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.