Multiplicative inverse has a lot of applications in various fields. When we divide a number by another number, we get quotient and remainder. The modulo operation returns the remainder after division. a mod n gives out the remainder when a is divided by n, where a is an integer and n is a positive integer. A modular multiplicative inverse of an integer a is an integer b such that the product ab is congruent to 1 modulo n, i.e. ab≡1 (mod n). Numerous calculations of modulo multiplicative inverses are necessary for a variety of asymmetric cryptographic algorithms such as RSA algorithm.. This paper aims at explaining the concept of modulo inverse and its application in cryptography as well as the various methods for computing the modulus. And the role of modulo inverse in the security of encryption and decryption.