Today, cryptographers have defined security objectives and notions that meet the security needs of users, such as confidentiality, integrity and authentication. Cryptography has become a scientific discipline in its own right, using mathematical and computational concepts to prove the security of schemes. However, new attacks periodically undermine user confidence. Recently, two attacks on the secure communications standard used on the Internet, Secure Socket Layer (SSL), were widely publicized in the press and on the Internet. These attacks do not call into question the systems' security credentials, but they do show that the adversaries' modeling is not ideal. Indeed, to treat a problem theoretically, scientists need to model reality. In cryptography, it is necessary to represent the adversary's goals and means, i.e. what it seeks to do and how it interacts with the system. This is where cryptography shows its limitations in the face of reality: it is difficult to study all possible adversaries exhaustively.
After recalling the design principles of cryptographic schemes for encryption and electronic signature, we will describe some of the limitations of current systems, demonstrating the difficulty of designing secure systems. This difficulty is today linked to the implementation of cryptographic schemes in computer systems such as smart cards, accelerator cards, etc. Finally, we'll give some examples of secure communications standards.