Abstract:
Quantum computation and quantum information have been one of the most
extensive fields of research for the past three decades. Many groundbreaking quantum algorithms have been designed, which can perform the assigned
tasks much faster than their classical counterparts. Shor's algorithm, one
of the most well-known quantum algorithms, can be used to prime factorize
large integers in polynomial time, while even the best classical integer factorization algorithms are exponential in time. As the security of most classical
cryptosystems rely on the di culty to prime-factorize large numbers, the
Shor's algorithm, if implemented on a scalable quantum computer, can compromise almost all of the classical cryptosystems that are widely used today.
Hence, the requirement of quantum cryptography is greatly essential. In this
thesis, I attempt to look into the possibility of exploiting quantum walks
for the purposes of quantum cryptography. Quantum walks are the quantum analogues of the classical random walks. Unlike classical random walks,
Quantum walks have unique properties such as superposition and entanglement of the position and the coin spaces, which can be exploited to design
unconditionally secure quantum cryptographic protocols. I propose two new
protocols, namely a Quantum Secure Direct Communication (QSDC) protocol and a Controlled Quantum Dialogue (CQD) protocol using discrete-time
quantum walks on a cycle. The proposed protocols have been shown to be
unconditionally secure against various attacks such as the intercept-resend
attack, the denial of service attack, and the man-in-the-middle attack. Additionally, the proposed CQD protocol is shown to be unconditionally secure
against an untrusted service provider. Also, it is shown that the proposed
protocols are more secure against the intercept resend attack as compared to
the qubit based LM05 protocol.
