Efficient computation of full Lucas sequences

Abstract
Recently, Yen and Laih (1995) proposed an algorithm to compute LUC digital signatures quickly. This signature is based on a special type of Lucas sequence Vk. The authors generalise their method to any type of Lucas sequence, and extend it to the ‘sister’ Lucas sequence, Uk. As an application, the order of an elliptic curve over GF(2m) is computed quickly.

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