# Questions about Private Oblivious Transfer Protocol

1. The receiver R chooses $$a,b,r$$ and computes as follows:

If σ = 0 then $$A = (g^a, g^b, g^{ab},g^r)$$.

If σ = 1 then $$A = (g^a, g^b, g^r, g^{ab})$$. R sends $$A$$ to S.

2. Denote $$(x,y,z_0,z_1)$$ the tuple received by S. Then, S checks that $$(x,y,z_0,z_1)\in G$$ and that $$z_0 \neq z_1$$. If not, it aborts outputting ⊥.

Otherwise, S chooses random $$u_0,u_1,v_0,v_1$$($$\in{1,2,...,q}$$) and computes the following four values:

$$w_0 = x^{u_0}·g^{v_0}$$, $$k_0 = {z_0}^{u_0}·y^{v_0}$$

$$w_1 = x^{u_1}·g^{v_1}$$, $$k_1 = {z_1}^{u_1}·y^{v_1}$$

S then encrypts $$m_0$$ under $$k_0$$ and $$m_1$$ under $$k_1$$.....

Here are my questions: Is it must necessary to choose random $$u_0,u_1,v_0,v_1$$, and what if $$u_0 = u_1, v_0 = v_1$$, in which situation the OT protocol seems work well and property of privacy keep unchanged.