This paper considers source coding problems with the requirements of perfect secrecy and zero error at receivers. In the problems considered in this paper, there is always one transmitter but there can be one or two receivers. Two different scenarios depending on whether the receivers' side information are present at the transmitter or not are considered. By deriving bounds on the probability masses of the cipher-text and the key, the minimum transmission rate and key rate are characterized. Although zero-error capacities are typically difficult to characterize, the perfect secrecy constraint turns out to be the key that simplifies the problems considered in this paper and makes them analytically tractable.