Group law and the Security of elliptic curves on F_p[e_1,...,e_n]F p [e1 ,...,e_n]
| Autor: | Chaichaa Abdelhak, Abdelalim Seddik, Souhail Mohamed |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Group Low
The Localization of the Ring Physics and Astronomy (miscellaneous) lcsh:T Group (mathematics) The maximal ideal Complexity lcsh:Technology Combinatorics Elliptic curve Management of Technology and Innovation The Discrete Logarithm Problem lcsh:Q lcsh:Science Engineering (miscellaneous) Mathematics |
| Zdroj: | Advances in Science, Technology and Engineering Systems, Vol 2, Iss 5, Pp 104-108 (2017) |
| ISSN: | 2415-6698 |
| DOI: | 10.25046/aj020517 |
| Popis: | In this paper, we study the elliptic curve E_{a,b}(A_P)E a,b (A P ), with A_PA P the localization of the ring A=F _p[e_1,...,e_n]A=F p [e 1 ,...,e n ] where e_ie_i=e_ie i e i =e i and e_ie_j=0e i e j =0 if i\neq ji≠j, in the maximal ideal P=(e_1,...,e_n)P=(e 1 ,...,e n ). Finally we show that Card(E_{a,b}(A_P))\geqslant (Card(E_{a,b}(F_p))-3)^n+Card(E_{a,b}(F_p))Card(E a,b (A P ))⩾(Card(E a,b (F p ))−3) n +Card(E a,b (F p )) and the execution time to solve the problem of discrete logarithm in E_{a,b}(A_P)E a,b (A P ) is \Omega(N)Ω(N), such that the execution time to solve the problem of discrete logarithm in E_{a,b}(F_p)E a,b (F p ) is O(\sqrt{N})O( N ). The motivation for this work came from search for new groups with intractable (DLP) discrete logarithm problem is there great importance. |
| Databáze: | OpenAIRE |
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