Search for: [Description = "Since the appearance of public\-key cryptography in Diffie\-Hellman seminal paper, many schemes have been proposed, but many have been broken. Indeed, for many people, the simple fact that a cryptographic algorithm withstands cryptanalytic attacks for several years is considered as a kind of validation. But some schemes took a long time before being widely studied, and maybe thereafter being broken. A much more convincing line of research has tried to provide “provable” security for cryptographic protocols, in a complexity theory sense\: if one can break the cryptographic protocol, one can efficiently solve the underlying problem. Unfortunately, very few practical schemes can be proven in this so\-called “standard model” because such a security level rarely meets with efficiency. A convenient but recent way to achieve some kind of validation of efficient schemes has been to identify some concrete cryptographic objects with ideal random ones\: hash functions are considered as behaving like random functions, in the so\-called “random oracle model”, block ciphers are assumed to provide perfectly independent and random permutations for each key in the “ideal cipher model”, and groups are used as black\-box groups in the “generic model”.In this paper, we focus on practical asymmetric protocols together with their “reductionist” security proofs. We cover the two main goals that public\-key cryptography is devoted to solve\: authentication with digital signatures, and confidentiality with public\-key encryption schemes."]

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