The insecurity of nyberg–rueppel and other DSA-like signature schemes with partially known nonces

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2146, Issue , 2001, Pages 97-109

  Mahassni, Edwin El ^a   Nguyen, Phong Q ^b   Shparlinski, Igor E ^a  

^a MACQUARIE UNIVERSITY   (Australia)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Closest vector problem; DSA; Exponential sums; Hidden number problem

Indexed keywords

ALGORITHMS; AUTHENTICATION; ELECTRONIC DOCUMENT IDENTIFICATION SYSTEMS; EXPONENTIAL FUNCTIONS;

CLOSEST VECTOR PROBLEM; DIGITAL SIGNATURE ALGORITHMS; DSA SIGNATURES; EXPONENTIAL SUMS; HIDDEN NUMBER PROBLEM; SIGNATURE SCHEME;

CRYPTOGRAPHY;

EID: 84958967057     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44670-2_9     Document Type: Conference Paper

References (23)

1. M. Ajtai, R. Kumar and D. Sivakumar, A sieve algorithm for the shortest lattice vector problem, Proc. 33rd ACM Symp. on Theory of Comput., Crete, Greece, July 6-8, 2001 601-610.
2. L. Babai, On Lovász lattice reduction and the nearest lattice point problem, Combinatorica, 6(1986), 1-13.
3. D. Boneh and R. Venkatesan, Hardness of computing the most significant bits of secret keys in Diffie–Hellman and related schemes, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1109(1996), 129-142.
4. D. Boneh and R. Venkatesan, Rounding in lattices and its cryptographic applications, Proc. 8-rd Annual ACM-SIAM Symp. on Discr. Algorithms, ACM, NY, 1997, 675-681.
5. M. Drmota and R. Tichy, Sequences, discrepancies and applications, Springer-Verlag, Berlin, 1997.
6. N. A. Howgrave-Graham and N. P. Smart, Lattice attacks on digital signature schemes, Designs, Codes and Cryptography, (to appear).
7. R. Kannan, Algorithmic geometry of numbers, Annual Review of Comp. Sci., 2(1987), 231-267.
8. S. V. Konyagin and I. E. Shparlinski, Character sums with exponential functions and their applications, Cambridge Univ. Press, Cambridge, 1999.
9. R. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley-Interscience, NY, 1974.
10. A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Mathematische Annalen, 261(1982), 515-534.
11. R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, Cambridge, 1997.
12. A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, FL, 1996.
13. C. J. Moreno and O. Moreno, Exponential sums and Goppa codes, I, Proc. Amer. Math. Soc., 111(1991), 523-531.
14. P. Q. Nguyen, The dark side of the hidden number problem: Lattice attacks on DSA, Proc. Workshop on Cryptography and Computational Number Theory, Singapore 1999, Birkhäuser, 2001, 321-330.
15. P. Q. Nguyen and I. E. Shparlinski, The insecurity of the Digital Signature Algorithm with partially known nonces, J. of Cryptology, to appear.
16. P. Q. Nguyen and J. Stern, The hardness of the hidden subset sum problem and its cryptographic implications, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1666(1999), 31-46.
17. H. Niederreiter, Random number generation and quasi–Monte Carlo methods, SIAM, Philadelphia, 1992.
18. K. Nyberg and R. A. Rueppel, Message recovery for signature schemes based on the discrete logarithm problem, J. Cryptology, 8(1995), 27-37.
19. B. Schneier, Applied cryptography, J. Wiley, NY, 1996.
20. C. P. Schnorr, A hierarchy of polynomial time basis reduction algorithms, Theor. Comp. Sci., 53(1987), 201-224.
21. C. P. Schnorr and M. Euchner, Lattice basis reduction: improved practical algorithms and solving subset sum problems, Math. Programming, 66(1994), 181-199.
22. V. Shoup, Number Theory C++ Library (NTL), Available at http://www.shoup.net/ntl/.
23. I. M. Vinogradov, Elements of number theory, Dover Publ., New York, 1954.