Schnorr group

A Schnorr group, proposed by Claus P. Schnorr, is a large prime-order subgroup of ${\displaystyle \mathbb {Z} _{p}^{\times }}$, the multiplicative group of integers modulo ${\displaystyle p}$ for some prime ${\displaystyle p}$. To generate such a group, generate ${\displaystyle p}$, ${\displaystyle q}$, ${\displaystyle r}$ such that

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