The conjugacy search problem in a group G is the problem of recovering an x ϵ G from given g ϵ G and h=x-1gx. Ko et al. proposed a new public key cryptosystem on braid groups based on the hardness of the conjugacy problem. The foundation of this system is quite different from widely used cryptosystems on number theory, even if there are some similarities in design. Most of the authentication and signature schemes, such as digital signature scheme, blind signature scheme, proxy blind signature, Zero-knowledge Undeniable Signature Scheme which are based on conjugacy problem are computationally hard. In this article, we review the different types of conjugacy problems used in the various schemes of cryptography. © 2016, International Journal of Pharmacy and Technology. All Rights Reserved.