# Tag Info

3

Is this hash almost-XOR-universal? No. Consider the two 1 block messages $M = \{0\}$ and $M' = \{2^{n-1}\}$. We have: $$H(M) = ((2\cdot 0 + 1)(2K+1) \bmod 2^{n+1}) /2 = K$$ and $$H(M') = ((2\cdot 2^{n-1} + 1)(2K+1) \bmod 2^{n+1})/ 2 = K + 2^{n-1} \bmod 2^n$$ As $H(M) \oplus H(M') = 2^{n-1}$ has a nontrivial probability of being true, $H$ is not ...

2

You can do either. In the first case you are going to have multiple tags, 1 for each chunk. In the latter, you will have a single tag. If you are downloading files that are approximately 1MB, I think #2 makes sense. If you are downloading files that are 1GB or 1TB, maybe #1 makes the most sense, as you can stop the download if one of the chunks is bad.

1

ANSI X9.9 uses DES for its crypto - these keys are 56 bits long, or 112 bits for 3DES. The financial world mostly moved to 3DES a few years back so keys will generally be 112 bits. Normally they have parity bits added (1 per 7 bits of key), so are transmitted as 64 bit (single DES) or 128 bit (triple DES) values. When presented in human-readable form, they ...

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