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0

We can present $\mathbb{Z}_m$ in different manner. For example, bellow sets are some equivalence classes of $\mathbb{Z}_3$ $$\{0,1,2\}, \{3,4,5\},\{-3,-2,-1\}. $$ Now, about your question If you select the numbers of $[-n,n]$ module a positive integer $m$ which $m\leq 2n+1$, you can construct $\mathbb{Z}_m$: $$\mathbb{Z}_m=\{i \pmod m \mid i\in[-n,n]\}$$ ...


7

What exactly does $0...0$ and $1...1$ mean usually? This simply means a (more or less) long string of $0$s or $1$s or more clearly $000000...000000$ and $111111...111111$. Related notiational notes, you may have to use soon: Sometimes the notation $0^n$ and $1^n$ is also used for these strings with exactly $n$ zeroes and ones. Even more generally ...


2

From context, it appears $\langle A,B \rangle$ simply denotes (some value unambiguously encoding) the pair of values $A$ and $B$. In general, when discussing high-level protocols, no specific encoding for such pairs (or more complex tuples of values) is specified. It is simply assumed that we can unambiguously store and transmit such structured data ...


-1

Triangular or angle-brackets represent inner product in linear algebra but it has nothing to do with the same notation in cryptography. Probably, that's why you're confused about it. I think, here it's used to show that $P_A$ "is made of" $X_A$ and $Y_A$. The reason I think so is that, there's such usage of angular brackets: $params= \langle G1, G2, e, ...



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