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Published in:
2014 | OriginalPaper | Chapter
Partial Key Exposure Attacks on Takagi’s Variant of RSA
Authors : Zhangjie Huang, Lei Hu, Jun Xu, Liqiang Peng, Yonghong Xie
Published in: Applied Cryptography and Network Security
Publisher: Springer International Publishing
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We present several attacks on a variant of RSA due to Takagi when different parts of the private exponent are known to an attacker. We consider three cases when the exposed bits are the most significant bits, the least significant bits and the middle bits of the private exponent respectively. Our approaches are based on Coppersmith’s method for finding small roots of modular polynomial equations. Our results extend the results of partial key exposure attacks on RSA of Ernst, Jochemsz, May and Weger (EUROCRYPT 2005) for moduli from
N
=
pq
to
N
=
p
r
q
(
r
≥ 2).