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Witness Recovery in SPDZ Offline Phase

I am currently reading SPDZ: https://eprint.iacr.org/2011/535.pdf. The MPC protocol uses an encryption scheme $operatorname{Enc}_{operatorname{pk}}(x,r)$ bases on Brakerski, V. Vaikuntanathan (Gentry) (e.g. https://link.springer.com/chapter/10.1007/978-3-642-22792-9_29) in the offline phase. Here $operatorname{pk}$ is the public key, $x$ the message, r the randomness used in the encryption. Is there a (reasonably fast) way to recover $x$ and $r$ from $operatorname{Enc}_{operatorname{pk}}(x,r)$::Listen

I am currently reading SPDZ: https://eprint.iacr.org/2011/535.pdf.
The MPC protocol uses an encryption scheme $operatorname{Enc}_{operatorname{pk}}(x,r)$ bases on Brakerski, V. Vaikuntanathan (Gentry) (e.g. https://link.springer.com/chapter/10.1007/978-3-642-22792-9_29) in the offline phase. Here $operatorname{pk}$ is the public key, $x$ the message, r the randomness used in the encryption. Is there a (reasonably fast) way to recover $x$ and $r$ from $operatorname{Enc}_{operatorname{pk}}(x,r)$ given the secret key $operatorname{sk}$.
E.g. Party 1 has $operatorname{sk}$, Party 2 constructs and broadcasts $operatorname{Enc}_{operatorname{pk}}(x,r)$, Party 1 wants to recover $x,r$. Note that Party 1 immediately gets $x!! mod p$ (for $p$ the plaintext modulus, $q$ the ciphertext modulus). It would also be helpful to find some $(x’,r’)$ with $|x’|_{infty}leq B_{plain}$, $|r’_i|_{infty}leq B_{rand}$ given the assumption that the original $x,r$ satisfied these bounds $|x|_{infty}leq B_{plain}$, $|r_i|_{infty}leq B_{rand}$. ($r=(r_1,r_2,r_3)=(u,v,w)$).
Any thoughts are highly appreciated – thank you in advance.

Coinbase NFT Marketplace Waitlist Soars Past 1.5 Million

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