Abstract
Small degree extensions of finite fields are commonly used for cryptographic purposes. For extension fields of degree 2 and 3, the Karatsuba and Toom Cook formulæ perform a multiplication in the extension field using 3 and 5 multiplications in the base field, respectively. For degree 5 extensions, Montgomery has given a method to multiply two elements in the extension field with 13 base field multiplications. We propose a faster algorithm, which requires only 9 base field multiplications. Our method, based on Newton’s interpolation, uses a larger number of additions than Montgomery’s one but our implementation of the two methods shows that for cryptographic sizes, our algorithm is much faster.
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El Mrabet, N., Guillevic, A., Ionica, S. (2011). Efficient Multiplication in Finite Field Extensions of Degree 5. In: Nitaj, A., Pointcheval, D. (eds) Progress in Cryptology – AFRICACRYPT 2011. AFRICACRYPT 2011. Lecture Notes in Computer Science, vol 6737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21969-6_12
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DOI: https://doi.org/10.1007/978-3-642-21969-6_12
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