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Reseach Article

A Flexible and Efficient Algorithm for Generating Prime Numbers using Biometric Identity (Bio-PNGA)

by B. Indrani, M. Karthigai Veni
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 155 - Number 14
Year of Publication: 2016
Authors: B. Indrani, M. Karthigai Veni
10.5120/ijca2016912384

B. Indrani, M. Karthigai Veni . A Flexible and Efficient Algorithm for Generating Prime Numbers using Biometric Identity (Bio-PNGA). International Journal of Computer Applications. 155, 14 ( Dec 2016), 16-23. DOI=10.5120/ijca2016912384

@article{ 10.5120/ijca2016912384,
author = { B. Indrani, M. Karthigai Veni },
title = { A Flexible and Efficient Algorithm for Generating Prime Numbers using Biometric Identity (Bio-PNGA) },
journal = { International Journal of Computer Applications },
issue_date = { Dec 2016 },
volume = { 155 },
number = { 14 },
month = { Dec },
year = { 2016 },
issn = { 0975-8887 },
pages = { 16-23 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume155/number14/26774-2016912384/ },
doi = { 10.5120/ijca2016912384 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:01:15.077178+05:30
%A B. Indrani
%A M. Karthigai Veni
%T A Flexible and Efficient Algorithm for Generating Prime Numbers using Biometric Identity (Bio-PNGA)
%J International Journal of Computer Applications
%@ 0975-8887
%V 155
%N 14
%P 16-23
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A biometric based security system provides best on both authentication and confidentiality for public shared secret information. Enormous numbers of papers have been published by the researchers in this field. The generation of prime numbers plays the most important role in the public-key schemes, essentially as a major primitive needed for the creation of key pairs or as a computation stage appearing during various cryptographic setups. Most of the researchers have been made strong mathematical studies on primality testing and an observed progressive increase of cryptographic usages, prime number generation algorithms. Still not quite investigated and most of the real-life implementations are providing poor performance. Most of the common prime number generators typically output n-bit prime in heuristic average complexity

References
  1. A.O.L. Atkin, D.J. Bernstein, Prime sieves using binary quadratic forms, Math. Comp. 73 (2004), pp. 1023-1030.
  2. Carl Pomerance; John L. Selfridge; Samuel S. Wagstaff, Jr. (July 1980). "The pseudoprimes to 25·109". Mathematics of Computation, 35 (151), pp. 1003–1026.
  3. Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation 35 (152): 1391–1417
  4. Adleman, Leonard M.; Huang, Ming-Deh (1992). Primality testing and Abelian varieties over finite field. Lecture notes in mathematics 1512. Springer-Verlag. ISBN 3-540-55308-8
  5. Chau, H. F.; Lo, H.-K. (1995). "Primality Test Via Quantum Factorization". arXiv:quant-ph/9508005
  6. J. Brandt and I. Damgard. “On generation of probable primes by incremental search”, In E. F. Brickell, editor, CRYPTO, volume 740 of Lecture Notes in Computer Science, pages 358–370. Springer, 1992.
  7. J. Brandt, I. Damgard, and P. Landrock. “Speeding up prime number generation”, In H. Imai, R. L. Rivest, and T. Matsumoto, editors, ASIACRYPT, volume 739 of Lecture Notes in Computer Science, pp. 440–449. Springer, 1991
  8. D. Eastlake 3rd, J. Schiller, and S. Crocker. “Randomness Requirements for Security”, RFC 4086 (Best Current Practice), June 2005
  9. G. H. Hardy and J. E. Littlewood. “Some problems of ‘partitio numerorum’: III. on the expression of a number as a sum of primes”, 44, pp. 1–70, 1922
  10. M. Joye and P. Paillier. “Fast generation of prime numbers on portable devices: An update”, In L. Goubin and M. Matsui, editors, CHES, volume 4249 of Lecture Notes in Computer Science, pp. 160–173. Springer, 2006.
  11. M. Joye, P. Paillier, and S. Vaudenay. “Efficient generation of prime numbers”, In Cetin Kaya Koc and C. Paar, editors, CHES, volume 1965 of Lecture Notes in Computer Science, pp. 340–354. Springer, 2000
  12. U. M. Maurer. “Fast generation of secure RSA-moduli with almost maximal diversity”, In EUROCRYPT, pp. 636–647, 1989.
  13. U. M. Maurer. “Fast generation of prime numbers and secure public-key cryptographic parameters”, J. Cryptology, 8(3), pp.123–155, 1995
  14. P. Mihăilescu. “Fast generation of provable primes using search in arithmetic progressions”, In Y. Desmedt, editor, CRYPTO, volume 839 of Lecture Notes in Computer Science, pp. 282–293. Springer, 1994.
  15. A. K. Jain, A. Ross: Introduction to Biometrics. In “Handbook of Biometrics”, A. Jain et al. (Eds), Springer, 2008
  16. Y. C. Feng, P. C. Yuen, A. K. Jain: “A Hybrid Approach for Face Template Protection”, In Proceedings of SPIE Conference of Biometric Technology for Human Identification, Orlando, USA, Vol. 6944, pp. 325, 2008
  17. P. Balakumar, R. Venkatesan: “A Survey on Biometrics-based Cryptographic Key Generation Schemes”, International Journal of Computer Science and Information Technology & Security, Vol. 2, No. 1, pp. 80-85, 2012
  18. A. K. Jain, A. Ross, S. Prabhakar: “An Introduction to Biometric Recognition”, IEEE Transactions on Circuits and Systems for Video Technology, Vol. 14, pp. 4-20, 2004
  19. B. Biggio: “Adversarial Pattern Classification. Doctoral dissertation”, University of Cagliari, Cagliari, Italy, 2010
  20. A. Jagadeesan, K. Duraiswamy: “Secured Cryptographic Key Generation From Multimodal Biometrics: Feature Level Fusion of Fingerprint and Iris”, International Journal of Computer Science and Information Security, Vol. 7, No. 2, pp. 28-37, 2010
  21. L. Hong, A. K. Jain, S. Pankanti: “Can Multibiometrics Improve Performance?”, In Proceedings of IEEE Workshop on Automatic Identification Advanced Technologies, pp. 59-64, NJ, USA, 1999
  22. A. K. Jain, A. Ross: Multi-Biometric Systems: “Special Issue on Multimodal Interfaces that Flex, Adapt, and Persist”, Communications of the ACM, Vol. 47, No. 1, pp. 34-40, 2004
  23. A. K. Jain, K. Nandakumar, A. Nagar: “Biometric Template Security”, EURASIP J. Adv. Signal Process, 2008:1-17, 2008
  24. J. Galbally, C. McCool, J. Fierrez, S. Marcel, J. Ortega-Garcia. “On the Vulnerability of Face Verification Systems to Hill-Climbing Attacks”, Pattern Recogn., 43(3) pp. 1027-1038, 2010
  25. S. Prabhakar, A. Jain: “Decision-Level Fusion in Fingerprint Verification”, Pattern Recognition, Vol. 35, pp. 861-874, 2002
  26. Z. Wang, E. Wang, S. Wang, Q. Ding: “Multimodal Biometric System Using Face-Iris Fusion Feature. Journal of Computers”, Vol. 6, No. 5, pp. 931-938, 2011
  27. K. Toh, J. Kim, S. Lee: “Biometric Scores Fusion Based on Total Error Rate Minimization”,. Pattern Recognition, Vol. 41, pp. 1066-1082, 2008
  28. A. Ross, R. Govindarajan: Feature Level Fusion in Biometric Systems. In proceedings of Biometric Consortium Conference, September 2004
  29. S. Adamović, M. Milosavljević: Information Analysis of Iris Biometrics for the Needs of Cryptology Key Extraction. Serbian Journal of Electrical Engineering, Vol. 10, No. 1, pp. 1-12, 2003
  30. C. Couvreur and J.-J. Quisquater. An introduction to fast generation of large prime numbers. Philips Journal of Research, vol. 37, pp. 231-264, 1982
  31. D.E. Knuth. The Art of Computer Programming - Seminumerical Algorithms, vol. 2, Addison-Wesley, 2nd ed., 1981
  32. R. Solovay and V. Strassen. A fast Monte-Carlo test for primality. SIAM Journal on Computing, vol. 6, pp. 84-85, 1977
  33. H.C. Pocklington. The determination of the prime or composite nature of large numbers by Fermat's theorem. Proc. of the Cambridge Philosophical Society, vol. 18, pp. 29-30, 1914
  34. A.O.L. Atkin and F. Morain. Elliptic curves and primality proving. Mathematics of Computation, vol. 61, pp. 29-68, 1993
  35. W. Bosma and M.-P. van der Hulst. Faster primality testing. In Advances in Cryptology-CRYPTO'89, vol. 435 of Lecture Notes in Computer Science, pp. 652-656, Springer-Verlag, 1990
  36. Carl Pomerance; John L. Selfridge; Samuel S. Wagstaff, Jr. (July 1980). "The pseudoprimes to 25·109". Mathematics of Computation 35 (151): 1003–1026. doi:10.1090/S0025-5718-1980-0572872-7
  37. Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). "Lucas Pseudoprimes", Mathematics of Computation 35 (152): 1391–1417
  38. Chau, H. F.; Lo, H.-K. (1995). "Primality Test Via Quantum Factorization". arXiv:quant-ph/9508005
  39. Adleman, Leonard M.; Huang, Ming-Deh (1992). Primality testing and Abelian varieties over finite field. Lecture notes in mathematics 1512. Springer-Verlag.
  40. http://biometrics.idealtest.org/dbDetailForUser.do?id=7
Index Terms

Computer Science
Information Sciences

Keywords

Biometric Identity Prime numbers Public Key Infrastructure (PKI).