Given two values

  • $r'-r \mod q$
  • $i - r \mod q$


  • $r',r$ 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 $Z_q$

  • $\begingroup$ 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)? $\endgroup$
    – kelalaka
    Nov 13 at 23:19
  • $\begingroup$ @kelalaka problem definition require sending two samples structured the way I mentioned above, $Q$ is quite bit lets say 128 bits long $\endgroup$ Nov 13 at 23:23
  • 1
    $\begingroup$ 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. $\endgroup$
    – kelalaka
    Nov 14 at 0:16
  • $\begingroup$ Note that this is considered homework and hints should and have been given in the comments... $\endgroup$
    – Maarten Bodewes
    Nov 14 at 0:51
  • $\begingroup$ it is not an homework though this is part of larger problem that I am proving $\endgroup$ Nov 14 at 1:03


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