{"slug": "gram-moments-and-pairwise-mixing-of-aes", "title": "Gram Moments and Pairwise Mixing of AES", "summary": "A new proof establishes that 4k+4 rounds of AES with independent uniform round keys, sampled once and retained across evaluations, have pairwise total variation distance below 2^{-14.3-73.1k} for every integer k≥0, tightening earlier almost-pairwise-independence analyses of the cipher. The work bounds local difference channels on additive maximum distance separable codes by retaining squared overlaps between channel responses as the second moment of a Gram matrix, separating activity-pattern error from residual variation across one to four words. As a result, 12, 16, and 20 AES rounds suffice for statistical accuracy of 2^{-128}, 2^{-192}, and 2^{-256} respectively, controlling any classical algorithm with a finite private seed making at most two adaptive forward queries.", "body_md": "Almost pairwise independence measures how closely a block cipher reproduces the joint output distribution of a uniform random permutation on two distinct plaintexts. Recent analyses of AES with independent round keys combine\nsmoothing from a fixed input difference with contraction over later rounds. The central difficulty is to control the dependencies created by diffusion. We develop a bound for local difference channels on additive maximum distance separable codes that retains the squared overlaps between channel responses, expressed as the second moment of a Gram matrix. This refines the activity-space analysis and strengthens both the initial estimate and the repeated contraction.\nWe prove that, for every integer $k\\ge0$, $4k+4$ rounds of AES with independent uniform round keys, sampled once and retained across evaluations, have pairwise total variation distance below $2^{-14.3-73.1k}$. The proof separates activity-pattern error from residual variation involving one, two, three, or four words. A fixed five-component comparison propagates these errors through each additional four-round block. Consequently, 12, 16, and 20 rounds suffice for statistical accuracy $2^{-128}$, $2^{-192}$, and $2^{-256}$, respectively. These bounds control the complete view of any classical algorithm with a finite private seed making at most two adaptive forward queries.", "url": "https://wpnews.pro/news/gram-moments-and-pairwise-mixing-of-aes", "canonical_source": "https://eprint.iacr.org/2026/2304", "published_at": "2026-10-01 22:45:14+00:00", "updated_at": "2026-10-19 10:47:10.658125+00:00", "lang": "en", "topics": ["artificial-intelligence", "machine-learning"], "entities": ["AES"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/gram-moments-and-pairwise-mixing-of-aes", "markdown": "https://wpnews.pro/news/gram-moments-and-pairwise-mixing-of-aes.md", "text": "https://wpnews.pro/news/gram-moments-and-pairwise-mixing-of-aes.txt", "jsonld": "https://wpnews.pro/news/gram-moments-and-pairwise-mixing-of-aes.jsonld"}}