We prove that \(4r + 4\) rounds of an AES variant with independent and uniform random round keys are \(\varepsilon \) -close to pairwise independent with \(\varepsilon = 2^{14}\, 2^{-40r}\) . This result follows from a near-optimal bound for a two-norm version of pairwise independence for the Shark construction, depending on the third singular value of the difference-distribution table of the S-boxes. Our analysis combines insights from cryptanalysis—in particular, truncated differentials—and linear algebra over the reals.