Abstract
In this paper, the complexity of a squaring operation using polynomial basis (PB) in a class of finite fields F2m is evaluated. The main results are as follows: 1. When the field is generated with an irreducible trinomial f(x) = xm + xk + 1, 1 ≤ k ≤ m/2 where both m and k are odd, a PB squaring operation requires m - 1/2 bit operations. 2. When the field is generated with an irreducible trinomial f(x0) = xm + xk + 1, 1 ≤ k ≤ m/2 where m + k is odd and k ≠ m/2 , a PB squaring operation requires m + k - 1/2 bit operations. 3. When the field is generated with an irreducible trinomial f(x) = xm+xm/2+1, a PB squaring operation requires m + 2/4 bit operations.
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© 2001 Springer-Verlag Berlin Heidelberg
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Wu, H. (2001). On Complexity of Polynomial Basis Squaring in F2m . In: Stinson, D.R., Tavares, S. (eds) Selected Areas in Cryptography. SAC 2000. Lecture Notes in Computer Science, vol 2012. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44983-3_9
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DOI: https://doi.org/10.1007/3-540-44983-3_9
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