  We present a tight security analysis of the Bennett-Brassard 1984 protocol
taking into account the finite size effect of key distillation, and achieving
unconditional security. We begin by presenting a concise analysis utilizing the
normal approximation of the hypergeometric function. Then next we show that a
similarly tight bound can also be obtained by a rigorous argument without
relying on any approximation. In particular, for the convenience of
experimentalists who wish to evaluate the security of their QKD systems, we
also give explicit procedures of our key distillation, and also show how to
calculate the secret key rate and the security parameter from a given set of
experimental parameters. Besides the exact values of key rates and security
parameters, we also present how to obtain their rough estimates using the
normal approximation.
