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Some Algorithms of Various Projective Coordinate Systems for ECC Using Ancient Indian Vedic Mathematics Sutras
[Full Text]
AUTHOR(S)
Manoj Kumar, Ankur Kumar
KEYWORDS
Dvandva-Yoga, Elliptic Curve Cryptography, Jacobian Projective, Lopez-Dahab Projective, Point addition, Point doubling, Standard Projective, Urdhva-Tiryagbhyam.
ABSTRACT
In this present approach, Some Algorithms of Various Projective Coordinate Systems for ECC (Elliptic Curve Cryptography) using AIVM (Ancient Indian Vedic Mathematics) sutras, has been studied. This work explained some useful Vedic sutra for multiplication calculation in cryptographic operations. In this paper, we have used some Vedic Mathematics Sutra to get minimum steps in the calculation of the addition algorithm, doubling algorithm and for improving the speed of processing time in the cryptographic operations, such as point addition, point doubling which occurs in the Elliptic curve cryptography over projective coordinate systems (Standard Projective, Jacobian Projective, Lopez-Dahab Projective). The coding and synthesis are done in MATLAB. The results proved that the Vedic Mathematics based schemes show better performance compared to the conventional method. The total delay in computation is reduced by Vedic mathematics Sutras (Urdhva-Tiryagbhyam, Dvandva-Yoga) with the help of MATLAB software.
REFERENCES
[1] Alkhatib M., Jaafar A., Zukerman Z., and Rushden M., “The Design of Projective Binary Edwards Elliptic Curves over GF (P) benefiting from mapping elliptic curves computation to variable degree of parallel design,” International Journal on Computer Science and Engineering, vol. 3, no. 4, pp. 1697-1712, 2011.
[2] Anchalya R., Chiranjeevi G. N., and Kulkarni S., “Efficient Computing Techniques using Vedic Mathematics Sutras,” International Journal of Innovative Research in Electrical Electronic Instrumentation and control engineering, vol. 3 no. 5, pp. 24-27, 2015.
[3] Deepa A., and Marimuthu C. N., “Squaring using Vedic Mathematics and its architectures a survey,” International Journal of Intellectual Advancements and Research in Engineering Computations, vol. 6, no. 1, pp. 214-218, 2018.
[4] Diffie W., and Hellman M., “New directions in Cryptography,” IEEE Transactions on information Theory, vol. 22 no. 6, pp. 644-654, 1976.
[5] Gaikwad K. M., and Chavan M. S., “Vedic Mathematics for Digital Signal Processing Operations: A Review,” International Journal of Computer Applications, vol. 131, no. 8, pp. 10-14, 2015.
[6] Gutub A.A.A., “Remodeling of Elliptic Curve Cryptography Scalar Multiplication Architecture using Parallel Projective Coordinate System,” International Journal of Computer Science and Security, vol. 4 no. 4, pp. 409-425, 2010.
[7] Hankerson D., Menzes A., and Vanstone S., “Guide to Elliptic Curve Cryptography,” Springer-Verlag, New York, 2004.
[8] Kan he A., Das S.K., and Singh A.K., “Design and implementation of low power multiplier using Vedic multiplication technique,” International Journal of Computer Science and Communication, vol. 3, no. 1, pp. 131-132, 2012.
[9] Koblitz N., “Elliptic Curve Cryptosystem,” Journal of Mathematics Computation, vol. 48 no. 177, pp. 203-209, 1987.
[10] Lisha A., and Monoth T., “Analysis of cryptography algorithms based on Vedic Mathematics,” International Journal of Applied Engineering Research, vol. 13, no. 3, pp. 68-72, 2018.
[11] Menezes A. J., “Elliptic Curve Public Key Cryptosystems,” Kluwer Academic Publishers, Springer, 1993.
[12] Nanda A., and Behera S., “Design and Implementation of Urdhva-Tiryagbhyam Based Fast Vedic Binary Multiplier,” International Journal of Engineering Research & Technology, vol. 3, no. 3, pp. 1856-1859, 2014.
[13] Pinagle S. D., “A Survey of Trends in Cryptography and Curve Cryptography,” International Journal of Scientific Research and Education, vol. 4, no. 50, pp. 5294-5301, 2016.
[14] Poornima M., Patil S. K., Kumar S., Shridhar K. P., and Sanjay H., “Implementation of multiplier using Vedic algorithm. International Journal of Innovative Technology and Exploring Engineering, vol. 2, no. 6, pp. 2278-3075, 2013.
[15] Salim S. M., and Lakhotiya S. A., “Implementation of RSA Cryptosystem using Ancient Indian Vedic Mathematics,” International Journal of Science and Research, vol. 4 no. 5, pp. 3221-3230, 2015.
[16] Sameer G., Sumana M., and Kumar S., “Novel High Speed Vedic Mathematics Multiplier using Compressors,” International Journal of Advanced Technology and Innovative Research, vol. 7 no. 2, pp. 0244-0248, 2015.
[17] Shembalkar S., Dhole S., Yadav T., Thakre P., “Vedic Mathematics Sutra- A Review,” International Conference on Recent Trends in Engineering Science and Technology, vol. 5, no. 1, p. 148-155, 2017.
[18] Shylashree N., Reddy D. V. N., and Sridhar V., “Efficient Implementation of Scalar Multiplication for Elliptic Curve Cryptography using Ancient Indian Vedic Mathematics over GF(p),” International Journal of Computer Applications, vol. 49 no. 7, pp. 0975-8887, 2012.
[19] Stallings W., “Cryptography and Network Security Principals and Practices,” Prentice Hall, India 2003.
[20] Thapliyal H., and Arbania H.R., “A Time-Area-Power Efficient Multiplier and Square Architecture Based on Ancient Indian Vedic Mathematics,” Proceedings of the 2004 International Conference on VLSI, Las Vegas, Nevada, pp. 434-439, 2004.
[21] Thomas C., Sheela G., and Saranya P. K., “A Survey on Various Algorithm Used for Elliptic Curve Cryptography,” International Journal of Computer Science and Information Technologies, vol. 5, no. 6, pp. 7296-7301, 2014.
[22] Tirthaji J. S. S. B. K., “Vedic Mathematics or Sixteen Simple Sutras from Vedas,” Motilal Bhandaridas Varanasi India, 1986.
[23] Warang M, and Tambe A., “A review on high speed complex multiplier using Vedic Mathematics: an effective tool,” International Journal of Advance Electrical Electronics Engineering, vol. 5, no. 1, pp. 26-28, 2016.
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