Number Theory and Cryptography: An Analytical Approach

P. N. V. Prasada Rao, B. Srinivasa Rao

Abstract


The more I have considered Computer Science, the more I see that it is truly a type of connected Mathematics. The two are regularly combined in University divisions, and numerous understudies study both for a more profound comprehension of the key procedures of PCs. As innovation advances, the abilities of PCs increment significantly. Basically, these capacities are simply numerical capacities that run speedier and control more information. To better my comprehension of PC innovation, I contemplated the science behind two long time (and everlastingly) executed PC forms: Cryptography and security.


References


Jackson, William. "Experts approve of new encryption standard." Government Computer news 16 Oct. 2000: 6. Academic OneFile. Web. 16 Nov. 2011.

Jallad, Kahil, Jonathan Katz, Jena J. Lee, and Bruce Schneier. Implementation of Chosen-Cyphertext Attacks against PGP and GnuPG. Information Security Conference, 2002. PDF.

Lv, Chuanfeng, and Qiangfu Zhao. "Integration of Data Compression and Cryptography: Another Way To Increase the Information Security." 21st International Conference on Advanced Networking and Applications

Workshops/Symposia 2 (2007): 543-47. Print.

Marshall, Dave. CS 421: Computer Network Security. Carroll College. Spring 2012. Lecture.

Nelson, Mark. LZW Data Compression." Dr. Dobb's Journal 1 Oct. 1989. Web. 19 Mar. 2012 http://marknelson.us/1989/10/01/lzw-data-compression/

Nelson, Mark, and Jean-loup Gailly. The Data Compression Book. University of Bahrain: College of Applied Studies. PDF Web. 19 Mar. 2012. http://sta_.uob.edu.bh/_les/781231507 _les/The-Data-Compression-Book-2ndedition.pdf

Null, Linda, and Julia Lobur. Essentials of Computer Organization and Architecture. Sudbury, MA: Jones & Bartlett Learning, 2012. Print.

R. P. Brent. An improved Monte Carlo factorization algorithm. BIT, 20(2):176–184, 1980.

E. R. Canfield, P. Erd˝os, and C. Pomerance. On a problem of Oppenheim concerning “factorisatio numerorum”. J. Number Theory, 17(1):1–28, 1983.

J. W. S. Cassels. Lectures on Elliptic Curves, volume 24 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 1991.

H. Cohen. A Course in Computational Algebraic Number Theory, volume 138 of Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1993.

H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, and F. Ver- cauteren, editors. Handbook of Elliptic and Hyperelliptic Curve Cryptography. Discrete Mathematics and Its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2006.

S. A. Cook. The complexity of theorem-proving procedures. In STOC ’71: Proceedings of the Third Annual ACM Symposium on Theory of Computing, pages 151–158, New York, NY, USA, 1971. ACM.

D. Coppersmith. Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm. Math. Comp., 62(205):333–350, 1994.

D. Coppersmith. Small solutions to polynomial equations, and low exponent RSA vulnerabilities. J. Cryptology, 10(4):233–260, 1997.

D. Coppersmith. Finding small solutions to small degree polynomials. In Cryptography and Lattices (Providence, RI, 2001), volume 2146 of Lecture Notes in Comput. Sci., pages 20–31. Springer, Berlin, 2001.

R. Crandall and C. Pomerance. Prime Numbers. Springer-Verlag, New York, 2001.


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