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Consider I have two polynomials $f_1$ and $f_2$ of the same degree. I want to secure them (using any kind of encryption except FHE) and outsource them to an untrusted server. I want him to compute the least common multiple (LCM) of these two polynomials and return it to me.

  • Question: Is there any protocol supporting above scenario ?

Or

Consider a more simpler scenario:

I have $C_1= a\cdot b \bmod p$ and $C_2=a \cdot d \bmod p$, where $p$ is a prime number. I want to outsource $C_1$ and $C_2$ using any form of encryption (other than FHE) and want to delegate GCD computation on these two values to a server without he knows the result (which is $a$).

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What ring are those polynomials over? $\;$ –  Ricky Demer Dec 23 at 18:54
    
@RickyDemer can be a field e.g. $\mathbb{Z}_p$ –  user13676 yesterday

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