Congruences

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 } .

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