Multiples of Primitive Polynomials and Their Products over GF(2)

  • Subhamoy Maitra
  • Kishan Chand Gupta
  • Ayineedi Venkateswarlu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2595)


A standard model of nonlinear combiner generator for stream cipher system combines the outputs of several independent Linear Feedback Shift Register (LFSR) sequences using a nonlinear Boolean function to produce the key stream. Given such a model, cryptanalytic attacks have been proposed by finding the sparse multiples of the connection polynomials corresponding to the LFSRs. In this direction recently a few works are published on t-nomial multiples of primitive polynomials. We here provide further results on degree distribution of the t-nomial multiples. However, getting the sparse multiples of just a single primitive polynomial does not suffice. The exact cryptanalysis of the nonlinear combiner model depends on finding sparse multiples of the products of primitive polynomials. We here make a detailed analysis on t-nomial multiples of products of primitive polynomials. We present new enumeration results for these multiples and provide some estimation on their degree distribution.


Primitive Polynomials Galois Field Polynomial Multiples Cryptanalysis Stream Cipher 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Subhamoy Maitra
    • 1
  • Kishan Chand Gupta
    • 1
  • Ayineedi Venkateswarlu
    • 1
  1. 1.Applied Statistics UnitIndian Statistical InstituteCalcuttaIndia

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