| Presentation | 2010-05-21 Applying Numerical Analysis Technique To Prime Factorization Masaaki SHIRASE, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | It is important to analyze the hardness of prime factorization which the security of RSA cryptosystems is based on. There are some methods for solving prime factorization such as the p method, the p-1 method, the elliptic curve method, the quadratic sieve, and the number field method. The number field sieve is the current fastest algorithm for solving prime factorization, and is a semi-exponential time algorithm whose cost is O(exp((64/9)^<1/3>) (ln n)^<1/3> (ln ln n)^<2/3>). As sieves for solving discrete logarithm problem have improved, the number field sieve may be improved, however, the author thinks it is impossible that the number field sieve becomes a polynomial time algorithm. This report considers the possibility of further speed-up of prime factorization by constructing a "finding divisor function" F(n,x) whose zeros are divisors of n and by applying a numerical analysis technique to the function. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | prime factorization / RSA cryptosystem / numerical analysis |
| Paper # | ISEC2010-9 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2010/5/14(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Information Security (ISEC) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Applying Numerical Analysis Technique To Prime Factorization |
| Sub Title (in English) | |
| Keyword(1) | prime factorization |
| Keyword(2) | RSA cryptosystem |
| Keyword(3) | numerical analysis |
| 1st Author's Name | Masaaki SHIRASE |
| 1st Author's Affiliation | Future University Hakodate() |
| Date | 2010-05-21 |
| Paper # | ISEC2010-9 |
| Volume (vol) | vol.110 |
| Number (no) | 44 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |