# Key Pair generation

There are \(n\) users. Each is assigned a unique integer \(i \in [1, q)\). Typically those are \(1 \leq i \leq n\). Each user generates a private key \(x_i \in Z_q^*\) and the corresponding public key \({y_i}_0 = G_0^{x_i}\), \({y_i}_1 = G_1^{x_i}\).

The private key is kept private and the public key is published.