An interactive multi-party system for collaboratively performing homomorphic operations, such that no party has access to unencrypted data or an unencrypted operator. A first party device may add noise to encrypted data and an encrypted linear operator to generate noisy encrypted data and a noisy encrypted operator, and transmit the noisy encrypted data and operator to a second party device possessing a secret decryption key for the encryption. The second party device may decrypt the noisy encrypted data and noisy encrypted operator to generate unencrypted noisy data and an unencrypted noisy operator, solve the linear operation using the unencrypted noisy data and an unencrypted noisy operator to generate a noisy solution, encrypt the noisy solution to the linear operation, and transmit it to the first party device. The first party device may then cancel the noise of the encrypted noisy solution to generate the encrypted solution to the linear operation.