Presentation | 2007-11-21 Small Secret Key Attack on Takagi's Variant of RSA (Part1) Noboru KUNIHIRO, Koichi ITOH, Kaoru KUROSAWA, |
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Abstract(in Japanese) | (See Japanese page) |
Abstract(in English) | For a variant of RSA with modulus N = p^rq and ed≡1 mod(p-1)(q-1), we show that a secret exponent d can be recovered in polynomial time if d < N^<(7-2√<7>/3(r+1)>. (Note that φ(N)≠(p-1)(q-1).) Boneh-Durfee's result for the standard RSA is obtained as a special case for r = 1. Our algorithm is based on Coppersmith's approach and is heuristic. Technically, we develop a method of a finding small root of a trivariate modular equation f(x,y,z)=x(y-1)(z-1)+1=0(mod e) under the condition such that y^rz = N. Our result cannot be obtained from the generic method of Jochemsz-May. We also performed some numerical experiments. In any examples, resultant was not vanished and the secret key was recovered. |
Keyword(in Japanese) | (See Japanese page) |
Keyword(in English) | lattice / LLL / trivariate polynomial / RSA |
Paper # | ISEC2007-90,OIS2007-62 |
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Committee | ISEC |
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Conference Date | 2007/11/14(1days) |
Place (in Japanese) | (See Japanese page) |
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Topics (in Japanese) | (See Japanese page) |
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Paper Information | |
Registration To | Information Security (ISEC) |
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Language | ENG |
Title (in Japanese) | (See Japanese page) |
Sub Title (in Japanese) | (See Japanese page) |
Title (in English) | Small Secret Key Attack on Takagi's Variant of RSA (Part1) |
Sub Title (in English) | |
Keyword(1) | lattice |
Keyword(2) | LLL |
Keyword(3) | trivariate polynomial |
Keyword(4) | RSA |
1st Author's Name | Noboru KUNIHIRO |
1st Author's Affiliation | The University of Electro-Communications() |
2nd Author's Name | Koichi ITOH |
2nd Author's Affiliation | Fujitsu Labs |
3rd Author's Name | Kaoru KUROSAWA |
3rd Author's Affiliation | Ibaraki University |
Date | 2007-11-21 |
Paper # | ISEC2007-90,OIS2007-62 |
Volume (vol) | vol.107 |
Number (no) | 345 |
Page | pp.pp.- |
#Pages | 8 |
Date of Issue |