Advances in Cryptology CRYPTO 2015 : 35th Annual Cryptology Conference Santa Barbara CA USA August 16 20 2015 Proceedings Part I Lattice based cryptography Cryptanalytic insights Modes and constructions Multilinear maps and IO Pseudorandomness Block cipher cryptanalysis Integrity Assumptions Hash functions and stream cipher cryptanalysis Implementations Multiparty computation Zero knowledge Theory Signatures Non signaling and information theoretic crypto Attribute based encryption New primitives Fully homomorphic functional encryption. The two volume set LNCS 9215 and LNCS 9216 constitutes the refereed proceedings of the 35th Annual International Cryptology Conference CRYPTO 2015 held in Santa Barbara CA USA in August 2015. The 74 revised full papers presented were carefully reviewed and selected from 266 submissions. The papers are organized in the following topical sections: lattice based cryptography; cryptanalytic insights; modes and constructions; multilinear maps and IO; pseudorandomness; block cipher cryptanalysis; integrity; assumptions; hash functions and stream cipher cryptanalysis; implementations; multiparty computation; zero knowledge; theory; signatures; non signaling and information theoretic crypto; attribute based encryption; new primitives; and fully homomorphic functional encryption.