Abstract
Root extraction is a classical problem in computers algebra. It plays an essential role in cryptosystems based on elliptic curves. In 2006, Barreto and Voloch proposed an algorithm to compute rth roots in \(\mathbb{F}_{q^m} \) for certain choices of m and q. If r || q − 1 and (m, r) = 1, they proved that the complexity of their method is \(\widetilde{\mathcal{O}}(r(\log m+\log\log q)m\log q) \). In this paper, we extend the Barreto-Voloch algorithm to the general case that r || q m − 1, without the restrictions r || q − 1 and (m, r) = 1 . We also specify the conditions that the Barreto-Voloch algorithm can be preferably applied.
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Cao, Z., Fan, X. (2011). Extension of Barreto-Voloch Root Extraction Method. In: Qing, S., Susilo, W., Wang, G., Liu, D. (eds) Information and Communications Security. ICICS 2011. Lecture Notes in Computer Science, vol 7043. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25243-3_15
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DOI: https://doi.org/10.1007/978-3-642-25243-3_15
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