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Feb 5, 2016 at 9:13 vote accept user153465
Feb 4, 2016 at 21:44 comment added fgrieu @user153465: the second paragraph in the answer tries to address that. The adversary is free to compute any function of $v_1$ and $v_2$, like $v_4(v_1,v_2)=(v_1+v_2)^{v_1-v_2}$, or $v_3(v_1,v_2)=v_1\cdot v_2$, anything goes, that has no influence on the demonstration given. This is just extra added to the question's statement, obscuring it, that we want to get rid of to focus on the expressions involving $a$, or $z_1$, $z_2$ or other things not known to the adversary.
Feb 4, 2016 at 9:26 comment added user153465 Thank you for the answer, it's very precise. I'm wondering why you did not discuss about $v_3$ in your answer. Why cannot we say $v_3$ contains random value $z_2$ that has already been used in $v_2$. Therefore, according to one-time-pad it may leak information as the random value has been used twice.
Feb 4, 2016 at 7:21 history edited fgrieu CC BY-SA 3.0
slightly simplify
Feb 4, 2016 at 7:16 history answered fgrieu CC BY-SA 3.0