I was wondering if someone could explain the Digit Extraction from HElib in simple words:

Apply a homomorphic (non-linear) digit-extraction procedure, computing $r$ ciphertexts that contain the digits $e − e′ + r − 1$ through $e − e′$ of the integers in the slots, respectively, relative to plaintext space mod-$p^r$. This requires that we generalize the bit-extraction procedure from [21] to a digit-extraction procedure for any prime power $p^r \ge 2$, this is done in Section 5.3. Once we extracted all these digits, we can combine them to get an encryption of the coefficients of $m$ in the slots relative to plaintext space modulo $p^r$.

  • $\begingroup$ I've added the relevant section to the question. Please point out what you don't understand from it, as others may find that a reasonable explanation. $\endgroup$
    – Maarten Bodewes
    Commented Jan 25 at 15:18
  • $\begingroup$ @MaartenBodewes Op simply doesn't want to read the referred article that the quote only mention it. $\endgroup$
    – kelalaka
    Commented Jan 25 at 16:34
  • $\begingroup$ I don't make those kind of assumptions, but as it is the question will probably be closed as "too broad". $\endgroup$
    – Maarten Bodewes
    Commented Jan 25 at 17:06
  • $\begingroup$ @MaartenBodewes, Thank you for the precise answer and for allowing me to narrow down my question. I will come back with more intelligent question if this question survives :-) $\endgroup$
    – kindi
    Commented Jan 25 at 18:31
  • $\begingroup$ @kelalaka, I have gone through so many articles/codes/other-materials to understand the tricks behind bootstrapping. Probably I might not have proper mathematical background to understand it. I will keep trying regardless of my inefficacy and online bullying. There always exists some altruist people (like @MaarteenBodewes) to help others. $\endgroup$
    – kindi
    Commented Jan 25 at 18:50


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