Before revision:  This was subsequently improved to a 1/\sqrt{\varepsilon\mathcal{O}\left({\varepsilon^{4/p}}\cdot n^{1-2/p}}\right) \mathcal{O}\left({\varepsilon^{4/p}}\cdot n^{1-2/p}}\right)  the first optimal dependence on the approximation factor. As in previous work, we obtain a general transformation that applies to any non-robust streaming algorithm and depends on the so-called flip number. However, the key technical innovation is that we apply the transformation to what we call a difference estimator for the streaming problem, rather than an estimator for the streaming problem itself. We then develop the first difference estimators for a wide range of problems. Our difference estimator methodology is not only applicable to the adversarially robust model, but to other streaming models where temporal properties of the data play a central role.(Abstract shortened to meet arXiv limit.)\left({\varepsilon^2}\cdot n^{1-2/p}}\right) 
After revision:  This was subsequently improved to a 1/\sqrt{\varepsilon\mathcal{O}\left({\varepsilon^{4/p}}\cdot n^{1-2/p}}\right) \mathcal{O}\left({\varepsilon^{4/p}}\cdot n^{1-2/p}}\right) the first optimal multi-pass F_p estimation algorithm up to \log n factors. Finally, we give an improved lower bound of \Omega\left({\varepsilon^2}\cdot n^{1-2/p}}\right)