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The Key exchange problems are of central interest in security world. The basic aim is that two people who can only communicate via an insecure channel want to find a common secret key without any attack. In this paper, the authors elaborated the process for well secured and assured for sanctity of correctness about the sender's and receiver's identity, as Key Agreement Protocol under the root problem in Non-Abelian Group (KAP-NAG).In recent years have emerged as suitable settings for cryptographic protocols. The idea of using the braid group as a platform for cryptosystems was first introduced in 1999 by Anshel, Anshel and Goldfeld.
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