Abstract

Over the past 20 years, numerous papers have been written on various aspects of ECC implementation. In this paper we investigate the superiority of the Arithmetic data compression technique over the Huffman data compression technique in reducing the channel bandwidth and the transmission time. The main purpose of data compression is to reduce the memory space or transmission time, while that of cryptography is to ensure the security of the data. Applying Data compression techniques not only reduces the bandwidth but also enhances the strength of the cryptosystem. It is also observed that even if the given string is doubled i.e. AAAA (4A’s) to AAAAAAAA (8A’s), the compression ratio remains constant. Further in Arithmetic Data Compression the compression ratio is 50% more when compared to the Huffman Data Compression and the ratio increases with increasing string length.

References

• N.Koblitz, CM-curves with good cryptographic properties in: Advances in cryptology, CRYPTO’91, Lecture note in Computer Science,Vol.576, Springer 1991, pp 279-287
• National Institute of Standards and Technology (NIST), Digital Signature Standards(DSS), Federal information processing standard, FIPS PUB 186-2, January 27,2000.
• Certicom Research, SEC 1: Elliptic Curve Cryptography, Standards for efficient cryptography, September, 2000
• Certicom Research, SEC 2: Recommended Elliptic Curve domain parameters, Standards for efficient cryptography, September 20,2000
• V. Miller, “Uses of elliptic curves in cryptography”, Advances in Cryptology– Crypto’85, Lecture Notes in Computer Science, 218 (1986), Springer-Verlag, 417-426.
• Certicom Corp., “ An Introduction to Information Security”, No. 1, March 1997.
• ANSI X9.63, Public Key Cryptography for the Financial Services Industry: Elliptic CurveKey Agreement and Key Transport Protocols, ballot version, May 2001.
• Internet Engineering Task Force, The OAKLEY Key Determination Protocol, IETF RFC 2412, November 1998.
• ISO/IEC 15946-3, Information Technology–Security Techniques– Cryptographic Techniques Based on Elliptic Curves, Part 3, Final Draft International Standard (FDIS), February 2001
• M. Jacobson, N. Koblitz, J. Silverman, A. Stein and E. Teske, “Analysis of the xednicalculus attack”, Designs, Codes and Cryptography, 20 (2000), 41-64.
• S. Arita, “Weil descent of elliptic curves over finite fields of characteristic three”, Advances in Cryptology–Asiacrypt 2000, Lecture Notes in Computer Science, 1976 (2000),Springer-Verlag, 248-259.
• Fernandes, A. “Elliptic Curve Cryptography”, Dr.Dobb’s journal, December 1999
• J.Solinas, “An improved algorithm for arithmetic on a family of elliptic curve”, Advances in Cryptology - CRYPTO '97, Lecture Notes in Computer Science, 1997, Volume 1294/1997, 357-371, DOI: 10.1007/BFb0052248 ,1294(1997). Springer-Verlog, 357-371
• J.Solinas,” Efficient arithmetic on koblitz Curves”, Design codes and cryptography, 19(2000), 195-249
• Huffman, David (1952) “A Method for the Construction of Minimum Redundancy Codes,” Proceedings of the IRE 40(9):1098–1101.
• O.Srinivasa Rao, S.Pallam Setty, “Efficient mapping methods of Elliptic Curve Crypto Systems” International Journal of Engineering Science and Technology, Vol. 2(8), 2010, pp. 3651-3656
• M.Prabu, R.Shanmugalakshmi “A Comparative and Overview Analysis of Elliptic Curve Cryptography over Finite Fields”2009, International Conference on Information and Multimedia Technology, IEEE computer society.
• Billy Bob Brumley and Kimmo U. Jarvinen, Member, IEEE “Conversion Algorithms and Implementations for Koblitz Curve Cryptography”, IEEE Transactions on computers Vol.59, No.1, January 2010
• Yong-hee Jang, Yong-jin Kwon “Efficient Scalar Multiplication Algorithms Secure against Power Analysis Attacks for Koblitz Curve Cryptosystems” 2010, 10th Annual International Symposium on Applications and the Internet, IEEE Computer Society
• Chang Shu, Soonhak Kwon, and Kris Gaj “Reconfigurable Computing Approach for Tate Pairing Cryptosystems over Binary Fields” IEEE Transactions on computers Vol.58, No.8, September 2009