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Given

  • two large primes $p$ and $q$,
  • two arbitrary odd integers $a$ and $b$,
  • $x \in Z_{n^2}^*$ where $n$ = $pq$,

find whether there exists numbers $c$ and $d$ that are distinct elements in $Z_{n^2} \setminus \{0,1\}$ such that $x = c^a.d^b \mod n^2$

I assume the problem is called higher residuosity problem if we ignore $b$ and $d$ and is easy to solve given the factorization?

  • Without at least a motivation for crypto use, I can't see why this isn't off topic. –  Sep 04 '14 at 17:57
  • I know questions must be beneficial to all and this one helps only me. But this is just a YES/NO question as to whether someone has come across a problem like this and if yes, probably a link would help. That's all. Thanks :) –  Sep 05 '14 at 04:40
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    Most cases you can solve by setting $d=1$. Do you have any further conditions on $x, a, b$ and $n$? – j.p. Sep 05 '14 at 12:00

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