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Advanced Course on Contemporary Cryptology, chapter Provable Security for PublicKey Schemes
 Advanced Courses CRM Barcelona. Birkhuser Publishers, Basel, juin 2005. ISBN: 376437294X (248
, 2005
"... Abstract. Since the appearance of publickey cryptography in the DiffieHellman seminal paper, many schemes have been proposed, but many have been broken. Indeed, for a long time, the simple fact that a cryptographic algorithm had withstood cryptanalytic attacks for several years was considered as a ..."
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Abstract. Since the appearance of publickey cryptography in the DiffieHellman seminal paper, many schemes have been proposed, but many have been broken. Indeed, for a long time, the simple fact that a cryptographic algorithm had withstood cryptanalytic attacks for several years was 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, this initially was a purely theoretical work: very few practical schemes could be proven in this socalled “standard model ” because such a security level rarely meets with efficiency. Ten years ago, Bellare and Rogaway proposed a tradeoff to achieve some kind of validation of efficient schemes, by identifying some concrete cryptographic objects with ideal random ones. The most famous identification appeared in the socalled “randomoracle model”. More recently, another direction has been taken to prove the security of efficient schemes in the standard model (without any ideal assumption) by using stronger computational assumptions. In these lectures, we focus on practical asymmetric protocols together with their “reductionist ” security proofs, mainly in the randomoracle model. We cover the two main goals that publickey cryptography is devoted to solve: authentication with digital signatures, and confidentiality with publickey encryption schemes. 1