This thesis is concerned with the design and analysis of practical provably-secure encryption schemes.We give several results that include new schemes with attractive tradeoffs between efficiency and security and new techniques for analyzing existing schemes.Our results are divided into three chapters, which we summarize below.The Twin Diffie-Hellman Problem. We describe techniques for analyzing encryption schemes based on the hardness of Diffie-Hellman-type problems. We apply our techniques to several specific cases of encryption, including identity-based encryption, to design a collection of encryption schemes that offer improved tradeoffs between efficiency and evidence for security over similar schemes. In addition to offering quantitative advantages over prior work in this area, our technique also simplifies security proofs for these types of encryption schemes.Our main tool in this chapter is the notion of Twin Diffie-Hellman Problems, which provide an intermediate step for organizing security reductions and reveal very simple variants of known schemes with correspondingly simple, but non-obvious, analyses.Non-Malleable Hash Functions. We consider security proofs for encryption that are carried out in the random oracle model, where one declares that a scheme's hash functions are ``off limits' for an attacker in order to make a proof go through.Such proofs leave some doubt as to the security of the scheme in practice, when attackers are free to exploit weaknesses in the hash functions.A particular concern is that a scheme may be insecure in practice no matter what very strong security properties its real hash functions satisfy.We address this doubt for an encryption scheme of Bellare and Rogaway by showing that, using appropriately strong hash functions, this scheme's hash functions can be partially instantiated in a secure way.
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