BENYOUNES, MalikaSupervisor: Ghadbane, Nacer2023-07-022023-07-022023-06-10http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/39824This memory of master degree Algebra and discrete mathematics lies within the theory of relation on free monoid and its applications in public key cryptography. In this work, we studied the following points :  Elementary notions on free monoid .  The languages of free monoid .  Presentation of monoid by generators and relations.  The public key cryptosystems based on Thue Monoid Morphism Interpretation (TMMI).enFree monoid, words and languages, the closure of a binary relationThesis