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Quantum Algorithms for Lattice Problems

eprint.iacr.org

51–60 of 127 posts

Re: Quantum Algorithms for Lattice Problems

#51
post #36

Earlier quoted context omitted.

I'm sure they have thought more about how to prioritize security threats than an anonymous internet commenter.

Arrogance.

A fitting reply to a total non-sequitur, more like. A huge corps handling of browser extensions has absolutely zero to do with encryption algorithms, and security is such a big field that "care about security" means nothing at all.

The comment was just a chance to vent anger at Google in an unproductive way.

Re: Quantum Algorithms for Lattice Problems

#52

Some post-quantum signatures like CRYSTALS-Dilithium are based on lattices. Makes me think that quantum key distribution (what I've been working on for the past 6 months) has a chance to actually become useful instead of being only of interest to academics and to a few companies that sell overpriced solutions to paranoids.

QKD does not solve the problem that quantum computers create, and cannot replace public key cryptography. That's a common misconception that the marketing departments of QKD research tries to keep alive.

Even under ideal conditions (whether these can exist is debatable), the best QKD gives you is a securely encrypted channel only when you already have a securely authenticated channel. The latter is extremely important, makes the whole thing mostly useless, and is often omitted by QKD advocates.

Re: Quantum Algorithms for Lattice Problems

#54
People seemed to be focusing on the fact that this wouldn’t break the NIST leading PQC public key cryptosystem, but I think that misses the point. This takes a problem at the core of this security, which previously only had an exponential approximation, and finds a polynomial approximation. Sure that polynomial is too high O(n^4.5) to break the leading proposed systems, but I mean are you really feeling safe when an exponential just changed to a polynomial?

An analogy would be something like this. Factoring is hard. We base RSA on the hardness of this problem and there we use numbers that are the product of two primes. Someone just found an algorithm that doesn’t work to find the product of two primes, but can take a product of four primes and return two products of two primes. Do you feel safe with RSA?

Anyway the paper could be wrong or it could be right, it will take a while for those in the field to dig through this. As a cautionary tale, there have been a few extra good quantum people who have proposed quantum attacks on lattice problems that have later been shown to have bugs.

Re: Quantum Algorithms for Lattice Problems

#55
post #52

Some post-quantum signatures like CRYSTALS-Dilithium are based on lattices. Makes me think that quantum key distribution (what I've been working on for the past 6 months) has a chance to actually become useful instead of being only of interest to academics and to a few companies that sell overpriced solutions to paranoids.

QKD does not solve the problem that quantum computers create, and cannot replace public key cryptography. That's a common misconception that the marketing departments of QKD research tries to keep alive. Even under ideal conditions (whether these can exist is debatable), the best QKD gives you is a securely encrypted channel only when you already have a securely authenticated channel . The latter is extremely importa…

If you don't have an authenticated channel, you are susceptible to a MITM attack which makes any asymmetric crypto useless. Thus I think there is an implicit assumption in any asymmetric crypto that you already have an authenticated channel. Or did I miss something?

Re: Quantum Algorithms for Lattice Problems

#56

Hello everyone. I am a college student and currently new to this field. If possible can somone explain in simple terms that what real future impacts would this paper can create?

It would be silly not to first ask your interpretation, given that you are a college student.

Since this is about quantum computing, real world effects are very likely to be none except an exorbitant amount of grant money.

Re: Quantum Algorithms for Lattice Problems

#57
post #2

From the paper: > Let us remark that the modulus-noise ratio achieved by our quantum algorithm is still too large to break the public-key encryption schemes based on (Ring)LWE used in practice. In particular, we have not broken the NIST PQC standardization candidates. For example, for CRYSTALS-Kyber [BDK+18], the error term is chosen from a small constant range, the modulus is q = 3329, the dimension is n = 256 · k w…

Factorization and discrete log are also polynomial on a quantum computer, and we are very good at just increasing bit widths. If CRYSTALS is also polynomial in BQP, there is very little reason to invest so much into it. I am still of the (very controversial) opinion that the only PQC algorithm worth investing in at the expense of classical algorithms is Classic McEliece. This is a code that has stood up to classical…

Thanks for your comment, very interesting. About your last paragraph : Do you know why NIST refuses hybridization, when European agencies imposes it ? What is the political behind it ?

Re: Quantum Algorithms for Lattice Problems

#58

Earlier quoted context omitted.

Factorization and discrete log are also polynomial on a quantum computer, and we are very good at just increasing bit widths. If CRYSTALS is also polynomial in BQP, there is very little reason to invest so much into it. I am still of the (very controversial) opinion that the only PQC algorithm worth investing in at the expense of classical algorithms is Classic McEliece. This is a code that has stood up to classical…

Thanks for your comment, very interesting. About your last paragraph : Do you know why NIST refuses hybridization, when European agencies imposes it ? What is the political behind it ?

The charitable interpretation I would give the NIST - and a very real concern - is that they are not sure that one form of cryptography doesn't weaken the other, without proofs. Since these cryptosystems also tend to work in different number fields, it's very hard to prove anything about their interactions at all.

We all know the uncharitable interpretation, that the PQC algorithms may be backdoored.

Re: Quantum Algorithms for Lattice Problems

#59
post #38

Earlier quoted context omitted.

… only if scalable quantum computers exist.

If scalable quantum computers do not exist, we do not need PQC.

FHE is still only known from lattices, and has nothing to do with post-quantum computers.

Re: Quantum Algorithms for Lattice Problems

#60
post #46
post #44

Earlier quoted context omitted.

Hemomorphic encryption is not the same thing as post quantum crypto?

Homomorphic Encryption does often use lattice mathematics

But classically secure FHE is still a useful thing (even if it is broken by hypothetical quantum computers).
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