<p>This work investigates the design problem of the non-strict stealthy attack strategy against the system state estimation. Distinct from the relevant results in which only historical data at a fixed time interval or side information are considered, a non-strict stealthy attack model with utilization of side information and maximum integration of historical data is proposed, which fully utilizes the intercepted data and additional measurement based on the storage capability and extra sensors with the aim of synergistically deteriorating the system estimation performance. Then, the recursion of the estimation error is derived to evaluate the impact caused by the attack, which is more complicated since the maximum integration of historical data leads to more intricate relationships between the partial terms. For the transformed constrained multi-variable optimization problem with more decision variables and the larger search space of the optimal solution, the optimal covariance of the modified innovation is derived by utilizing the Lagrange multiplier method and proved to be time-invariant. After that, the optimal attack matrices are integrated into a combinatorial form and obtained based on the semi-definite programming. Finally, the validity of the theoretical analysis is verified with the given simulation examples.</p>