Abstract
Recently Okamoto and Shiraishi proposed a public key authentication system [1]. The security of the scheme is based on the difficulty of solving quadratic inequalities. This new system is interesting since the amount of computing needed for the proposed scheme is significantly less than that needed for an RSA encryption.
This report is an investigation into the security of the proposed digital signature scheme. We demonstrate that if the system is used as it is presented, an opponent could sign messages without factoring the modulus. Further, we suggest a modification which may not have the same flaw as the proposed scheme.
This work performed at Sandia National Laboratories supported by the U. S. Dept. of Energy under contract No. DE-AC04-76DP00789.
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References
T. Okamoto, A. Shiraishi, “A Fast Signature Scheme Based on Quadratic Inequalities,” Proc. of the 1985 Symposium on Security and Privacy, April 1985, Oakland, CA.
H. Ong, C. P. Schnorr, and A. Shamir, “An Efficient Signature Scheme Based on Quadratic Equations,” Proc. 16th ACM Symp. Theor. Computing (1984), 208–216.
J. M. Pollard, “Solution of x2-kY 2 ≡ m (mod n),” Private communication with C. P. Schnorr, June 29, 1984.
H. Ong, C. P. Schnorr, and A. Shamir, “Efficient Signature Schemes Based on Polynomial Equations,” to appear in Crypto’84, Lecture Notes in Computer Science, Springer-Verlag, NY (1984).
D. Estes, L. Adleman, K. Kompella, K. McCurley, G. Miller, “Breaking the Ong-Schnorr-Shamir Signature Scheme for Quadratic Number Fields,” to appear.
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© 1986 Springer-Verlag Berlin Heidelberg
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Brickell, E.F., DeLaurentis, J.M. (1986). An Attack on a Signature Scheme Proposed by Okamoto and Shiraishi. In: Williams, H.C. (eds) Advances in Cryptology — CRYPTO ’85 Proceedings. CRYPTO 1985. Lecture Notes in Computer Science, vol 218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39799-X_4
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DOI: https://doi.org/10.1007/3-540-39799-X_4
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