Abstract
This chapter consists of three sections on arithmetic operations in the field GF(2m) with normal-basis representations and the implementation of those operations. The first section—a short one—is on addition and squaring; both are very simple operations with a normal basis. The second section is on multiplication, a more complicated operation than the preceding two. And the last section is on exponentiation, inversion, and division.
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Notes
- 1.
Note that this is another reason why the representation of the multiplicative identity element must be (11⋯1), given that (00⋯0) is already taken for the additive identity element.
- 2.
If m ≤ 2000, then it is not hard to find a suitable polynomial [2].
- 3.
The Hamming weight.
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R. Omondi, A. (2020). Normal-Basis Arithmetic. In: Cryptography Arithmetic. Advances in Information Security, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-030-34142-8_11
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DOI: https://doi.org/10.1007/978-3-030-34142-8_11
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