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There are libraries allowing to do that: PBC: C library JPBC : Java library Hope it helps.


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One way to do this, if you're working with a multiplicative group $Z^*_p$, is to pick a prime $p$ so that $p-1$ has a large prime factor $q$; once you have this, then to generate a generator of order $q$, you pick a random value $h$, compute $g = h^{(p-1)/q}$, and if that is not 1, then $g$ is a generator of your group. Obvious questions: How do you find ...


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The simplest case for you is to consider prime number p of the form $p=2.p_1+1$. Where p1 is also prime. The structure of the multiplicative group of $\mathbb{Z}_n = \{1,2, ... ,p-1 \}$ splits into 3 subgroups of order 2, $p_1$, p-1. Only quadratic non residue residue have maximal order. elements of order 2 are 1 and p-1. The quadratic residue are those ...



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