We have no reason to believe that Apple's second, secret perceptual hash provides any meaningful protection against such attacks. At best, we can hope that it'll allow early detection of attacks in a few cases, but chances are that's the best it can do. We might not ever learn: Apple now has a very strong incentive not to admit to any evidence of abuse or to any faults in their algorithm.
(Sorry, this is going to be long. I know understand most/all of this stuff, it's mostly there to provide a bit of context for the users reading our exchange)
The term "hash function" is a bit of a misnomer here. When people hear "hash", they tend to think about cryptographic hash functions, such as SHA256 or BLAKE3. When two messages have the same hash value, we say that they collide. Fortunately, cryptographic hash functions have several good properties associated with them: for example, there is no known way to generate a message that yields a given predetermined hash value, no known way to find two different messages with the same hash value, and no known way to make a small change to a message without changing the corresponding hash value. These properties make cryptographic hash functions secure, trustworthy and collision-resistant even in the face of powerful adversaries. Generally, when you decide to use two unrelated cryptographic hash algorithms instead of one, executing a preimage attacks against both hashes becomes much more difficult for the adversary.
However, as you know, the hash functions that Apple uses for identifying CSAM images are not "cryptographic hash functions" at all. They are "perceptual hash functions". The purpose of a perceptual hash is the exact opposite of a cryptographic hash: two images that humans see/hear/perceive (hence the term perceptual) to be the same or similar should have the same perceptual hash. There is no known perceptual hash function that remains secure and trustworthy in any sense in the face of (even unsophisticated) adversaries. In particular, preimage attacks against perceptual hashes are very easy, compared to the same attacks against cryptographic hashes.
Using two unrelated cryptographic hashes meaningfully increases resistance to collision and preimage attacks. Using ROT13 twice does not increase security in any meaningful sense. Using two perceptual hashes, while not as bad, is still much closer to the "using ROT13 twice for added security" than to the "using multiple cryptographic hashes" end.
Finding a SHA1 collision took 22 years, and there are still no effective preimage attacks against it. Creating the NeuralHash collider took a single week. More importantly, even if you were to use two unrelated perceptual hash functions, executing a preimage attacks against both hashes need not become much more difficult for the adversary: easy * easy is still easy. Layering cryptography upon cryptography is meaningful, but only as long as one of the layers is actually difficult to attack. This is not the case for perceptual hashes. In fact, in many similar contexts, these adversarial attacks tend to transfer: if they work against one technique or model, they often work against other models as well [3]. In the attack discussed above, the adversary has nearly full control over the "visual derivative", so even a very unsophisticated adversary can subject the target thumbnail itself to the collider before performing the resizing attack, and hope that it transfers against the second hash. If the second hash is a variant of NeuralHash (somewhat likely, it could even be NeuralHash performed on the thumbnail itself; we don't know anything about it!), or if it's a ML model trained on the same or similar datasets (quite likely), or if it's one of the known algorithms (say PhotoDNA) then some amount of transfer is likely to happen. And given an adversary that is going to distribute a large number of photos anyway, a 10% success rate is more than enough. Given the diminished state space (fixed size thumbnails, almost certainly smaller than 64x64 for legal reasons), a 10% success rate is completely plausible even with these naive approaches. An adversary that has some (even very little information) about the second hash algorithm can do much more sophisticated stuff, and perform much better.
But what if we boldly rule out all transfer results? Doesn't Apple keep their algorithm secret?! Can we think of the weights (coefficients) of the second perceptual hash as some kind of secret key in the cryptographical sense? Alas, no. Apple would have to make sure that all the outputs of the secret perceptual hash are kept secret as well. Due to the way perceptual hashing algorithms work, they provide a natural training gradient having access to sufficiently many input-outputs examples is probably enough to train a high-fidelity "clone" that allows one to generate adversarial examples and perform successful preimage attacks even if the weights of the clone are completely different from the secret weights of the original network. This can be done with standard black box techniques [4]. It's much harder (but nowhere near crypto hard, still perfectly plausible) to pull this off when they have access to one bit of output (match or no match). A single compromised Apple employee can gather enough data to do this given the ability to observe some inputs and outputs, even if said employee has no access to the innards or the magic numbers. The hash algorithm is kept secret because if it wasn't, an attack would be completely trivial: but an adversary does not need to learn this secret to mount an effective attack.
These are just two scenarios. There are many others. "Nobody has ever demonstrated such an attack working end-to-end" is not a good defense: it's been two weeks since the system was rolled out, and once an attack is executed, we probably won't learn about it for years to come. But the attacker can be rewarded way before "due process" kicks in: e.g. if a victim ever gets a job where they need to obtain a security clearance, the Background Investigation Process will reveal their "digital footprint", almost certainly including the fact that the NCMEC got a report about them, even if the FBI never followed up on it. That will prevent them from being granted interim determination, and will probably lead to them being denied a security clearance. If you pull off this attack on your political opponents, you can prevent them from getting government jobs, possibly without them ever learning why. And again, this is one single proposed attack. There were at least 6 different attacks proposed by regular HN users in the recent threads!
As a more general observation, cryptography tends to be resistant to attacks only if one can say things such as "the adversary cannot be successful unless they know some piece of information k, and we have very good mathematical reasons (e.g. computational hardness) to believe that they can't learn k". The technology is flawed: even the state-of-the-art in perceptual hashes does not satisfy this criterion. Currently, they are at best technicool gadgets, but layering technicool upon technicool cannot make their system more secure.And Apple's system is a high-profile target if there ever was one.
Barring a major breakthrough in perceptual hashing (one that Apple decided to keep secret and leave out of both whitepapers), the claim that the secret second hash will prevent collision attacks is not justified. The chances of such a secret breakthrough are very slim: it'd be like learning that SpaceX has already built a base on the Moon and has been doing regular supply runs with secret spaceships. Vaguely plausible in theory (SpaceX has people who do rocketry, Apple has people who do cybersecurity), but vanishingly unlikely in practice.
And that's before we mention that the mere existence of the collider made the entire exercise completely pointless: the real pedos can now use the collider to effectively anonymize their CSAM drops, making sure that all of their content collides with innocnent photos, and ensuring that none of the images will be picked up by NeuralHash anyway. For all practical purposes, Apple's CSAM detection is now _only_ an attack vector, and nothing else.
[3] https://arxiv.org/abs/1809.02861
[4] https://towardsdatascience.com/adversarial-attacks-in-machin...