Registration Phase. In this phase, the home agent (HA) must choose a public key cryptosystem based on the Chebyshev chaotic map; the corresponding public key is (x; Ts(x)), and his private key is s. When a mobile user (MU ) wants to register to the home agent HA, MU chooses her or his identity IDMU and password pw, selects a random number b, and submits IDMU and h(pw b) to HA for registration over a secure channel. HA computes V = EKS(IDMU h(pw b)), where KS is a secret key kept by HA, and issues a smart card to MU over a secure channel, which contains V , x, Ts(x), EK(·) and a one-way hash function h(·). When MU receives the smart card, he or she stores b into the smart card. Finally, the smart card contains b, V, x, Ts(x), EK( ), h( ) . This phase is outlined in Fig. 1.
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Sources: Research Paper, Chaotic Maps Based Mutual Authentication and Key Agreement Using Smart Cards for Wireless Communications