Abstract
We use bounds of exponential sums to show that for a wide class of parameters the modification of the DSA signature scheme proposed by A.K. Lenstra at Asiacrypt '96 is as secure as the original scheme.
Chapter PDF
Similar content being viewed by others
References
V. Boyko, M. Peinado and R. Venkatesan, Speeding up discrete log and factoring based schemes via precomputations, Proc.EUROCRYPT’ 98, Lect.Notes in Comp. Sci., Springer-Verlag, Berlin, 1403 (1998), 221–235.
S.W. Graham and C.J. Ringrose, Lower bounds for least quadratic nonresidues, Analytic number theory,Progr.Math., 85, Birkhäuser, Boston, MA, 1990, 269–309.
A. Granville and K. Soundararajan, Large character sums, J.Amer.Math.Soc. (to appear); available from http://www.ams.org/jams/.
A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. de Théorie des Nombres de Bordeaux, (1993), 411–484.
N.A. Howgrave-Graham and N.P. Smart, Lattice attacks on digital signature schemes, Designs, Codes and Cryptography (to appear).
A.K. Lenstra, Generating standard DSA signatures without long inversions, Proc. ASIACRYPT’ 96, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1163 (1996), 57–64.
R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, Cambridge, 1997.
A.J. Menezes, P.C. van Oorschot and S.A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, FL, 1996.
W. Narkiewicz, Classical problems in number theory, Polish Sci. Publ.,Warszawa, 1986.
P. Nguyen, The dark side of the Hidden Number Problem:Lattice attacks on DSA, Proc.Workshop on Cryptography and Computational Number Theory, Singapore 1999, Birkhäuser, 2000 (to appear).
P. Nguyen and I.E. Shparlinski, The insecurity of the Digital Signature Algorithm with partially known nonces, Preprint, 2000, 1–26.
P. Nguyen and J. Stern, The hardness of the hidden subset sum problem and its cryptographic implications, Proc.CRYPTO’ 99, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1666 (1999), 31–46.
K. Nyberg and R.A. Rueppel, Message recovery for signature schemes based on the discrete logarithm problem, J. Cryptology, 8 (1995), 27–37.
B. Schneier, Applied cryptography, John Wiley, NY, 1996.
P.J. Stephens, An average result for Artin’ s conjecture, Mathematika, 16 (1969), 178–188.
S. Vaudenay, On the security of Lenstra’ s DSA variant, Presented at the Rump Session of ASIACRYPT’ 96; available from http://lasecwww.epfl.ch/pub/lasec/doc/lenstra.ps
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lenstra, A.K., Shparlinski, I.E. (2001). On the Security o Lenstra’ s Variant o DSA without Long Inversions. In: Kim, K. (eds) Public Key Cryptography. PKC 2001. Lecture Notes in Computer Science, vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44586-2_5
Download citation
DOI: https://doi.org/10.1007/3-540-44586-2_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41658-6
Online ISBN: 978-3-540-44586-9
eBook Packages: Springer Book Archive