Oblivious Transfer Protocol

Cryptography plays an important role in modern life in politics, economy, military and daily life. Oblivious transfer (OT) is used as a key component in many applications of cryptography.In Chapter 1, we first provide some preliminary of cryptography and quantum mechanics. Secondly, we analysis the researches on oblivious transfer, discuss the possibility for further research.In Chapter 2, we first present the definitions of various oblivious transfer, including (statistical secure) 1-out-of-2 bit (string) oblivious transfer, (statistical secure) 1-out-of-n bit (string) oblivious transfer, (statistical secure) m-out-of-n bit (string) oblivious transfer, analysis the relations among the OT's and have the following main results:· 1-out-of-2 bit oblivious transfer can be used to construct 1-out-of-2 string oblivious transfer, and vice versa;· 1-out-of-2 bit oblivious transfer can be used to construct 1-out-of-n bit oblivious transfer, and vice versa;· 1-out-of-2 bit oblivious transfer can be used to construct m-out-of-n bit oblivious transfer, and vice versa.In Chapter 3, we construct a m-out-of-n oblivious transfer directly based on public key system with better efficiency.Quantum cryptography is one of the new research directions of cryptography. Quantum key distribution is proved to be feasible both in theory and in application. In 1994, Crepeau presented a quantum oblivious transfer scheme based on the security of quantum bit commitment. However, quantum bit commitment was proved to be impossible by Lo and also by Mayers. So, the quantum oblivious transfer based on quantum bit commitment is un-secure.In Chapter 4, we construct a quantum 1-out-of-2 weak oblivious transfer only based on quantum mechanics. The scheme satisfied the correctness, weak privacy for Alice and weak privacy for Bob.In 2000, Aharonov, etc presented a quantum weak bit commitment. In Chapter 5, we extend the work of Crepeau. constructs a quantum m-out-of-n oblivious transfer scheme. The protocol satisfies the following 3 conditions: correctness, privacy for Alice and privacy for Bob.In Chapter 6, we show a new scheme, quantum random string oblivious transfer (QRSOT). In QRSOT, Alice has n bits b₁, b₂, … ,b_n, after the interaction with Bob, Bob knows that he gets around p · n bits (p ∈ (0,1)) from the n bits, Alice cannot know which particular bits Bob gets. This scheme is a generalization of oblivious transfer. The difference between QRSOT and l-out-of-2 oblivious transfer is that, in QRSOT, Bob cannot choose a particular bit determinately, he can only know that he get a particular bit negatively. Furthermore, Bob can get around p · n bits with a little bias. The probability that he gets more than (p + δ) · n bits or less than (p - δ) · n bits (δ∈(0,1)) is less than εⁿ (ε_δ < 1).Finally, in Chapter 7, we have a conclusion and provide some works for further research.