This article provides an up-to-date overview of public-key cryptosystems. First, we explain the context at the economic level, and the implications for international relations issues. Then, we describe how secret-key cryptology works with some examples (DES, Triple DES, AES). We explain the limitations of this approach and introduce the concept of public-key cryptology through further examples. Their strengths depend on mathematical problems, which we summarize. The concept of PKI (Public-Key Infrastructure) is then introduced, which shows how to combine efficiently both secret-key and public-key cryptology. One of the main issues of public-key cryptology is the possibility to construct digital signatures. All these techniques may be combined with digital watermarking and information hiding, in order, for instance, to trace data and protect owner's copyrights. All these research areas (cryptology, digital watermarking, steganography) are very active. As an example, we shortly describe a new public-key cryptosystem based on Drinfeld modules, which is patent pending.
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