This volume contains articles representing the courses given at the 2005 RSME Santalo Summer School on 'Recent Trends in Cryptography'. The main goal of the Summer School was to present some of the recent mathematical methods used in cryptography and cryptanalysis. The School was oriented to graduate and doctoral students, as well as recent doctorates. The material is presented in an expository manner with many examples and references. The topics in this volume cover some of the most interesting new developments in public key and symmetric key cryptography, such as pairing based cryptography and lattice based cryptanalysis.