -1) The linear recursive sequence generation method based on the single-point feedback mode will inevitably lead to a strong contradiction between the complexity of the output sequence and the output efficiency of the sequence, and it is impossible to take into account both the complexity of the sequence and the output efficiency of the sequence

When the minimum ternary weight of the sequence characteristic polynomial is slightly larger, the efficiency of this generation method will be very low, resulting in the output speed of the sequence is far from meeting the requirements of the sequence cipher design

Images