This paper focuses on the application of factorial and binomial identities in computing, communication, and cybersecurity in connection with the symmetric and asymmetric encryptions. We can use the binomial identities and theorem in factorials as an effective security algorithm to protect the computing systems, programs, and networks. In this connection, binomial expansions which are equal to multiples of 2 with non-negative exponents, and its relations are given in this article. MSC Classification codes: 05A10, 40A05 (65B10)