Design And Analysis Of Post-quantum Secure Functional Encryption

With the coming of quantum communication and quantum computer,designing suitable cryptosystems for a post-quantum world have become a hot topic at present.Lattice-based cryptography has been attracted attentions since it has many excellent features such as apparent resistance to quantum attacks,relatively efficient implementations.Functional encryption is another hot topic recently.This novel paradigm not only provides both finegrained access and computing on encrypted data,but breaks all-or-nothing access model.However,most of works in this area are based on the restricted functions,such as Boolean formulas,inner product functions.Additionally,the well-known schemes for general circuits(arbitrary efficiently-computable functions)relied on multilinear maps or indistinguishability obfuscation.Unfortunately,all known candidate multilinear maps as well as indistinguishability obfuscation have been broken recently.This thesis aims at the following topics.The first goal is an attempt to build practical functional encryption without these “strong tools”.This thesis attains the aim by using the lattice techniques.Our contributions can be summarized as follows:Propose a special functional encryption system with public index: ABE,with shorter secret keys and ciphertexts.Construct a stateless functional encryption for inner products with constant-size secret-keys.Present a SIM secure functional encryption scheme for regular circuits,which is bootstrapped from linear FE based on randomized encodings tool.The next goal is to discuss some functionalities in functional encryption,such as revocable,homomorphic,leakage resilient,function private.They are significant for a scheme in a real world.Our contributions can be summarized as follows:Construct revocable hierarchical identity-based encryption scheme.This system not only relieves some pressure of the key generation center,but improves the flexible access control.Provide a succinct attribute-based homomorphic encryption from lattices.Regev's LWE cryptosystem itself is somewhat homomorphic except for homomorphic multiplication.Based on key switching techniques,the noise will be substantially small.Discuss how to construct leakage-resilient cryptosystem from lattices.Specially,we give a construction of attribute based hash proof system.Analysis the definition and implementation of function private.The most previous constructions only guarantee data privacy and ignore the function privacy.