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The notation $H:\mathbb G_1\to\{0,1\}^n$ means that $H$ takes as input an element of $\mathbb G_1$, and produces as output an $n$-bit bistring. The notation $H_1:\mathbb G_2\to\{0,1\}^n$ similarly means that $H_1$ takes as input an element of $\mathbb G_2$, and produces as output an $n$-bit bistring. The notation $H_2:\{0,1\}^n\times\{0,1\}^n\to\{0,1\}^n$ ...


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