Congruences

2020-01-04 本文已影响0人张如成

Basic symbols

Let $Z_{n}$ denotes all the integers model $n$ , which can also be written as $[n]$ , for example:

$Z_{2}=[-2,-1,0,1,2]$ , $Z_{5}=[-5,-4,-3,-2,-1,0,1,2,3,4,5]$

while in the cryptography world, we hope each element in an integer set should have a inverse.

Unfortunately, not every $Z_{n}$ satisfy, so we introduce a new notion $Z_{n}^*$ .

Let $Z_{n}^*$ denotes all the subset in $Z_{n}$ , let $\alpha \in Z_{n}^*$ , then $\alpha$ should have a inverse integer $\frac{1}{\alpha }$ which also belongs to $Z_{n}^*$ , we list the elements of $Z_{15}^*$ , and for each $\alpha \in Z_{15}^*$ , we also have $\frac{1}{\alpha }$ .

Congruences

Basic symbols

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