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Altcoin Roundup: Holding Bitcoin? Here’s how to put it to work in DeFi

BTC is back at all-time highs, meaning it’s even easier for holders to capitalize on the lucrative yield opportunities DeFi offers to investors who are willing to stake their tokens.

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.

Altcoin Roundup: Holding Bitcoin? Here’s how to put it to work in DeFi

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