Abstract
A variant of Schnorr’s signature scheme called RDSA has been proposed by I. Biehl, J. Buchmann, S. Hamdy and A. Meyer in order to be used in finite abelian groups of unknown order such as the class group of imaginary quadratic orders. We describe in this paper a total break of RDSA under a plain known-message attack for the parameters that were originally proposed. It recovers the secret signature key from the knowledge of less than 10 signatures of known messages, with a very low computational complexity.
We also compare a repaired version of RDSA with GPS scheme, another Schnorr variant with similar properties and we show that GPS should be preferred for most of the applications.
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I. Biehl, J. Buchmann, S. Hamdy, and A. Meyer. A Signature Scheme Based on the Intractability of Computing Roots. Designs, Codes and Cryptography, 25(3):223–236, March 2002.
J. Buchmann and S. Hamdy. A Survey on IQ Cryptography. In Public-Key Cryptography and Computational Number Theory, pages 1–15. Walter de Gruyter, 2001.
A. Fiat and A. Shamir. How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In Advances in Cryptology — proceedings of CRYPTO’ 86, Lecture Notes in Computer Science volume 263, pages 186–194. Springer-Verlag, 1987.
M. Girault. Self-Certified Public Keys. In Advances in Cryptology — proceedings of EUROCRYPT’ 91, Lecture Notes in Computer Science volume 547, pages 490–497. Springer-Verlag, 1992.
N. Howgrave-Graham and N.P. Smart. Lattice attacks on digital signature schemes. Design, Codes and Cryptography, 23:283–290, 2001.
A. Joux and J. Stern. Lattice reduction: A toolbox for the cryptanalyst. Journal of Cryptology, 11(3):161–185, 1998.
A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovász. Factoring polynomials with rational coefficients. Mathematische Annalen, 261, 1982.
P.Q. Nguyen and I.E. Shparlinski. The Insecurity of the Digital Signature Algorithm with Partially Known Nonces. Journal of Cryptology, 15(3):151–176, 2002.
NIST. Digital Signature Standard (DSS). Federal Information Processing Standards PUBlication 186-2, february 2000.
D. Pointcheval and J. Stern. Security Arguments for Digital Signatures and Blind Signatures. Journal of Cryptology, 13(3):361–396, 2000.
J. M. Pollard. Monte Carlo Methods for Index Computation (mod p). Mathematics of Computation, 32(143):918–924, July 1978.
G. Poupard and J. Stern. Security Analysis of a Practical “on the fly” Authentication and Signature Generation. In Advances in Cryptology-proceedings of EUROCRYPT’ 98, Lecture Notes in Computer Science volume 1403, pages 422–436. Springer-Verlag, 1998.
C. P. Schnorr. Efficient Identification and Signatures for Smart Cards. In Advances in Cryptology — proceedings of CRYPTO’ 89, Lecture Notes in Computer Science volume 435, pages 235–251. Springer-Verlag, 1990.
C. P. Schnorr. Efficient Signature Generation by Smart Cards. Journal of Cryptology, 4(3): 161–174, 1991.
V. Shoup. Lower Bounds for Discrete Logarithms and Related Problems. In Advances in Cryptology-proceedings of EUROCRYPT’ 97, Lecture Notes in Computer Science volume 1233, pages 256–266. Springer-Verlag, 1997.
P. C. van Oorschot and M. J. Wiener. On Diffie-Hellman Key Agreement with Short Exponents. In Advances in Cryptology — proceedings of EUROCRYPT’ 96, Lecture Notes in Computer Science volume 1070, pages 332–343. Springer-Verlag, 1996.
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© 2003 International Association for Cryptologic Research
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Fouque, PA., Poupard, G. (2003). On the Security of RDSA. In: Biham, E. (eds) Advances in Cryptology — EUROCRYPT 2003. EUROCRYPT 2003. Lecture Notes in Computer Science, vol 2656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39200-9_29
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DOI: https://doi.org/10.1007/3-540-39200-9_29
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