In this article we establish new inequalities, both conditional and unconditional, for the restriction problem associated to hyperbolic, or one-sheeted, hyperboloid in three dimensions, endowed with a Lorentz-invariant measure. These inequalities are unconditional (and optimal) bilinear range q>103. Nous obtenons des nouvelles inégalités pour le problème de la transformée Fourier associé à l'hy...