Chosen-Ciphertext Secure Encryption From Hard Algebraic Set Systems

The authors put forward the new abstract framework of "Hard algebraic set systems" that allows to construct efficient chosen-ciphertext secure encryption schemes under computational (rather than decisional) intractability assumptions. The framework can be instantiated with both RSA and Di e-Hellman type assumptions, but in itself is completely abstract. One of the main fields of interest in cryptography is the design and the analysis of the security of encryption schemes in the Public-Key setting (PKE schemes). The notion of security against Chosen-Ciphertext Attack (IND-CCA security) is due to Rackoff and Simon and is now widely accepted as the standard security notion for public-key encryption schemes.