Abstract
Vanstone and Zuccherato [3] propose a cryptographic system based on an elliptic curve modulo a composite number. We show that the composite numbers so constructed are easily factored, rendering the system insecure.
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References
D. Coppersmith, “Finding a small root of a bivariate integer equation; factoring with high bits known,” Advances in Cryptology — EUROCRYPT '96, Ueli Maurer (Ed.), Springer LNCS Volume 1070, 1996, pages 178–189.
D. Coppersmith, “Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities,” Journal of Cryptology, Volume 10 Number 4, Autumn 1997, pages 233–260.
S. A. Vanstone and R. J. Zuccherato, “Elliptic curve cryptosystems using curves of smooth order over the ring Zn,” IEEE Trans. Inform. Theory, Volume IT-43, 1997, pages 1231–1237.
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© 1998 Springer-Verlag Berlin Heidelberg
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Coppersmith, D. (1998). Specialized integer factorization. In: Nyberg, K. (eds) Advances in Cryptology — EUROCRYPT'98. EUROCRYPT 1998. Lecture Notes in Computer Science, vol 1403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054152
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DOI: https://doi.org/10.1007/BFb0054152
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