Authentication in Quantum Key Distribution : Security Proof and Universal Hash Functions

Abstract: Quantum Key Distribution (QKD) is a secret key agreement technique that consists of two parts: quantum transmission and measurement on a quantum channel, and classical post-processing on a public communication channel. It enjoys provable unconditional security provided that the public communication channel is immutable. Otherwise, QKD is vulnerable to a man-in-the-middle attack. Immutable public communication channels, however, do not exist in practice. So we need to use authentication that implements the properties of an immutable channel as well as possible. One scheme that serves this purpose well is the Wegman-Carter authentication (WCA), which is built upon Almost Strongly Universal2 (ASU2) hashing. This scheme uses a new key in each authentication attempt to select a hash function from an ASU2 family, which is then used to generate the authentication tag for a message.The main focus of this dissertation is on authentication in the context of QKD. We study ASU2 hash functions, security of QKD that employs a computationally secure authentication, and also security of authentication with a partially known key. Specifically, we study the following.First, Universal hash functions and their constructions are reviewed, and as well as a new construction of ASU2 hash functions is presented. Second, security of QKD that employs a specific computationally secure authentication is studied. We present detailed attacks on various practical implementations of QKD that employs this authentication. We also provide countermeasures and prove necessary and sufficient conditions for upgrading the security of the authentication to the level of unconditional security. Third, Universal hash function based multiple authentication is studied. This uses a fixed ASU2 hash function followed by one-time pad encryption, to keep the hash function secret. We show that the one-time pad is necessary in every round for the authentication to be unconditionally secure. Lastly, we study security of the WCA scheme, in the case of a partially known authentication key. Here we prove tight information-theoretic security bounds and also analyse security using witness indistinguishability as used in the Universal Composability framework.