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 Paper Abstract and Keywords Presentation 2010-03-05 16:10 A study on the probabilistic algorithm to solve the elliptic curve discrete logarithm problemOsamu Ashihara, Yoshitaka Sagara, Nobuhide Sakuragi, Tomoko K. Matsushima (Polytechnic Univ.) Abstract (in Japanese) (See Japanese page) (in English) In this paper a probabilistic algorithm to solve the ECDLP is presented. This scheme uses the symmetry of the elliptic curve, and can be applied to a wide class of elliptic curves. In the proposed scheme a large number of random integers $H_i \in \{0,1,\cdots, g-1\} \; (i=1,2,\cdots)$ are generated to calculate the points $Q+[H_i]P \; (i=1,2,\cdots)$, where $Q = [K_{secret}]P$ and $g$ is the order of the point $P$. Then, the scheme tries to find a pair of points $Q+[H_i]P$ and $Q+[H_j]P$ whose $X$-coordinates are the same value but $H_i \ne H_j$, i.e., one in the pair is the inverse of the other. If such a pair is found, the secret $K_{secret}$ can be calculated by $2K_{secret}+H_i+H_j \equiv 0 \pmod{g}$. We investigate the probability to find such a pair among $m$ random points on an elliptic curve. The probability of finding one or more pairs would be 1/2 when $m$ is of the order of $\sqrt{g}$. Furthermore, we discuss the techniques to reduce the size of disk storage and to parallelize the operation with multiple computers. It is also shown that the proposed algorithm can be extended to solve the usual discrete logarithm problem (DLP). Keyword (in Japanese) (See Japanese page) (in English) ECDLP / elliptic curve / discrete logarithm problem / public key cryptography / / / / Reference Info. IEICE Tech. Rep., vol. 109, no. 445, ISEC2009-137, pp. 373-380, March 2010. Paper # ISEC2009-137 Date of Issue 2010-02-25 (IT, ISEC, WBS) ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380

 Conference Information Committee IT ISEC WBS Conference Date 2010-03-04 - 2010-03-05 Place (in Japanese) (See Japanese page) Place (in English) Nagano-Engineering Campus, Shinshu University Topics (in Japanese) (See Japanese page) Topics (in English) Paper Information Registration To ISEC Conference Code 2010-03-IT-ISEC-WBS Language English (Japanese title is available) Title (in Japanese) (See Japanese page) Sub Title (in Japanese) (See Japanese page) Title (in English) A study on the probabilistic algorithm to solve the elliptic curve discrete logarithm problem Sub Title (in English) Keyword(1) ECDLP Keyword(2) elliptic curve Keyword(3) discrete logarithm problem Keyword(4) public key cryptography Keyword(5) Keyword(6) Keyword(7) Keyword(8) 1st Author's Name Osamu Ashihara 1st Author's Affiliation Polytechnic University (Polytechnic Univ.) 2nd Author's Name Yoshitaka Sagara 2nd Author's Affiliation Polytechnic University (Polytechnic Univ.) 3rd Author's Name Nobuhide Sakuragi 3rd Author's Affiliation Polytechnic University (Polytechnic Univ.) 4th Author's Name Tomoko K. Matsushima 4th Author's Affiliation Polytechnic University (Polytechnic Univ.) 5th Author's Name 5th Author's Affiliation () 6th Author's Name 6th Author's Affiliation () 7th Author's Name 7th Author's Affiliation () 8th Author's Name 8th Author's Affiliation () 9th Author's Name 9th Author's Affiliation () 10th Author's Name 10th Author's Affiliation () 11th Author's Name 11th Author's Affiliation () 12th Author's Name 12th Author's Affiliation () 13th Author's Name 13th Author's Affiliation () 14th Author's Name 14th Author's Affiliation () 15th Author's Name 15th Author's Affiliation () 16th Author's Name 16th Author's Affiliation () 17th Author's Name 17th Author's Affiliation () 18th Author's Name 18th Author's Affiliation () Speaker 4 Date Time 2010-03-05 16:10:00 Presentation Time 25 Registration for ISEC Paper # IEICE-IT2009-129,IEICE-ISEC2009-137,IEICE-WBS2009-108 Volume (vol) IEICE-109 Number (no) no.444(IT), no.445(ISEC), no.446(WBS) Page pp.373-380 #Pages IEICE-8 Date of Issue IEICE-IT-2010-02-25,IEICE-ISEC-2010-02-25,IEICE-WBS-2010-02-25