Satellite's communication system is used to communicate under significant distance and circumstances where the other communication systems are not comfortable.Since all the data are exchanged over a public channel, so the security of the data is an essential component for the communicating parties. Both key exchange and authentication are two cryptographic tools to establish a secure communication between two parties. Currently, various kinds of authentication protocols are available to establish a secure network, but all of them depend on number-theoretical (discrete logarithm problem/factorization assumption) hard assumptions. Due to Shor's and Grover's computing algorithm number theoretic assumptions are breakable by quantum computers. Although Kumar and Garg have proposed a quantum attack-resistant protocol for satellite communication, it cannot resist stolen smart card attack. We have analyzed that how Kumar and Garg is vulnerable to the stolen smart card attack using differential power analysis attack described in He et al and Chen and Chen. We have also analyzed the modified version of signal leakage attack and sometimes called improved signal leakage attack on Kumar and Garg's protocol.We have tried to construct a secure and efficient authentication protocol for satellites communication that is secure against quantum computing. This is more efficient as it requires only three messages of exchange. This paper includes security proof and performance of the proposed authentication and key agreement protocol.

In this paper, we study the simplified generalized Gauss–Newton method in a Hilbert scale setting to get an approximate solution of the ill-posed operator equation of the form {F(x)=y} where {F:D(F)\subseteq X\to Y} is a nonlinear operator between Hilbert spaces X and Y. Under suitable nonlinearly conditions on F, we obtain an order optimal error estimate under the Morozov type stopping rule.

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