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Research on Counting of Primitive σ-LFSR

Guang Zeng

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Abstract

σ-LFSR is a kind of word-oriented Linear Feedback Shift Register(LFSR) with high efficiency and good cryptographic properties, especially its software implementation is efficient for modern processors.Through the coordinate sequences and base discriminance of primitive σ-LFSR, this paper converts the study of counting to the basis of liner space, and through the pairs of relatively prime polynomials on F2 with degree smaller than n, the counting formula of primitive σ-LFSR on F4 is obtained.

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What this paper is about

σ-LFSR is a kind of word-oriented Linear Feedback Shift Register(LFSR) with high efficiency and good cryptographic properties, especially its software implementation is efficient for modern processors.Through the coordinate sequences and base discriminance of primitive σ-LFSR, this paper converts the study of counting to the basis of liner space, and through the pairs of relatively prime polynomials on F2 with degree smaller than n, the counting formula of primitive σ-LFSR on F4 is obtained.

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Available abstract

σ-LFSR is a kind of word-oriented Linear Feedback Shift Register(LFSR) with high efficiency and good cryptographic properties, especially its software implementation is efficient for modern processors.Through the coordinate sequences and base discriminance of primitive σ-LFSR, this paper converts the study of counting to the basis of liner space, and through the pairs of relatively prime polynomials on F2 with degree smaller than n, the counting formula of primitive σ-LFSR on F4 is obtained.

Key concepts: Linear feedback shift register, Computer science, Shift register, Cryptography, Prime (order theory), Degree (music), Arithmetic, Basis (linear algebra)

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