An elliptical cryptographic algorithm for RF wireless devices

ABSTRACT

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.

REFERENCES

• 1: The case for Elliptical Cryptography. 2007. <http://www.nsa.gov/ia/industry/crypto_elliptic_curve.cfm>.
• 2: Gao, S., J. Howell, and D. Panario. 1999. Irreducible polynomials of given forms. In Finite fields: theory, applications and algorithms, ed. R. C. Mullin and G. L. Mullen, 225:45--54. Contemporary Mathematics, Amer. Math. Soc.
• 3: Robert Szewczyk , Eric Osterweil , Joseph Polastre , Michael Hamilton , Alan Mainwaring , Deborah Estrin, Habitat monitoring with sensor networks, Communications of the ACM, v.47 n.6, June 2004 [doi>10.1145/990680.990704]
• 4: Hitchcock, Y., E. Dawson, A. Clark, and P. Montague. 2003. Implementing an efficient elliptic curve crypto-system over GF(p) on a smart card. ANZIAM Journal 44(E):354--377.
• 5: Daniel V. Bailey , Christof Paar, Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms, Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology, p.472-485, August 23-27, 1998
• 6: Gupta, V., D. Stebila, S. Fung, S. Chang Shantz, N. Gura, and H. Eberle. 2004. Speeding up secure web transactions using elliptic curve cryptography. In 11th Network and Distributed System Security Symposium, 231--239. February 5--6, 2004, San Diego, CA.
• 7: Adrian Perrig , John Stankovic , David Wagner, Security in wireless sensor networks, Communications of the ACM, v.47 n.6, June 2004 [doi>10.1145/990680.990707]
• 8: El-Gamal, T. 1985. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Info. Theory 31:469--472.
• 9: Ronald Watro , Derrick Kong , Sue-fen Cuti , Charles Gardiner , Charles Lynn , Peter Kruus, TinyPK: securing sensor networks with public key technology, Proceedings of the 2nd ACM workshop on Security of ad hoc and sensor networks, October 25-25, 2004, Washington DC, USA [doi>10.1145/1029102.1029113]
• 10: Vipul Gupta , Matthew Millard , Stephen Fung , Yu Zhu , Nils Gura , Hans Eberle , Sheueling Chang Shantz, Sizzle: A Standards-Based End-to-End Security Architecture for the Embedded Internet (Best Paper), Proceedings of the Third IEEE International Conference on Pervasive Computing and Communications, p.247-256, March 08-12, 2005 [doi>10.1109/PERCOM.2005.41]
• 11: National Institute of Standards and Technology. 1999. Recommended elliptic curves for federal government use, August 1999.
• 12: Chris Karlof , Naveen Sastry , David Wagner, TinySec: a link layer security architecture for wireless sensor networks, Proceedings of the 2nd international conference on Embedded networked sensor systems, November 03-05, 2004, Baltimore, MD, USA [doi>10.1145/1031495.1031515]