Abstract
Currently, nonlinear Boolean functions are actively investigated worldwide. However, many questions remain unanswered. The theory of nonlinear Boolean functions that are suitable for use in cryptographically strong algorithms is significantly incomplete. Despite the existence of numerous publications on these themes, many issues related to the interconnection of design characteristics affecting the generator’s performance and its cryptographic characteristics still remain unsolved. The possibility of generating a special type of sequence, called de Bruijn sequence, at minimal hardware and software costs to implement nonlinear Boolean functions in stream encryption systems, is the main subject of this work. The paper presents the possible structure boundaries (algebraic degree of a Boolean function, the number of monomials in a function) of iterative de Bruijn sequence bitrate generators for various generated sequence characteristics, such as linear complexity and autocorrelation function. The profile of the linear complexity of the studied sequences is close to the expected value of the linear complexity, as well as for a truly random sequence.
Highlights
The analysis of the following modern stream cypher schemes: SNOW 2.0 [1], Decim [2], KCipher-2 [3], Sosemanuk [4], Grain [5], MICKEY 2.0 [6] and Trivium [7] shows that the main components are the iterative bitrate generators, as well as the function of complication that forms an output unit from several combinations of inner state bits.Iterative bitrate stream generators are usually formed based on Linear Feedback Shift Register (LFSR)
The registers that form the de Bruijn sequence meet these requirements. Such sequence can be generated by Nonlinear Feedback Shift Register (NLFSR)
As it can be seen from the obtained results, the M-NLFSRs overwhelming majority have the maximum linear complexity or it differs from the maximum by several units
Summary
The analysis of the following modern stream cypher schemes: SNOW 2.0 [1], Decim [2], KCipher-2 [3], Sosemanuk [4], Grain [5], MICKEY 2.0 [6] and Trivium [7] shows that the main components are the iterative bitrate generators, as well as the function of complication that forms an output unit from several combinations of inner state bits. Iterative bitrate stream generators are usually formed based on Linear Feedback Shift Register (LFSR) Their main function is to guarantee the uniqueness of the generator’s inner state for a rather long period of time while it is working and make sure that good local statistical properties are provided. If it is possible to form the LFSR forming the de Bruijn sequence of the required size, its structure will be so complex that its implementation in encryption systems, as an iterative generator, will be unacceptably resource-consuming. The work presents the obtained results that reflect the interrelation of the constructive characteristics of the LFSR (such as the maximum algebraic degree, the number of monomials) and some necessary cryptographic properties of the sequence it forms (autocorrelation and linear complexity)
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