all 5 comments

sorted by: hot top controversial new old
[–] 7 points 1 month ago

The practical risk is limited, but still significant. Applying the attack against the deprecated use of 1024-bit keys took a handful of months on an academic CPU cluster, significantly less than the current estimates for 1024-bit factoring that would require resources that only nations or companies with massive resources could achieve. Widely used RSA implementations are also safe.

Nonetheless, the research has taken cryptographers by surprise because it introduces signature forgery, a new way to break RSA keys without factoring. Equally important, this novel method reduces the required computing resources by orders of magnitude.

  • source
  • [–] 2 points 1 month ago* (3 children)
  • [–] 4 points 1 month ago (2 children)

    ECDSA has already pretty much replaced RSA anyway.
    This'll help convince the last stragglers though, at least until a PQ solution gets widely adopted.

  • source
  • parent
  • hideshow 2 child comments
  • 36 comments in c/technology@lemmy.world view that post
    [–] 42 points 1 month ago

    This is interesting but it's essentially a protocol attack against a certain type of RSA signature. It talks about PKCS5 not being affected. Says nothing about OAEP which I'd hope also holds up.

  • source
  • [–] 18 points 1 month ago (1 child)

    So for RSA without padding, a threat actor could request lots of tokens (without getting rate-limited?), and use that as information to more precisely focus efforts to brute-force the key, and thereby reducing the number of operations required to do so? Or am I misunderstanding it?

  • source
  • hideshow 1 child comment
  • [–] 16 points 1 month ago

    Oh good, more bad news

  • source
  • [–] 16 points 1 month ago (-1 children)

    The practical risk is limited, but still significant. Applying the attack against the deprecated use of 1024-bit keys took a handful of months on an academic CPU cluster, significantly less than the current estimates for 1024-bit factoring that would require resources that only nations or companies with massive resources could achieve. Widely used RSA implementations are also safe.

    Bold emphasis is mine. It's a nothing Burger article.

  • source
  • hideshow -1 child comments
  • load more comments (-1 replies)
    [–] 4 points 1 month ago
    [+] -10 points 1 month ago (30 children)

    tell me again why people still use RSA?

  • source
  • hideshow 30 child comments
  • [–] 8 points 1 month ago (7 children)

    RSA has been around a long time and is relatively easy to understand and implement. But for new deployments we're supposed to use ECC instead. The comment earlier about P vs NP is unfortunately confused. Factoring is not known to be NP-hard and it probably isn't.

  • source
  • parent
  • hideshow 7 child comments
  • [+] 1 point 1 month ago
    [removed by mod]
  • source
  • parent
  • [–] 1 point 1 month ago (-1 children)

    Fwiw, bitcoin mining amounts to brute forcing SHA256 rather than ECC. Tendency these days for ECC (like in TLS) is to use Curve25519 rather than secp256k1. PQ (post quantum) is an entirely different topic and is in the direction of much more complicated schemes. RSA (or rather, integer factoring) has a long history of falling to better and better attacks, with a (now expired) 512 bit CA certificate recently having been factored on a single workstation. The first fielded deployment was at a nuclear lab and it used 336 bit keys! The big crypto nerds all seem to prefer ECC to RSA now. I tend to defer to them.

  • source
  • parent
  • hideshow -1 child comments
  • [+] 1 point 1 month ago
    [removed by mod]
  • source
  • parent
  • [–] 3 points 1 month ago (-1 children)

    I would say, there are known sub-exponential algorithms for factoring, while nothing better than (exponential) brute force is known for ECC. So, slightly better algorithms that erode RSA further are incremental improvements, while anything sub-exponential at all for ECC would be a breakthrough. Of course as someone once said, predictions are hard to make, especially about the future.

  • source
  • parent
  • hideshow -1 child comments
  • [+] 1 point 1 month ago
    [removed by mod]
  • source
  • parent
  • [–] 1 point 1 month ago (-1 children)

    You could say the same things about AES keys being short.

  • source
  • parent
  • hideshow -1 child comments
  • [+] 1 point 1 month ago*
    [removed by mod]
  • source
  • parent
  • [–] 1 point 1 month ago (-1 children)

    Most of us don't have control over the public keys we use. We connect to a web site with a browser, and the server supplies the public key.

    If you want public keys for your own purposes, I guess nothing stops you from generating 4096 bit (or whatever) ECC keys. Of course the arithmetic will be slow.

    If you're really paranoid about potential math advances affecting ECC and/or RSA, then you may be best off avoiding public key schemes altogether. Just use secret keys, and maybe Merkle tree signatures.

  • source
  • parent
  • hideshow -1 child comments
  • [+] 1 point 1 month ago
    [removed by mod]
  • source
  • parent
  • load more comments (-2 replies)
  • load more comments (-2 replies)
  • load more comments (-2 replies)
  • load more comments (-2 replies)
  • [–] 1 point 1 month ago (3 children)

    We can actually make stronger claims about factoring. We know for certain do that it is not in NP hard, so you are correct there

    And I'm not exactly a security expert, but moving away from RSA at this point makes sense. Early assumptions about the difficulty of factoring large semi-primes certainly hasn't panned out (in particular in light of the growing risk of quantum computers.)

  • source
  • parent
  • hideshow 3 child comments
  • [–] 3 points 1 month ago (2 children)

    We know for certain do that it is not in NP hard

    It's likely to be NP-intermediate (outside of P, but not NP-hard), but it is not known.

    (@Kairos@lemmy.today)

    Factoring is at most NP-complete because we have a polynomial time verification for it.

    That means it's in NP. These terms mean very precise things and it's easy to get confused, but at the end of the day the new paper didn't find a faster way to factor.

  • source
  • parent
  • hideshow 2 child comments
  • [–] 1 point 1 month ago* (1 child)

    I'm not confused. I've been teaching this subject for over a decade.

    I'm not certain are you arguing with me?

    I was largely agreeing with you.

  • source
  • parent
  • hideshow 1 child comment
  • [–] 0 points 1 month ago* (last edited 1 month ago) (1 child)

    You wrote "we know for certain do that it [factoring] is not in NP hard". That sentence is 1) borderline ungrammatical (we usually use NP-hard as an adjective, though it also denotes a set); and 2) in error. We suspect factoring is not NP-hard but we don't know for certain (consider what happens if P=NP). The error suggests confusion about what these terms mean. If you're really teaching this subject, can I ask what textbook you are using?

  • source
  • parent
  • hideshow 1 child comment
  • No, we don't use it as an adjective. It is a set. That's literally all it is.

    And predicating anything on the assumption that P equals NP is rather absurd. Of course, we can't rule it out as a possibility. But virtually nobody in the discipline believes that to be the case. And honestly, why would it be? If there were polynomial time solutions to that many problems of that degree of importance, surely we would have discovered something by now.

  • source
  • parent
  • [–] 0 points 1 month ago*

    No, we don’t use it as an adjective.

    From the first sentence of https://en.wikipedia.org/wiki/NP-hardness : "In computational complexity theory, a computational problem H is called NP-hard if...".

    Of course, we can’t rule it out as a possibility.

    Exactly, we don't know for certain. Of course it's very unlikely, but in math when we say we know something for certain, it means there's a theorem to that effect. There reason to think that factoring is not NP-hard but we don't know for certain. If you still claim otherwise, can you cite a theorem?

    Anyway, yes, you're confused, and at this point you're spouting misinformation. You might consider reading a book or taking a class.

    If there were polynomial time solutions to that many problems of that degree of importance, surely we would have discovered something by now.

    It's still an open problem, there's a $1 million Clay prize waiting for you to claim it if you have a proof either way.

  • source
  • parent
  • load more comments (-1 replies)
  • load more comments (-1 replies)
  • [–] 1 point 1 month ago (3 children)

    Factoring is at most NP-complete because we have a polynomial time verification for it.

  • source
  • parent
  • hideshow 3 child comments
  • [–] 0 points 1 month ago (2 children)

    Factoring is not NP-complete because it is not a member of NP-hard.

    You are correct that verifiability is in there, but you have to also be able to do the reduction.

    There are plenty of problems out there where we lack polynomial time solutions, while the problem also lacks the expressiveness required to reduce back and forth.

  • source
  • parent
  • hideshow 2 child comments
  • [–] 1 point 1 month ago* (1 child)

    Factoring is not in any category because we don't have a proof for it. As it stands, the algorithms we have require exponential time in the worst case, but solutions can be verified in polynomial time, which is NP-complete. I said "at most" for a reason.

    Also, every algorithm is verifiable. If there's no better way to do it then re-running the algorithm and that algorithm is exponential, then it's NP-Hard.

  • source
  • parent
  • hideshow 1 child comment
  • Factoring is in a category. Everything computable exists somewhere. We know factoring to be in NP.

    What I was disagreeing with was the "at least" and "at most" characterization of NP completeness. It is a set, not a boundary. The actual diagram of the complexity zoo is much more complicated than concentric circles.

    And for verifiability, I was not referring to it as an existential sort of thing. I was simply saying that I agreed with you in that particular facet, but it isn't sufficient to describe NP completeness. You also need NP-hardness.

  • source
  • parent
  • load more comments (-2 replies)
  • [–] 6 points 1 month ago (20 children)

    RSA is secure because it relies on P vs NP. Very basically, RSA multiplies 2 very large prime numbers together to encrypt things. We rely on something similar for secure Internet connections

  • source
  • parent
  • hideshow 20 child comments
  • [–] 7 points 1 month ago (4 children)

    it relies on P vs NP

    That is incorrect. It relies on perceived difficulty of factoring large semi-prime. P equals NP is related, of course, if it happens to be an NP-intermediate problem, but the difficulty of factoring is not because it's NP-complete.

    There are already classical algorithms that are sub-exponential to solve the problem. If it were the case that the problem was NP-complete, then we would have had a big advance in our theory and practice based on it.

  • source
  • parent
  • hideshow 4 child comments
  • [–] -5 points 1 month ago (3 children)

    I'm not about to get into the weeds about P vs NP to explain a concept to someone that doesn't know much about encryption in the first place. I'm aware that factoring isn't really NP complete, but P vs NP is about solving vs verifying solutions for something in Polynomial time, which can't be done via brute force for RSA keys.

  • source
  • parent
  • hideshow 3 child comments
  • [–] 6 points 1 month ago (2 children)

    really NP complete

    I don't care who you want to get in the weeds with or what you wish to spar about, you're just not correct.

    There is no almost NP complete. There are strong and weak variants, sure, and those have particular implications.

    But you're drawing conclusions that don't exist from definitions that you clearly don't understand.

    Signed: Somebody who has taught theory of computation for over a decade.

  • source
  • parent
  • hideshow 2 child comments
  • [–] -2 points 1 month ago (1 child)

    If you want to be pedantic, fine. Integer factoring is not in P. Therefore the math used to encrypt RSA is not in P. The usage of integer factoring to encrypt therefore means it can't be decrypted in P using brute force. That's the point I'm making.

  • source
  • parent
  • hideshow 1 child comment
  • We actually don't know if integer factorization is not in P, though.

    Right now, I think most of us would guess that it is a prime candidate for NP Intermediate. Hence why I mentioned it earlier.

    And you absolutely can solve it in polynomial time just not with classical architectures.

  • source
  • parent
  • [–] 4 points 1 month ago (14 children)

    but do we not have other, much more secure encryption that is just as easy to employ?

  • source
  • parent
  • hideshow 14 child comments
  • [–] 6 points 1 month ago (7 children)

    Yes it's becoming more common to have Elliptic Curve keys. But many still use RSA.

  • source
  • parent
  • hideshow 7 child comments
  • [–] 1 point 1 month ago* (6 children)

    Elliptical curve for RSA was immediately phased out as soon as it was proven that the NIST was influenced by the NSA to implement it

  • source
  • parent
  • hideshow 6 child comments
  • [–] 7 points 1 month ago (4 children)

    And if I remember correctly, I believe it has more weaknesses (especially potential unknown ones) than RSA.

    But it's definitely more efficient on embedded hardware, and for sure still gets used in that space. Not that I'd know cough cough

  • source
  • parent
  • hideshow 4 child comments
  • [–] 2 points 1 month ago (1 child)

    And if I remember correctly, I believe it has more weaknesses (especially potential unknown ones) than RSA.

    what are those weaknesses? so far I have only read for users that ECC is more secure than RSA

    But it's definitely more efficient on embedded hardware,

    not only on embedded hardware, but everywhere and also in network transfer because of the smaller keys

  • source
  • parent
  • hideshow 1 child comment
  • [–] 2 points 1 month ago* (last edited 1 month ago)

    Tl;dr - Choosing parameters for ECC is very important but also very difficult. Also, ECC is more resistant to quantum algorithms than RSA.

    I didn't know about the PQC readiness of ECC so thank you!

    To my understanding, picking the right ECC parameters is critical to ensuring large enough entropy that it can't be brute forced. There are a lot of weak and easy to compromise parameters, and a lot of trust has to be put in the standards organizations declaring which ones are "safe" like the NIST curves. Or you can choose your own, with a lot of risk associated.

    There's also the fact that I believe there's more potential to leak info/expose side channels on the embedded devices running these protocols (I've personally had to worry at work!)

    interesting about the security, it looks like ECC is arguably more secure against quantum algorithms? I first learned about all of this stuff about 10 years ago, and I only vaguely remember reading about the pqc resistance. Thanks for the update on that!

    Edit: But I want to be clear I'm not a security expert, just some lady whose had to deal with embedded cryptography from time to time.

  • source
  • parent
  • [–] 1 point 1 month ago

    Elliptical curve for RSA was immediately phased out

    what? when did RSA want to use elliptical curves? its a completely different technology. and ECC itself was not phased out of anywhere. certain curves were, not ECC as a whole.

  • source
  • parent
  • [–] 8 points 1 month ago* (4 children)

    There are tradeoffs with encryption. RSA is so secure, that the US government has tried to insert a mathematic backdoor into the key selection because that's the easiest method to attack the encryption. RSA uses thousands of bits for their encryption, making it inefficient for most attacks. The attack detailed in this article is on one of the weaker RSA algorithms, with only 1024 bits. The high end RSA uses 4096 bits or more, I believe the algorithm has increased the bit length to officially support 8192.

    On the other side of RSA is another secure algorithm called AES. It can go up to 512 bits, but it hashes the key to meet the key length instead of relying on generating huge prime numbers. It makes it more resilient to certain types of attacks, but the bit limitation makes it easier to brute force or use rainbow tables.

  • source
  • parent
  • hideshow 4 child comments
  • [–] 2 points 1 month ago (1 child)

    Thanks for this answer. The article makes it sound as though even the 4096-bit versions are now more or less trivial to defeat given a bit of money for a capable machine and this new method:

    Even for 2048- and 4096-bit keys, the method reduces the security of RSA to unacceptable levels. The National Security Agency, National Institute of Standards and Technology, and European Union Agency for Network and Information Security require that any cryptosystem should provide a level of no less than 128 or more bits, meaning the operations required must exceed 2^128.

    The forgery attack drops these levels to 2^65, 2^90, and 2^119 for 1024-, 2048-, and 4096-bit keys respectively. These levels may further drop because Heninger’s team did all the coding by hand and used no AI or GPUs in performing the forgeries. The researcher said these tools will “almost certainly” drop the security levels further.

  • source
  • parent
  • hideshow 1 child comment
  • [–] 4 points 1 month ago

    Just to put a bit of context on those, OpenAI said they used 180,000 GPUs for training their GPT-5 model. As I understand it, each GPU has ~16,000 cores, and each of those cores does a couple billion operations per second. With that cluster, 2^65 operations takes a couple seconds, 2^90 takes many years, and 2^119 is off in "the sun has grown to surround the Earth" territory. The NSA is concerned with protecting their stuff against organizations with hundreds of billions of dollars, and a hundred of years of time to dedicate dozens or hundreds of people to breaking it. "Not good enough" in that context is a very different bar than what most people have to worry about.

    You also need to provide them 2^43 unsalted responses, which is more than a casual few.

  • source
  • parent
  • 2 comments in c/cybersecurity@infosec.pub view that post
    [–] 5 points 1 month ago* (1 child)

    An attack on Privacy Pass would require an attacker to request 2^43^ tokens from Cloudflare, Apple, or another organization.

    An attack on Privacy Pass would require an attacker to request tokens from Cloudflare, Apple, or another organization 2^43 times.

    ... is there a button I can push to summon a copy editor?

    Personally I'd go with the former, probably not both simultaneously.

  • source
  • hideshow 1 child comment
  • 1 comment in c/cybersecurity@sh.itjust.works view that post
    [–] 4 points 1 month ago

    “If this result holds up under peer review, it would indeed be a conceptual break-through,” Karsten Nohl, a cryptography expert and the head of innovation at Allurity, said in an interview.

    Emphasis mine. It's also only problematic for blind-signature types.

    The attack works only against blind-signature implementations of RSA. The overwhelming majority of RSA in use today provides PKCS or PSS padding, a format that adds data to the plaintext before it’s encrypted.

    So even if it passes peer review, it's only an issue for older implementations.

  • source
  • 1 comment in c/crypto@infosec.pub view that post
    [–] 6 points 1 month ago* (last edited 1 month ago)

    The forgery attack drops these levels to 2^65, 2^90, and 2^119 for 1024-, 2048-, and 4096-bit keys respectively.

    Well that's terrifying, and all the more reason to get off of RSA signatures and onto anything else, probably EdDSA. Even though the article and paper don't address the real-world systems which use padding, the algorithmic safety that underpins RSA is under serious scrutiny. It's hard to see how RSA 4096-bit keys can remain as a first choice, when this type of attack exists and there are credible alternatives, both PQC and not.

    The fact of the matter is that for signatures where there isn't an HNDL problem, we still have the issue of being confident in the signature years after signing. Will an RSA-4096 signed blob be acceptable in 20 years? Do we really think RSA will be above reproach by then? Signers in 2026 might do well to at least have a second signature scheme in place to doubly sign their blobs, and to maybe revalidate then doubly re-sign older blobs previously signed with just their RSA keys, to maintain their provenance for decades to come.

  • source