We study, to all orders in perturbative QCD, the universal behavior of the saturation momentum Qs(L) controlling the transverse momentum distribution of a fast parton propagating through a dense QCD medium with large size L. Due to the double logarithmic nature of the quantum evolution of the saturation momentum, its large L asymptotics is obtained by slightly departing from the double logarithmic limit of either next-to-leading log (NLL) BFKL or leading order DGLAP evolution equations. At fixed coupling, or in conformal N = 4 SYM theory, we derive the large L expansion of Qs(L) up to order α 3/2 s . In QCD with massless quarks, where conformal symmetry is broken by the running of the strong coupling constant, the one-loop QCD β-function fully accounts for the universal terms in the Qs(L) expansion. Therefore, the universal coefficients of this series are known exactly to all orders in αs.