We study problems in the white-box adversarially robust streaming model. Recently, the question of adversarially robust streaming, where the stream is allowed to depend on the randomness of the streaming algorithm, has gained a lot of attention. In this work, we consider a strong white-box adversarial model (Ajtai et al. PODS 2022), in which the adversary has access to all past random coins and the parameters used by the streaming algorithm. We also consider and define a related white-box adversarially robust distributed model. We consider the sparse recovery problem, which has been used for tasks such as distinct element estimation, low rank approximation of matrices and tensors, and finding a maximum matching. The main drawback of all previous work is that it requires a random oracle, which is especially problematic in the streaming model since the amount of randomness is counted in the space complexity of a streaming algorithm. Another issue with previous constructions is that many of them suffer from either large update time or rely on non-standard cryptographic assumptions. We construct a near-optimal solution for the sparse recovery problem in white-box adversarial streams, based on the more standard subexponentially secure Learning with Errors assumption. Importantly, our solution is the first without a random oracle and with polylogarithmic per item processing time. We also give related results in the distributed model. Our constructions are based on homomorphic encryption schemes satisfying very mild structural properties that are currently satisfied by most known schemes.