@inproceedings{1933ae96b0d8446ebec66e996de96cb7,
title = "The multi-variable modular polynomial and its applications to cryptography",
abstract = "We prove the extension of the H{\aa}stad algorithm to the multi-variable modular polynomial. Although the H{\aa}stad attack is one of the strongest known attacks on RSA-type cryptosystems, the original H{\aa}stad 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.",
author = "Tsuyoshi Takagi and Shozo Naito",
year = "1996",
month = jan,
day = "1",
doi = "10.1007/bfb0009515",
language = "English",
isbn = "3540620486",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "386--396",
editor = "Tetsuo Asano and Yoshihide Igarashi and Hiroshi Nagamochi and Satoru Miyano and Subhash Suri",
booktitle = "Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings",
address = "Germany",
note = "7th International Symposium on Algorithms and Computation, ISAAC 1996 ; Conference date: 16-12-1996 Through 18-12-1996",
}