In this paper, we presented a new key exchange method based on decomposition problem for elliptic curve cryptography. We showed that our key exchange method was not only an alternative method for designing keys in cryptography, but it also has improved security condition from the previous key exchange based on decomposition problem over non-commutative groups. We proposed elliptic an curve cryptography to be the new platform for our key exchange protocol and showed how it was implemented. The security of our protocol was based on discrete logarithm problem, which was not infeasible and strictly difficult to retrieve in elliptic curve cryptography without any prior knowledge.
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