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While not saying how they did it, shouldn't they be able to prove it? By showing some colliding hashes or so?

It's not just that, they're claiming computationally feasible preimage attack, something which AFAIK has not been feasibly achieved in SHA1 (SHAttered is a collision attack).

A preimage attack still isn't feasible for MD5. What an absolutely ridiculous claim they made.

To play devil's advocate, the hashes might imply details of how it was done.

Unlikely, but regardless if they have a preimage attack they could simply release a collision.

That is a much lower standard than a preimage (and trivial if you do have the computational ability to preimage), and was sufficient to declare SHA1 broken (SHAttered is a public collision, AFAIK there still is no preimage against a "full strength" SHA1).

There's no feasible preimage against even md5 still.

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