Done on 20121105: Plan for lectures to come. Some publicity about DL record for GF(2^619) Congruences of squares; Dixon; CFRAC; Ideas behind QS, but not going into sieving yet. Adleman's algorithm for discrete logs. Subtletlies on the linear system being solved. Elements for analysis. Canfield-Erdos-Pomerance as an L function. Exercices for the last 15mn. Asymptotic row weight in algorithms based on smoothness tests. Minimum safe key length as a function of time in presence of a subexponential attacker algorithm.