Abstract
This article is concerned with various arithmetic operations inGF(2m). In particular we discuss techniques for computing multiplicative inverses and doing exponentiation. The method used for exponentiation is highly suited to parallel computation. All methods achieve much of their efficiency from exploiting a normal basis representation in the field.
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References
G. Agnew, R. Mullin, and S. Vanstone, An implementation for a fast public key cryptosystem,J. Cryptology,3(2), 63–79.
W. Diffie and M. Hellman, New directions in cryptography,IEEE Trans. Inform. Theory,22(6) (1976), 644–654.
T. Itoh, O. Teechai, and S. Tsujii, A fast algorithm for computing multiplicative inverses inGF(2t) using normal bases,J. Soc. Electron. Comm. (Japan),44 (1986), 31–36.
H. W. Lenstra, Jr., and R. J. Schoof, Primitive normal bases for finite fields,Math. Comp.,48 (1987), 217–232.
O. Ore, On a special class of polynomials,Trans. Amer. Math. Soc.,35 (1933), 559–584.
T. Rosati, A high speed data encryption processor for public key cryptography,Proceeding of the IEEE Custom Integrated Circuits Conference, San Diego, May 1989, pp. 12.3.1–12.3.5.
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Communicated by Ernest F. Brickell
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Agnew, G.B., Beth, T., Mullin, R.C. et al. Arithmetic operations inGF(2m). J. Cryptology 6, 3–13 (1993). https://doi.org/10.1007/BF02620228
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DOI: https://doi.org/10.1007/BF02620228