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Poly1305 itself has the requirement that its keys can only ever be used to generate a tag for a single message. That means that when Poly1305-AES (or another Poly1305-based authenticated encryption algorithm) is used as intended, the Poly1305 authentication key will be different for each message even if a key is reused. However, the various Poly1305-based ...


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The MAC under attack is built from a hash $h$ (assumed to process a hashed message by splitting it in blocks processed only once, as most hashes do), with a key split into $K_1$ and $K_2$ of equal size. It computes the MAC of a message $x$ as $$\operatorname{MAC}_{K_1\mathbin\|K_2}(x)=h(K_1\mathbin\|x\mathbin\|K_2)$$ The attack in the paper recovers $K_1$ ...


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Can we get the $msg$ from this? Yes, as long as we know the nonces, and as long as $msg$ is no more than $128n$ bits long, and $n$ isn't too incredibly huge (the latter might not be a required assumption, I just need it for my approach). Poly1305 can be modeled as computing a tag this way: $$tag = c_a r^a + c_{a-1} r^{a-1} + … + c_1 r^1 + z - 2^{128} k \...


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