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Reseach Article

Cryptanalysis of RSA with Small Prime Difference using Unravelled Linearization

by Santosh Kumar.r, Narasimham.c, Pallam Setty.s
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 61 - Number 3
Year of Publication: 2013
Authors: Santosh Kumar.r, Narasimham.c, Pallam Setty.s
10.5120/9907-4499

Santosh Kumar.r, Narasimham.c, Pallam Setty.s . Cryptanalysis of RSA with Small Prime Difference using Unravelled Linearization. International Journal of Computer Applications. 61, 3 ( January 2013), 14-16. DOI=10.5120/9907-4499

@article{ 10.5120/9907-4499,
author = { Santosh Kumar.r, Narasimham.c, Pallam Setty.s },
title = { Cryptanalysis of RSA with Small Prime Difference using Unravelled Linearization },
journal = { International Journal of Computer Applications },
issue_date = { January 2013 },
volume = { 61 },
number = { 3 },
month = { January },
year = { 2013 },
issn = { 0975-8887 },
pages = { 14-16 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume61/number3/9907-4499/ },
doi = { 10.5120/9907-4499 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:08:05.094514+05:30
%A Santosh Kumar.r
%A Narasimham.c
%A Pallam Setty.s
%T Cryptanalysis of RSA with Small Prime Difference using Unravelled Linearization
%J International Journal of Computer Applications
%@ 0975-8887
%V 61
%N 3
%P 14-16
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In 2002, de Weger showed that choosing an RSA modulus with a small difference of primes improves the attack given by Boneh-Durfee. For this attack, de Weger used the complicated geometrical progressive matrices, introduced by Boneh-Durfee. In this paper, we analyzed by using another technique called unravelled linearization.

References
  1. R. Rivest, A. Shamir and L. Adleman," A Method for Obtaining Digital Signatures and Public-Key Cryptosystems", Communications of the ACM, vol. 21, No. 2, pp. 120-126,1978.
  2. Wiener, M. : Cryptanalysis of short RSA secret exponents, IEEE Transactions on Information Theory 36, 553-558 (1990).
  3. Boneh, D. , Durfee, G. : Cryptanalysis of RSA with Private Key d Less Than N^0. 292, Advances in Cryptology-EUROCRYPT99, Lecture Notes in Computer Science 1592, Berlin: Springer 1999,pp. 1-11.
  4. Nick Howgrave-Graham, N. : Finding small roots of univariate modular equations revisited, In Cryptology and Coding, Lecture Notes in Computer Science 1335, Berlin: Springer-Verlag 1997, pp. 131-142.
  5. J. Blomer and A. May. Low secret exponent RSA revisited. In J. H. Silverman, editor,CaLC, volume 2146 of Lecture Notes in COMPUTER Science, pages 4-19. Springer, 2001.
  6. De Weger, B. : Cryptanalysis of RSA with small prime difference, Applicable Algebra in Engineering, Communication and Computing, Vol 13(1), 17-28 (2002).
  7. Hermann, M. , May, A. ,: Maximizing Small Root Bounds by Linearization and Applications to Small Secret Exponent RSA, In Practice and Theory in Public Key Cryptography (PKC 2010), Lecture Notes in Computer Science 6056, Berlin: Springer-Verlag 2010,pp. 53-69.
  8. A. Lenstra, H. Lenstra, L. Lovasz ," Factoring Polynomials with Rational Coeffiecients", Mathematiche Annalen 261, pp. 515-534, 1982.
  9. R. Santosh kumar, C. Narasimham, S. Pallam setty, "Lattice based tools for cryptanalysis in various applications", springer-LNICST, 84:530-537, 2012.
  10. R. Santosh kumar, C. Narasimham, S. Pallam settee," Lattice bases attacks on short secret exponent RSA: A Survey", International Journal of Computer Applications (0975 – 8887) Volume 49– No. 19, July 2012.
  11. Victor Shoup. NTL: A library for doing number theory. Website: http://www. shoup. net/ntl/.
Index Terms

Computer Science
Information Sciences

Keywords

Lattice reduction RSA Cryptanalysis Unravelled linearization