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Can we do modulus switching for number theoretic encryption such as Paillier or ElGamal?

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    $\begingroup$ In theory I guess you could, but what would be the purpose of it? $\endgroup$
    – pg1989
    Apr 28 '16 at 21:12
  • $\begingroup$ What is "modulus switching" ? $\endgroup$
    – fkraiem
    Apr 29 '16 at 1:55
  • $\begingroup$ @fkraiem Just change the modular to a larger number. Like FHE. $\endgroup$
    – Jan Leo
    Apr 29 '16 at 7:37
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Security goals like confidentiality is the reason to ask for encryption. Modulus is chosen (for particular group types) on the grounds of hard problems associated with that groups; encryption strength is defined by level of hardness of that problems.

It would be nice to discover a hard problem related to some change of modulus, comparable to indistinguishability of Diffie-Hellman tuples of 4 group elements for ElGamal or $n$-th roots for Paillier with modulus $n^2$.

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