Ah, thanks for the correction. Do I have the soundness bit right? I guess it might apply even if the proof system is only computationally sound, since the simulator has to be efficient, right?
Cryptographer here, but this is not my area and I've only skimmed the paper. As far as I can tell, it's a purely theoretical result but a really cool one. Wall of text that might be wrong, as a rough summary of the result as I understand it:
There are different definitions of "zk", of "proof". Eg do "proofs" of false statements not exist, or are they just hard to find? If they exist but are hard to find, then it's often called an "argument" instead, which is the "AR" in zk-SNARKs and zk-STARKs.
One common definition of zero-knowledge protocols is that you can make an efficient simulator that makes convincing transcripts of the protocol without knowing the relevant secret (up to and including whether the statement to be proved/argued is even true). For interactive proofs, the simulator is usually supposed to output a transcript of the messages sent between the prover and the verifier, and the trick to making the simulator work is to choose later messages before earlier ones (e.g. challenges before commitments). But in non-interactive proofs, there's only one message, so that trick doesn't work and the simulator would have to output the proof itself.
The Goldreich-Oren result shows that this definition of ZK conflicts with soundness, unless the type of problem you're doing ZK proofs for was easy to begin with. IIUC this is for a simple reason: if a simulator can efficiently output a convincing proof of any true statement of the type your zk proof system covers (this is the zero-knowledge property); and if for false statements there is no proof that will convince the verifier (soundness); then you have an efficient algorithm for checking whether the statement is true or not, which is just to check whether your simulator convinces the verifier. This means that the underlying problem is by definition easy, so there's not much point to having zk proofs for it.
Goldreich-Oren doesn't apply to zk-SNARKs or zk-STARKs, because they are not perfectly sound, and in particular because you can get around the impossibility using the trusted setup in zk-SNARKs (essentially a secret key that lets you efficiently prove false statements) and/or by messing around with the random oracle model (pretend that the hash functions are replaced by magic, and then let the simulator tinker with that magic). Also zk-S?ARKs are arguments of knowledge (not just e.g. "a discrete log of this point exists" but "the prover knows the discrete log") which also changes the model.
As I understand it, the new result is basically to make your proof a NIWI-proof ("Non-Interactive Witness Indistinguishable proof", a weaker notion of zk-proof) that:
* Either [real statement you're trying to prove]
* or else [false statement that's almost impossible to prove false], e.g. "there are contradictions in your axiom system".
Such a proof can be made perfectly sound, since NIWI can be perfectly sound, and the second half is supposed to be false. There's no simulator, but if the false statement were true then there would be a simulator, where you always feed the NIWI eg a contradiction in the axiom system, instead of a proof of the real statement. (The definition of NIWI is that it should be hard to distinguish the proof resulting from these two cases.) The new paper also argues that this result, where there's no simulator but it's hard to prove that there's no simulator, is almost as good as the simulator actually existing.
Probably in practice you wouldn't do this, but you would instead try to make sure that a zk-SNARK, zk-STARK, NIWI etc is good enough in your use case.
I've hung out with a lot of pharma folks, and the business is really complicated. Most of the companies aim to both help people and to make a lot of money, and will choose projects based on some balance of those -- sometimes in dubiously ethical ways (e.g. tweaking formulations of existing products to extend the patent) and sometimes in basically fine ways (e.g. lots of the improvements in diabetes management which have helped a ton of people; at least the targeting is fine here though often not the pricing). Obviously chronic diseases that affect lots of rich people are a prime target to make money, so drug companies make lots of drugs for these, and they usually aren't curative because chronic diseases are hard to cure (but see e.g. Hep C which is now curable). There are also companies with rich investors who want to cure death, or at least cure particular diseases that they fear or have a genetic predisposition to (lots of unethical behavior from a certain now-defunct company that tried to do this).
For cancer in particular, pharmas don't (and mostly can't) just target a drug to chronically treat some cancer over the long term but not cure it. Instead they pick some target that's believed to contribute to development (/ metastasis / treatment resistance / whatever) in whatever cancer, and make a drug to interfere with it or to target an immune response to cells that make it. If it's stable, nontoxic, and looks potentially effective enough they'll take it to clinical trials. During clinical trials they'll find out whether it does nothing, gives you a few extra months, or has a chance at curing the disease. Usually the answer is that it does nothing or almost nothing, or isn't worth the side effects, and then the company wasted its time and money. Drugs with a chance to cure common types of cancer can be enormous successes -- see eg Herceptin.
Cancers are difficult diseases and it's rare to find something that reliably cures them. But drug companies aren't pulling their punches. Like they would never say "oh this drug clears breast cancer too reliably, we should make it less effective so that people will be more likely to die but also might take it for longer".
If I understand correctly, Baillie-PSW has been shown to be correct for all integers < 2^64, so for 64-bit ints you might use (some variant of) that instead of M-R.
Edited to add: Sieving has got to be much faster than M-R if you want all primes of a certain size. You would use M-R or Baillie-PSW if you are testing them one at a time.
I picked Hunter's Point because I used to live near it. The problems from decommissioning radioactive ships are bad, but they're far from the only pollution that was there. Lots of VOCs, solvents, oils, radiation from other stuff (eg, glow-in-the-dark equipment made with radium), heavy metals, pesticides, PCBs, and what have you.
But sure, there are other shipyards they cleaned up in less than three decades.
Yeah. It's especially relevant for the author's focus on shipbuilding. The old shipyard at Hunter's Point in San Francisco is horribly polluted, and they've been working to decontaminate it for more than three decades in order to reclaim the land for other uses (in particular, housing). Treasure Island and Yerba Buena Island also have a lot of pollution from the former naval base there. There is a cost to overregulation, and there is a cost to underregulation.
And OK, sure, there's a lot of industry that ought to happen somewhere. Someone has to build ships and electronics and whatever, and if California's code is too strict then it just becomes NIMBYism. But if some company moves their gigafactory to Reno for easier permitting, I don't whether (or more likely by how much) CA is too strict, or NV is too lax. And I know that CA has NIMBYish and overregulatory tendencies, but given the clear bullshit on this website, I'm not inclined to give it the benefit of the doubt either.
I'm especially doubtful when it says "THE classic example of what you can't do in CA" is auto paint shops ("Impossible"!) ... but then the detail it gives is that they're "effectively impossible" to permit in the Bay Area AQMD, that being only one of the state's 35 AQMDs (albeit one of the larger ones).
The laptop keyborad is good enough, but I'd enjoyed using the Kineses before. I moved long distance and the Kinesis was bulky and didn't make the cut for things to haul. Once I was settled I started looking to set up a proper office again, and that included a keyboard. But I didn't find one that was enough better than a laptop keyboard to get regular use.
In addition to what others have pointed out, many of these aren't actually missing from traditional dictionaries: they're just inflected differently. So your example lists phrases like "operating systems", "immune systems" and "solar systems" as missing from traditional dictionaries, but at least the online OED and M-W have "operating system", "immune system" and "solar system" in them. It's just that your script is apparently listing the plural as a separate phrase.
On languages other than English: in general, different languages do word division very differently. At least in German and Dutch, many of those phrasal verbs are separable, meaning that they are one word in the infinitive but are multiple words in the present tense. So for example, where in English you would say "I log in to the website", in Dutch it would be "Ik log in op de website". "Log in" is two words in both cases, but in Dutch it's the separated form of the single-word separable verb inloggen ("I must log in now" = "Ik moet nu inloggen"). The verb is indeed separable in that the two words often don't end up next to each other: "I log in quickly" = "Ik log snel in".
Dutch, like German, has lots of compounds. But there are also agglutinative languages, which have even more complex compound words, perhaps comprising a whole sentence in another language. Eg (from Wikipedia) Turkish "evlerinizdenmiş" = "(he/she/it) was (apparently/said to be) from your houses" or Plains Cree "paehtāwāēwesew" = "he is heard by higher powers"; and these aren't corner cases, that's how the language works.
I got one with low-force switches. It's very comfortable to type on, but between the low-force switches and slightly different layout from a regular keyboard (column-staggered, concave, symbols in different locations) I make more mistakes. So I usually type on my laptop instead, especially while coding.
My phrase "how economists expect you to set it" is probably wrong here, since I'm not an economist, I've just read the most basic theory about how to use this tool, and also used it myself (on eBay, you know, years ago when the site was mostly auctions). So I don't really know what "economists expect", but rather the basic guidelines for using this tool. You got me there.
> I think this is the problem. When most sciences observe reality diverge from the model, they see that as a flaw in the model. When economists (at least you HN "economists") observe reality diverge from the model, they seem to see that as a flaw in reality.
But like, to double-check here: "reality" means your imagined use of a tool that you do not in fact use, right? Like you say you "don't do auctions" and I'm trying to explain what that option is for, and you're countering that the basic "how to use this tool" explanation is a wrong model of reality?
I'm not defending "you shouldn't ever need to snipe, just bid your max price" as a hard principle, just trying to explain where the idea comes from. Sniping can be strategic for lots of reasons: you don't have to commit to a bid until the last second (in case you find a similar item for cheaper elsewhere), you deny other people information, you might avoid anxiety from wondering whether your bid will win, etc.
That said, the max price is supposed to be a price where you are not especially happy to get the item at that price, but not really sad either, a price where you would say "well, I hoped for better but I guess that's a fair deal". That's not realistically pinned down to the cent. But if you set a max price at $5000 and would be happy to get the item at $5000.02 (for some reason other than satisfaction from sniping), then you set your max price wrong, or at least differently from how economists expect you to set it.
It's not supposed to be some red line absolute max price, but rather "how much is this item worth to you?" You set that as your max bid price. If you get it at auction for less than that, you got a good deal, but if you buy it for more, you got a bad deal. If someone outbids you, then maybe it was worth it to them, but you (supposedly) would not have wanted to buy the item for that much, and would rather use your money for something else.
For tricky-to-price items like unique art pieces, the idea that you can pin this down might be a fantasy, but for commodity items it's pretty reasonable. If you can buy the same thing at costco dot com for $500, then it's probably not worth more than $500 to you, and if at auction you get outbid and it sells for $500.01 then you'll shrug and go order the same thing for a cent less, having wasted only a few minutes of your time. If the item you're bidding on is discontinued (e.g. it's last year's model) but you can buy a slightly better one for $550, and you can spare that extra $50, then again you won't be too sad about getting outbid. Online auctions are more popular for used items, but again in that case you usually still have an idea of what a used item is worth to you.
See also the paper Ribbon filter: practically smaller than Bloom and Xor: https://arxiv.org/abs/2103.02515, which is a similar idea though not by the same authors.
IIRC, binary fuse filters are faster to construct than ribbon filters, but typically not quite as space-efficient. There are also frayed ribbon filters (by me) which are slower and more complex to construct but more space-efficient. There's no paper for those, just a Rust implementation.
Ribbon filters are deployed in Mozilla's Clubcard for distributing compressed certificate revocation lists: https://github.com/mozilla/clubcard and https://jmschanck.info/papers/20250327-clubcard.pdf. CRLs are an almost ideal application of this sort of compressed set tech, since the aggregator runs batch jobs and needs to distribute the set to very many clients. It's not perfectly ideal because CRLs require frequent updates and none of these methods support delta updates. There is a straightforward but inelegant workaround, which is to send a compressed set that represents the delta, and query both on the client.
A second special case of this theorem is Pascal's theorem, which says (roughly) that a variant of the elliptic curve group law also works on the union of a conic C and a line L (this union, like an elliptic curve, is cubic), where the group elements are on the conic. One point O on the conic is marked as the identity. To add points A+B, you draw a line AB between them, intersect that with the fixed line L in a point C, draw a second line CO back through the marked identity point, and intersect again with the conic in D:=A+B. This procedure obviously commutes and satisfies the identity law, and according to Pascal's theorem it associates.
Under a projective transformation, if the conic and line don't intersect, you can send the line to infinity and the conic to the units in (IIRC) a quadratic extension of F (e.g. the complex unit circle, if -1 isn't square in F). Since the group structure is defined by intersections of lines and conics, projective transformations don't change it. So the group is isomorphic to the group of units in an extension of F. If they do intersect ... not sure, but I would guess it instead becomes the multiplicative group in F itself.
The multiplicative group of F can be used for cryptography (this is classic Diffie-Hellman), as can the group of units in an extension field (this is LUCDIF, or in the 6th-degree case it's called XTR). These methods are slightly simpler than elliptic curves, but there are subexponential "index calculus" attacks against them, just like the ones against the original Diffie-Hellman. The attack on extension fields got a lot stronger with Joux's 2013 improvements. Since no such attack is known against properly chosen elliptic curves, those are used instead.
Annoyingly, while that d = e^-1 usually isn't used in practice (except in cases where you care about side-channel / fault resistance more than the 4x speedup), the Carmichael totient itself still is used in practice. At least if you want to conform to FIPS 186-5 / SP800-56B, which says that the private key includes d = e^-1 mod the Carmichael totient LCM(p-1,q-1), even if you're going to use the CRT. And that means you have to compute LCM(p-1,q-1), which also has side-channel considerations.
Do the standards require strong primes for RSA? I think FIPS doesn't ... it gives you that option, either for the legacy reasons or to get a proof with Pocklington's theorem that (p,q) really are prime, but just choosing a random (p,q) and running enough rounds of Miller-Rabin on them is considered acceptable IIRC.
Grover's algorithm is not quite as powerful as popularly described. In particular, it (roughly) divides the number of times you need to run AES by the number of times you run it sequentially. So it effectively square-roots the time requirement rather than the difficulty, and those are very different if the attack is parallel.
Eg if you were planning on breaking AES-128 by running 2^30 cores for 2^98 AES calls, it now only takes about 2^49 calls per core (2^79 total effort) plus the overhead of Grover's algorithm itself. There are also huge overheads from running everything on a quantum computer, some of which are theoretically avoidable (100x cost for error correction; gates take one clock cycle) and some of which are probably not (you must rewrite AES so that all computations are reversible). So breaking AES-128 might eventually be feasible, but AES-192 probably would not be.
There is a theoretical barrier against efficiently parallelizing Grover: all generic quantum brute-force algorithms (the kind that would work against a random function in a black box) require Omega(searchspace / depth) queries, at least for some model that may not quite match reality. (Edit: Omega and not O, since it's a lower bound)
Of course, AES isn't a random function in a black box, so there may be better attacks against it, but I'm not aware of any.