The problem of extracting the highest possible amount of key-related information using the lowest possible number of measurements is one of the central questions in side-channel attacks against embedded implementations of cryptographic algorithms. To address it, this work proposes a novel framework enhancing side-channel collision attacks with divide-and-conquer attacks such as differential power analysis (DPA). An information-theoretical metric is introduced for the evaluation of collision detection efficiency. Improved methods of dimension reduction for side-channel traces are developed based on a statistical model of euclidean distance. Experimental results confirm that DPA-combined collision attacks are superior to both DPA-only and collision-only attacks. The new methods of dimension reduction lead to further complexity improvements. All attacks are treated for the case of AES-128 and are practically validated on a widespread 8-bit RISC microcontroller.