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 $\operatorname{Enc}_{\operatorname{pk}}(x,r)$ based 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.