| Presentation | 2011-07-13 Solving DLP with Auxiliary Input over an Elliptic Curve Used in TinyTate Library(Part II) Yumi SAKEMI, Tetsuya IZU, Masahiko TAKENAKA, Masaya YASUDA, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find a positive integer α from elements G, αG, α^dG in an additive cyclic group generated by G of prime order r and a positive integer d dividing r-1. In 2010, Sakemi et al. implemented Cheon's algorithm for solving DLPwAI, and solved a DLPwAI in a group with 128-bit order r in about 131 hours with a single core on an elliptic curve defined over a prime finite field which is used in the TinyTate library for embedded cryptographic devices. However, since their implementation was based on Shanks' Baby-step Giant-step (BSGS) algorithm as a sub-algorithm, it required a large amount of memory (246 GByte) so that it was concluded that applying other DLPwAIs with larger parameter is infeasible. In this article, we implemented Cheon's algorithm based on Pollard's ρ-algorithm in order to reduce the required memory. As a result, we have succeeded solving the same DLPwAI in about 136 hours by a single core with less memory (0.5 MByte). |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Discrete logarithm problem with auxiliary input(DLPwAI) / Cheon's algorithm / implementation / TinyTate library |
| Paper # | ISEC2011-26,SITE2011-23,ICSS2011-31,EMM2011-25 |
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| Committee | SITE |
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| Conference Date | 2011/7/5(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Social Implications of Technology and Information Ethics (SITE) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Solving DLP with Auxiliary Input over an Elliptic Curve Used in TinyTate Library(Part II) |
| Sub Title (in English) | |
| Keyword(1) | Discrete logarithm problem with auxiliary input(DLPwAI) |
| Keyword(2) | Cheon's algorithm |
| Keyword(3) | implementation |
| Keyword(4) | TinyTate library |
| 1st Author's Name | Yumi SAKEMI |
| 1st Author's Affiliation | FUJITSU LABORATORIES Ltd., Secure Computing Lab.() |
| 2nd Author's Name | Tetsuya IZU |
| 2nd Author's Affiliation | FUJITSU LABORATORIES Ltd., Secure Computing Lab. |
| 3rd Author's Name | Masahiko TAKENAKA |
| 3rd Author's Affiliation | FUJITSU LABORATORIES Ltd., Secure Computing Lab. |
| 4th Author's Name | Masaya YASUDA |
| 4th Author's Affiliation | FUJITSU LABORATORIES Ltd., Secure Computing Lab. |
| Date | 2011-07-13 |
| Paper # | ISEC2011-26,SITE2011-23,ICSS2011-31,EMM2011-25 |
| Volume (vol) | vol.111 |
| Number (no) | 124 |
| Page | pp.pp.- |
| #Pages | 8 |
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