Abstract
We prove the extension of the Håstad algorithm to the multi-variable modular polynomial. Although the Håstad attack is one of the strongest known attacks on RSA-type cryptosystems, the original Håstad attack is generally not applicable to multi-variable cryptosystems, where the plain text space (the encryption domain) is multi-variable. As an application of our extension, we attack RSA-type cryptosystems over elliptic curves and show the critical number of encrypted texts.
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© 1996 Springer-Verlag Berlin Heidelberg
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Takagi, T., Naito, S. (1996). The multi-variable modular polynomial and its applications to cryptography. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009515
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DOI: https://doi.org/10.1007/BFb0009515
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