# computational indistinguishable/distinguishable?

Let $a,b,c,d$ be selected at random from $Z_q$. Consider the following two distributions $X_1$ and $Y_1$:

$X_1={(r_1\cdot a, r_2\cdot b, r_3\cdot c, (r_1+r_2-r_3)\cdot d)}$ where $r_1,r_2,r_3$ selected random from $Z_q$

$Y_1={(u_1,u_2,u_3,u_4)}$ where $u_1,u_2,u_3,u_4$ selected random from $Z_q$

I have two questions:

• Are these two distributions computationally indistinguishable?
• How should I formally write the proof?
• Looks like homework; I'll give a hint: the first distribution seems to have less entropy, i.e., less random values picked. Can you invent a way to check that? – Ruben De Smet Jun 1 '18 at 20:10
• No, this is not a homework assignment. I am working on a research project and things are boiled down to this. – mohsen pourpouneh Jun 1 '18 at 20:28
• This question is curiously similar to crypto.stackexchange.com/questions/59722/leak-information so maybe you two can collaborate if you are taking the same class. – kodlu Jun 2 '18 at 2:08
• Assuming that "selected (at) random" means with uniform distribution, what are the probabilities of the first components of $X_1$ rsp. $Y_1$ to be zero? What are the probabilities for $X_1$ rsp. $Y_1$ to be zero? – j.p. Jun 2 '18 at 19:25