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What do you mean by "at least as secure"?

They are different algorithms, so I don't see how their security can be provably related.



Saying "BLAKE2 is at least as secure as SHA-256" is saying that:

1. The best known attacks against SHA-256 have a cost of 2^i for some value of i.

2. The best known attacks against BLAKE2 have a cost of 2^j for some value of j.

3. j >= i




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