  Quantum cryptography was proposed as a counter to the capacity of quantum
computers to break classical cryptosystems. A broad subclass of quantum
cryptography, called quantum key distribution (QKD), relies on quantum
mechanical process for secure distribution of the keys. Quantum channels are
inherently noisy, and therefore these protocols will be susceptible to noise as
well. In this paper, we study the performance of two QKD protocols - BB84 and
E91 under thermal relaxation error. We show that while E91 protocol loses its
security immediately due to loss of entanglement, the performance of BB84
protocol reduces to random guessing with increasing time. Next, we consider the
action of an Eve on the BB84 protocol under thermal relaxation noise, who is
restricted to guessing the outcome of the protocol only. Under this
restriction, we show that Eve can still do better than random guessing when
equipped with the characteristics of the noisy channel. Finally, we propose a
modification of the BB84 protocol which retains the security of the original
protocol, but ensures that Eve cannot get any advantage in guessing the
outcome, even with a complete channel information.
