# Proving if two samples hides a value?

Given two values

• $$r'-r \mod q$$
• $$i - r \mod q$$

Where

• $$r',r$$ sampled randomly from $$Z_q$$
• while i is pick arbitrarily from $$Z_q$$ and a secret

Can we claim that this hides $$i$$?

Here is my sketch: Distribution of above samples is indistinguishable to

• $$r'' \mod q$$
• $$i - r \mod q$$

Where $$r''$$ is randomly picked from $$Z_q$$ If that is true then clearly it is indistinguishable from following as r is randomly picked

• $$r'' \mod q$$
• $$r''' \mod q$$

$$r'''$$ is randomly picked from $$Z_q$$

• Welcome to Cryptography.SE Why there are two values? The second is enough. What is the probability of an adversary guessing $i$ from $i - r \bmod q$ ($Q$ is really bad there)? Nov 13 at 23:19
• @kelalaka problem definition require sending two samples structured the way I mentioned above, $Q$ is quite bit lets say 128 bits long Nov 13 at 23:23
• I think the question ask to use contrapositive, assume it doesn't hide, then you can get $r$ there you can conclude that the adversary can find the random coins. Nov 14 at 0:16
• Note that this is considered homework and hints should and have been given in the comments... Nov 14 at 0:51
• it is not an homework though this is part of larger problem that I am proving Nov 14 at 1:03