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I am reading Applebaum et al..

In Lemma 1. (page 7), Applebaum et al. proved the decision to search reduction when the modulus $q=p^e$ for prime $p$.

In the proof, they define the hybrid distribution $A^i_{\mathbf{s},\chi}$ and say "By a hybrid argument and standard amplification techniques, we can use an algorithm $D$ that distinguishes between $A_{\mathbf{s},\chi}$ and $U$ to solve for $\mathbf{s^\prime}=\mathbf{s} \mod p$".

I don't understand this step clearly.

Also, I cannot find the full version that includes the "entire proof".

Could anyone please tell me the details about this step?

In particular, how to use the "standard amplification techniques"?

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    $\begingroup$ Did you contact the authors? Usually, they wrote an extended version of their papers. $\endgroup$ – kelalaka Feb 24 at 11:53
  • $\begingroup$ @kelalaka I have sent an email to all authors of this paper on 26.2.2020, but I have not received any reply yet. $\endgroup$ – M.Z. Mar 1 at 7:41

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