Algorithms for exponentiation in finite fields
Journal of Symbolic Computation
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Modern Computer Algebra
A computational introduction to number theory and algebra
A computational introduction to number theory and algebra
Efficient Computation of Roots in Finite Fields
Designs, Codes and Cryptography
On taking roots in finite fields
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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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 Fqm for certain choices of m and q. If r || q-1 and (m, r) = 1, they proved that the complexity of their method is Õ(r(log m+ log log q)m log q). In this paper, we extend the Barreto-Voloch algorithm to the general case that r ∥ qm - 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.