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Simple method to find trace of arbitrary element of a finite field

Simple method to find trace of arbitrary element of a finite field

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A novel technique is described for computing the trace over GF(2) of an element from a given finite field GF(2m). This technique requires a primitive polynomial of degree m and a division circuit only, i.e. the usual knowledge of a table of powers of a primitive element of GF(2m) is not required. The computation of the minimal polynomial of an element of GF(2m) is derived as a function of the trace and of a sub-trace function.

Inspec keywords: polynomials; Galois fields; signal processing

Other keywords: trace function; arbitrary element; Galois fields; division circuit; subtrace function; finite field; primitive polynomial; GF(2m)

Subjects: Information theory; Information theory; Algebra; Signal processing and detection; Algebra

References

    1. 1)
      • R.J. McEliece . (1987) Finite fields for computer scientists and engineers.
    2. 2)
      • B. Schneier . (1996) Applied cryptography.
    3. 3)
      • F.J. MacWilliams , N.J.A. Sloane . (1977) The theory of error-correcting codes.
    4. 4)
      • G.J. Simmons . (1992) Contemporary cryptology.
    5. 5)
      • J.A. Gordon . Very simple method to find the minimum polynomial of an arbitrary nonzero element of a finite field. Electron. Lett. , 25 , 663 - 664
    6. 6)
      • S. Wicker . (1995) Error control systems for digital communication and storage.
    7. 7)
      • R. Lidl , H. Niederreiter . (1994) Introduction to finite fields and their applications.
    8. 8)
      • S. Lin , D.J. Costello . (1983) Error control coding: fundamentals and applications.
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