In this paper, we propose a new asymmetric cryptographic algorithm (HOOD CRYPT) based on the Elliptical Curve Cryptographic approach. The algorithm describes how an orthogonal frequency division multiplexing (OFDM) based RF wireless system can be encrypted using planner matrix Elliptical Curve Cryptography (ECC). The newly described asymmetric algorithm can be applied to the OFDM transmission scheme in the design of more robust and secure cryptography in portable wireless devices. An analysis of the proposed algorithm is made using the discrete logarithm approach. Two methods, namely, Pollard's rho Attack and Index Calculus are investigated with respect to the new algorithm. We found that our method makes it even more difficult to break the ECC encryption.