This thesis focuses on i ndex c alculus a lgorithm of e lliptic c urves that was proposed by Gaudry . In the second step, b y applying Weil restriction technique on summation polynomials as defined by Samaev, one can obtain a system of polynomial equations. The system corresponds to a hidden constant in the complexity of Gaudry\\' s algorithm. It is then shown that this system is invariant for J acobi intersection curve and E dwars curves under d ihedral Coxter group