| In The Second Theory of Cryptography Conference (TCC 2005), Boneh, Goh, and Nissim proposed a new structure of bilinear groups that have a composite order and a new cryptosystem which is intractable on a decisional problem over the subgroup in such structure [BGN05]. Their proposal, which referred to as the BGN cryptosystem by researchers, receive much attention and is quickly followed by two publications in CRYPTO'05 [BI05, OI05].; The BGN cryptosystem is a dual homomorphic public-key cryptosystem that enables the evaluation of 2-DNF (disjunctive normal form) formulas on ciphertexts. In their work, Boneh et. al. also presented three applications, namely private information retrieval with reduced computational complexity, an e-voting system without non-interactive zero knowledge proofs, and a protocol for universally verifiable computation. Few number of works also produced from the BGN public-key system, include non-interactive zero-knowledge proof (NIZK), obfuscated ciphertext mixing, and signature.; In this thesis, the author performs in-depth study of the BGN public-key cryptosystem and existing literatures on its applications. The author observes two properties of BGN, namely the indistinguishability of the BGN ciphertexts of sum and product of two messages, and the verifiability of elements from composite prime subgroups in BGN settings. The author further proposes three new applications of BGN, namely the protocols for authentication, oblivious transfer, and proof-of-visit respectively. |
