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articles:mathematics:crypto:diffie-hellmann [2010/07/11 13:48] ali |
articles:mathematics:crypto:diffie-hellmann [2010/08/21 22:12] (current) ali |
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| <latex> | <latex> | ||
| \begin{eqnarray*} | \begin{eqnarray*} | ||
| - | \bar{a}&=&\{x\in\mathbb{Z},xRa\}\\ | + | \bar{a} & = &\{x\in\mathbb{Z},xRa\}\\ |
| &=& \{x\in\mathbb{Z},n\ divide\ x-a\}\\ | &=& \{x\in\mathbb{Z},n\ divide\ x-a\}\\ | ||
| &=& \{x\in\mathbb{Z},\exists{k}\in \mathbb{Z}\ such\ that\,x-a=kn\}.\\ | &=& \{x\in\mathbb{Z},\exists{k}\in \mathbb{Z}\ such\ that\,x-a=kn\}.\\ | ||
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| for n=7 let's calculate <latex>\bar{2}</latex>. | for n=7 let's calculate <latex>\bar{2}</latex>. | ||
| it is easy to see that the elements of <latex>\bar{2}</latex> are of the form: | it is easy to see that the elements of <latex>\bar{2}</latex> are of the form: | ||
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| <latex> | <latex> | ||
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| </latex> | </latex> | ||
| - | <note tip><latex>\bar{n}=\bar{0} \text{ in } \mathbb{Z}/n\mathbb{Z}</latex></note> | + | <note tip><latex> $\bar{n} = \bar{0} \text{ in } \mathbb{Z}/n\mathbb{Z}$</latex></note> |
| We note <latex>\mathcal{A}/R</latex> the set of the all equivalence classes of <latex>\mathcal{A}</latex> for the relation R, in particular for the relation defined above (1) on <latex>\mathbb{Z}</latex>, we note <latex>\mathbb{Z}/n\mathbb{Z}</latex> the set of equivalence classes of <latex>\mathbb{Z}</latex>. | We note <latex>\mathcal{A}/R</latex> the set of the all equivalence classes of <latex>\mathcal{A}</latex> for the relation R, in particular for the relation defined above (1) on <latex>\mathbb{Z}</latex>, we note <latex>\mathbb{Z}/n\mathbb{Z}</latex> the set of equivalence classes of <latex>\mathbb{Z}</latex>. | ||