In this thesis we apply techniques from computer algebra and languagetheory to speed up the elementary operations in some specific towers of finitefields. We apply our construction to the problem of computing isogeniesbetween elliptic curves and obtain faster (both asymptotically and in practice)variants of Couveignes’ algorithm.The document is divided in four parts. In Part...

Furthermore, by using [2, p. 230, (1)] a computable representation for the G-function in (1) (and hence also for F,112(s)) may be given in terms of essentially a linear combination of four hypergeometric functions OF3[b2s2 /16] provided that no two of the parameters {1, 1 1+v-P1v-P) differ by an integer. This result for Fv-112(s) is given (correctly) in [3, p. 353, (9)] so that the proposed int...

although old texts are distorted or changed due to various reasons such as unfamiliarity of writers who take them away from their origin and make it difficult to achieve a correct edition by using of the manuscripts, especially when there is a unique manuscript of the text or the existing manuscript is different with the other available versions, the correction of each text should be usually do...