Comment by swordswinger12 | Hacker News Reader

Comment by swordswinger12 | Hacker News Reader

THIS PAPER IS:

a nice, thought-provoking paper that is nevertheless purely speculative, and also more than a little tongue-in-cheek in parts. (Note that one of the keywords is "Make RSA Great Again".) It's basically pointing out that there is a small gap between the costs of legitimately using RSA and factoring via Shor's algorithm. With truly massive keys, this gap can be exploited to provide concrete security guarantees for RSA even in the presence of fast quantum computers.

THIS PAPER IS NOT:

a revolutionary new quantum factoring algorithm. They show how to apply quantum Grover search to a particular step of a known factorization algorithm based on elliptic curves.

QUANTUM COMPUTING DOES:

break public-key cryptosystems based on the hardness of factoring and finding discrete logarithms. Additionally, it gives a quadratic speedup in generic search problems (via Grover search) which effectively halves the key size of symmetric encryption schemes and yields faster algorithms for things like finding collisions in hash functions.

QUANTUM COMPUTING (PROBABLY) DOES NOT:

break all asymmetric cryptography. There is no known proof of this, but it's widely believed that asymmetric cryptosystems based on different hardness assumptions are not vulnerable to (non-generic) attacks by quantum computers.

"With truly massive keys"

My favorite quote from the paper on that topic is

"Something expensive might nevertheless be useful if it is the least expensive way to achieve the user’s desired security goal"

Post quantum crypto isn't the end of crypto, is the end of the meme that nation-state-proof cryptography is "too cheap to meter" (A nuclear power phrase from the old days)

The pre-quantum landscape is cheap unbreakable algos implemented in easily breakable ways as a part of easily breakable systems, so there's quite a bit of criminal activity going on out there. The post-quantum landscape is very expensive unbreakable algos implemented by professionals because the cost (computational and financial) is large. The involvement of professionals indicates that criminal activity based on breaking crypto implementations is likely to drop.

Its likely that Hollywood style multiple levels of crypto will soon exist. The days of being able to keep the NSA out of your wifi access point will be over unless you're willing to spend ridiculous amounts of money. However, for a very modest expense it'll still be possible to keep your neighbor off your wifi, wide open to nation states, sure. But my wifi leaching neighbor is a more realistic adversary than the entire NSA.

I disagree with the premise. There's no reason to assume that we can't implement a quantum-resistant asymmetric encryption system that is no more computationally expensive than what we already have.

Hell, there's already work out there (http://eprint.iacr.org/2014/599.pdf) for a quantum-resistant key exchange algorithm that's fast enough to have only 21% less throughput than traditional elliptic Diffie-Hellman.

Thats a good paper. I thought about it awhile and would retract my remarks of it being expensive and replace it with being expensive or risky. Also there's the problem of "what is the definition of post quantum" where a lot of people call 1995 or so after Shor "PQ", and maybe I'd retract that part of my comment and call it something like "way way long time in the future, which by whatever definition of post quantum, is also post quantum, lets call it 3000 AD"

The trick in the big-key RSA paper is knowing how Shor works, because the average big-O is low for a randomly selected large number, but the maximal number of ops that could be required is extremely large and yet that number is "easily" constructible. So merely intentionally and methodically (and expensively) manufacture a "poison pill" composite that Shor can't possibly factor because that number was constructed specifically to make Shor algo fail, and you're RSA system will be good.

The algo in your linked paper is very convenient. However its newer and not as seasoned and the wolves are snapping at its heels there was that paper around Thanksgiving last year (which did get retracted) claiming to partially quantum break LWE.

https://arxiv.org/abs/1611.06999

I'd like to see a proof that there exists no possible theoretical quantum speedup against LWE. Yes I know there isn't one in currently described or implemented, I mean I can't find a proof that there cannot exist an attack against LWE. Or, a proof that a non-quantum attack against LWE cannot exist because in the end that would imply 1=2 or something invalid so by induction its unbreakable.

In the year 3000 I think the odds are good that algos will still have a large ratio between the average ops when run against a random number vs the maximal ops when run against a constructable poison pill designed to require maximum number of ops. Yet in the year 3000 I would not put faith in any one algo that hadn't been broken by mid-2017 will never be broken. It seems better to bet on math as a field continuing to have algos with a wide spread, than to bet on any one algo.

In that way I think it likely we'll get stuck with something like big key RSA over a long enough time period.

While at the same time I can agree with you, yes in the post-quantum world starting in '94 and LWE starting in 2005 there was a post-quantum era from 2005 to at least mid 2017 where LWE was a fast unbroken post-quantum system. Will that end-date continue to 3000 AD?

Right now I'm thinking about if the Shor trick could be applied to a theoretically quantum broken RLWE-KEX. Random Discrete Gaussian Sampling is random... Is it possible to calculate poison pill samples that would mess up a theoretically broken RLW-KEX (depending a lot on the characteristics of an imaginary break?) I found slides by Peikert online about how those samples are selected, which I haven't made sense of yet.

> "what is the definition of post quantum" where a lot of people call 1995 or so after Shor "PQ"

I use the term quantum-resistant, which I think is more clear: crypto for which Grover's algorithm or Shor's algorithm cannot efficiently break it.

> The algo in your linked paper is very convenient. However its newer and not as seasoned

Totally agree, but it does show that you shouldn't just assume quantum-resistant crypto is necessarily computationally expensive.

> I'd like to see a proof that there exists no possible theoretical quantum speedup against LWE.

Don't hold your breath :). We don't even have a proof that integer factoring can't be broken in polynomial time in classical computers. We don't even know if one can make public key crypto unbreakable to classical computers (equivalent to P vs. NP problem). And the relationship of BQP (problems solvable in polynomial time on a quantum computer) to P and NP is still an open problem. It could turn out BQP=P, and quantum computers don't even give an asymptotic speedup over classical computers (I don't think that's likely, but it hasn't been proven one way or the other).

LWE isn't the only problem that's believed to be quantum-hard that can be used for a reasonably efficient DH primitive. Curve isogenies also appear to work, and they can take advantage of a tremendous amount of optimization work we've already done for curve math. There are also other CVP/SVP lattice problems. And this is sticking to problems that give us the same protocol-level interface; there are also quantum-hard public key algorithms that don't do that.

The more important point here, though, is that there's nothing particularly "expensive" about this stuff. It's all slower than RSA and curves, but (in particular) curves have gotten much faster over the last 10 years, and obviously computers are getting faster and silicon offloads less expensive, so the performance setback here isn't that big.

I'm also not sure why you have so much confidence in the conventional strength of RSA.

... not, by the way, that I'm willing to stipulate that LWE is all that risky; the underlying problems in LWE are also very well studied, preceding concerns about QC by a long time.

I don't think this is a reasonable summary of the landscape of PQ asymmetric cryptography. PQ crypto is based on different hard problems than RSA, which makes it seem extremely complicated and exotic, but that's true --- when you get into the nuts and bolts and equivalences and theory --- of "conventional" asymmetric crypto as well.

It's certainly not the case that PQ crypto requires enormous investments. Google ran a long quiet experiment where they used RLWE alongside ECDHE for users, and none of those users even noticed.

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