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Original Articles

Computing Prime Factorization And Discrete Logarithms: From Index Calculus To Xedni Calculus

Pages 573-590 | Published online: 15 Sep 2010

References

  • Agrawal , M , Kayal , N. and Saxena , N. 2002 . Primes is in P, 6 August 2002. Dept of Computer Science and Engineering , Kanpur , , India : Indian Institute of Technology .
  • Brent , R. P. Some parallel algorithms for integer motorisation . Proc. Fifth International Euro-Par Conference . Sept 1-3 1999 , Toulouse , France. pp. 1 – 22 . Springer-Verlag . Lecture Notes in Computer Science 1685
  • Brent , R. P. Recent progress and prospects for integer factorisation algorithms . Proc. COCOON 2000 . July 2000 , Sydney . pp. 3 – 22 . Springer-Verlag . Lecture Notes in Computer Science 1858
  • Bressoud , D. M. 1989 . Factorization and Primality Testing , Undergraduate Texts in Mathematics Springer-Verlag .
  • Cohen , H. 1993 . A Course in Computational Algebraic Number Theory , Graduate Texts in Mathematics 138 Springer-Verlag .
  • Cook , S. 2000 . The P versus NP Problem, April, 2000 , Manuscript prepared for the Clay Mathematics Institute for the Millennium Prize Problems . (revised November, 2000}
  • Crandall , R. and Pomerance , C. 2001 . Prime Numbers-A Computational Perspective , Springer-Verlag .
  • Garey , M. R. and Johnson , D. S. 1979 . Computers and Intractability-A Guide to the Theory of NP-Completeness , W. H. Freeman and Company .
  • Garrett , P. 2001 . Making, Breaking Codes-An Introduction to Cryptology , Prentice-Hall .
  • Huizing , R. M. 1995 . An Implementation of the Number Field Sieve, Note NM-R9511 , Amsterdam : Centre for Mathematics and Computer Science (CWI} .
  • Jacobson , M. J. , Koblitz , N. , Silverman , J. H. , Stein , A. and Teske , E. 2000 . Analysis of the Xedni calculus attack . Designs, Codes and Cryptography , 20 : 41 – 64 .
  • Koblitz , N. 2000 . “ A survey of number theory and cryptography. ” . In Number Theory , Edited by: Bambah , P. , Dumir , V C. and Hans-Gill , R. J. 217 – 239 . Birkhäser .
  • Koblitz , N. “ Cryptography ” . In Mathematics Unlimited-2001 and Beyond , Edited by: Enguist , B. and Schmid , W. 749 – 769 . Springer-Verlag .
  • Lensba , H. W. Jr. 1987 . Factoring integers with elliptic curves . Annals of Mathematics , 126 : 649 – 673 .
  • Lenstra , A. K. and Lenstra , H. W. Jr. , eds. 1993 . The Development of the Number Field Sieve , Lecture Notes in Mathematics 1554 Springer-Verlag .
  • McCurley , K. S. 1990 . “ The discrete logarithm problem. ” . In Cryptology and Computational Number Theory, Proceedings of Symposia in Applied Mathematics , Edited by: Pomerance , C. Vol. 42 , 49 – 74 . American Mathematics Society .
  • Mestre , J. F. 1986 . Formules Explicites et Minoration de Conducteurs de Variétés algébriques . Compositio Mathematica , 58 : 209 – 232 .
  • Miller , V. 1986 . Uses of elliptic curves in cryptography, Advances in Cryptology, CRYPTO '85, Proceedings , Lecture Notes in Computer Science 218 417 – 426 . Springer-Verlag . 1986
  • Montgomery , P. L. 1994 . A survey of modem integer factorization algorithms . CWl Quartery , 7 (4} ) : 337 – 366 .
  • Pomerance , C. 1996 . A tale of two sieves . Notice of the AMS , 43 (12} ) : 1473 – 1485 .
  • Shor , P. 1997 . Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer . SIAM Journal on Computing , 26 (5} ) : 1484 – 1509 .
  • Silverman , J. H. 1994 . The Arithmetic of Elliptic Curves , Graduate Texts in Mathematics 106 Springer-Verlag .
  • Silverman , J. H. 2000 . The Xedni calculus and the elliptic curve discrete logarithm problem . Designs, Codes and Cryptography , 20 : 5 – 40 .
  • Silverman , J. H. and Suzuki , J. 1998 . “ Elliptic curve discrete logarithms and the index calculus ” . In Advances in Cryptology-ASIACRYPT '98 , Lecture Notes in Computer Science 1514 110 – 125 . Springer-Verlag .
  • Williams , C. P. and Clearwater , S. H. 1998 . Explorations in Quantum Computation. The Electronic Library of Science (TELOS} , Springer-Verlag .
  • Van , S. Y. 2002 . Number Theory for Computing , 2nd ed. , Springer-Verlag .

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