In this thesis, we study the security of advanced cryptographic primitives against adversaries that behave closer to real-life scenarios. Namely, they can adaptively update their strategy during the attack, based on previously obtained information, possible from external sources like corrupted users.
We construct Distributed Pseudorandom Functions that still output random-looking values, even when the adversary can adaptively corrupt some servers. Such a system assumes that the secret key is shared among multiple servers that have to combine their partial evaluations in order to obtain a pseudorandom value.
We also prove security against adaptive corruptions, in the stronger simulation-based security model, for Inner Product Functional Encryption. Such a public-key scheme encrypts vectors x and can issue multiple secret keys associated to key vectors y. The decryptor learns the partial information <x,y> but nothing else. This primitive can compute statistics (e.g., weighted sums or means) on a database, while keeping each individual input private. We also construct a labeled variant, wherein each database entry is encrypted by a different client, called Multi-Client Functional Encryption.
We finally provide a new construction of Non-Interactive Zero-Knowledge proof, which convinces a verifier of the validity of some NP statement without leaking anything else. In addition, an adversary obtaining many simulated proofs for possibly false statements cannot produce a valid proof of its own for a false statement. This primitive is used as a building-block for public-key encryption schemes with advanced security properties.
Gratuit
Disciplines