Encrypted Matrix-Vector Products from Secret Dual Codes

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Motivated by applications to efficient secure computation, we consider the following problem of encrypted matrix–vector product (EMVP). Let $\mathbb F$ be a finite field. In an offline phase, a client uploads an encryption of a matrix $M \in \mathbb F^{m\times \ell}$ to a server, keeping only a short secret key. The server stores the encrypted matrix \(\hat{M}\). In the online phase, the client may repeatedly send encryptions \(\hat{ q}_i\) of query vectors \(q_i \in \mathbb F^\ell\), whi