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# System prepended metadata

title: 資安導論 HW5

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# 資安導論 HW5

### (a)
P 不等於 Q
$\lambda=(\frac{4-7}{5-1})\ mod\ p\ if\ {p\neq Q}$
$=\frac{-3}{4}=5 (mod23)$
$X_R =(5^2-1-7)=17(mod23)$
$Y_R =(5\times(1-17)-7)=5(mod23)$
$\therefore P+Q=(17,5)$

### (b)
P 等於 Q
$\lambda=\frac{3\times1^2+1}{2\times7}=\frac{2}{7}=20(mod23)$
$X_R =(20^2-1-1)=7(mod23)$
$Y_R =(20\times(1-7)-7)=11(mod23)$
$\therefore 2P=(7,11)$
