Abstract: The resilient function is one of the multiple-output Boolean functions, An important work the resilient function has to do is to prevent the information eavesdropping. The more numbers of the resilient functions have the more safety the cryptographic system will be. On the other hand, construction, as well as enumeration in (n,m,1)-resilient functions, has to be paid more attention to. Construction and enumeration were studied when the order of resiliency was t=1,n-m＞t, upon which, three classes of (n,m,1)-resilient functions, based on the construction of n-variables balanced correlation-immune functions of the first-order, and on the equivalence between resilient functions and large sets of orthogonal arrays(a group of orthogonal arrays), are implemented in the case of n-m＞t=1. Also, an enumeration lower bound of a (n,m,1)-resilient function was presented.

Key words: resilient functions, orthogonal array, enumeration, quantum crypto-graphic key distribution