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this post was submitted on 11 Feb 2024
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Even for a 4096 bit hash (which isn't used afaik, usually only 1024 bit is used (but this could be outdated)), you only need to change 4096 bits on average. Even for a still 1080p image, that's 1920x1080 pixels. If you change the least significant bit of each color channel, you get 6,220,800 bits you can change within anyone noticing. That means on average there are 1,518 identical-looking variations of any image with a given 4096 bit hash, on average. This goes down a lot when you factor in compression: those least significant bits aren't going to stay the same. But using a video brings it up by orders of magnitude: rather than one image, you can tweak colors in every frame The difficulty doesn't come from the existence, it comes because you need to check 2⁵¹² = 10¹⁵⁴ different images to guarantee you'll find a match. Hash functions are designed to take a while to compute, so you'd have to run a supercomputer for an extremely long time to brute force a hash collision
Most hash functions are 256 bit (they're symmetric functions, they don't need more in most cases).
There are arbitrary length functions (called XOF instead of hash) which built similarly (used when you need to generate longer random looking outputs).
Other than that, yeah, math shows you don't need to change more data in the file than the length of the hash function internal state or output length (whichever is less) to create a collision. The reason they're still secure is because it's still extremely difficult to reverse the function or bruteforce 2^256 possible inputs.
Yeah I was using a high length at first because even if you overestimate, that's still a lot. I did 512 for the second because I don't know a ton about cryptography but that's the largest SHA output