31–40 of 41 posts
Is ECC at all mathematically related to Kepler's equation? (although now that i look at it, I'm not confident that is a trapdoor function because while its much easier to code one way than the other, the sin function itself needs an iterative approximation).
It's important to note that most ECC is not quantum-resistant and will be obsoleted in the coming years following completion of NIST's post-quantum cryptography competition. Indeed, OpenSSH recently enabled PQC by default (NTRU Prime over X25519) [1]. ECC has, at best, a short-to-medium term lifespan right now. 1. https://www.zdnet.com/article/openssh-now-defaults-to-protec...
I'd say by far the most important thing will stay resistance to unknown classical algorithms, at least until trends change.
Earlier quoted context omitted.
AFAIK post-quantum crypto all has larger key sizes and much(?) worse performance. Has that changed? If not, I don't see ECC becoming obsolete any time soon.
I thought ring-lwe was pretty good. It's at least very embarrassingly parallel
Ring-LWE is faster than ECC, but has keys and ciphertexts of 600+B instead of as few as 32 B (for eg curve/ed25519). NTRU is pretty similar, with slower key generation and slightly smaller ciphertexts. If you go to the bleeding edge, you might be able to cut these to 300-400 bytes with severe compromises in eg error rate and security margin. There are also structured code-based systems with fairly similar sizes to the Ring-LWE ones, but they aren't finalists.
McEliece is fast to encrypt and decrypt and has small ciphertexts (as few as 128 bytes), but has enormous public keys (multi-hundred KB) that are also slow to generate. The biggest benefit of McEliece is that we're pretty confident it will hold up to analysis.
SIKE (an alternate) has reasonable keys and ciphertexts (200-250 B) but is pretty slow, on the order of 5ms on a laptop for the smallest parameters. The bleeding-edge CSIDH is much slower, but has even smaller keys, but we can't be at all confident that CSIDH is secure.
On the sig side, Falcon is fast but extremely complicated, and has as low as ~660B sigs. Its main competitor, Dilithium, is modestly slower and larger, and also significantly simpler. The much more conservative SPHINCS+ is very slow and produces ~8kB sigs.
It's important to note that most ECC is not quantum-resistant and will be obsoleted in the coming years following completion of NIST's post-quantum cryptography competition. Indeed, OpenSSH recently enabled PQC by default (NTRU Prime over X25519) [1]. ECC has, at best, a short-to-medium term lifespan right now. 1. https://www.zdnet.com/article/openssh-now-defaults-to-protec...
A funny story related to ECC: I was hanging out with a friend of mine about 10 years ago, and I was asking him what he was researching (he is a math professor in Colorado). He told me he was researching Ecliptic curves and their properties. So I said, "oh you must be really interested in elliptic curve cryptography then!" and he said, "what's that?". He was so deeply into math theory that he hadn't even looked at or…
A funny story related to ECC: I was hanging out with a friend of mine about 10 years ago, and I was asking him what he was researching (he is a math professor in Colorado). He told me he was researching Ecliptic curves and their properties. So I said, "oh you must be really interested in elliptic curve cryptography then!" and he said, "what's that?". He was so deeply into math theory that he hadn't even looked at or…
I was taking a chemistry class where we were learning by rote how to apply the Grand Orthogonality Theorem. We were clearly computing inner products, but I couldn't suss out the big picture and the chem professor didn't know either, so I went to the math department and joined a seminar, which happened to be almost nextdoor to the chemistry class. The professor teaching it had never heard of the applications to chemistry/spectroscopy, though he was delighted to find out.
Not 30 yards apart, two groups of people were approaching the same subject from opposite angles with zero awareness of each other.
Silos are amazing.
It's important to note that most ECC is not quantum-resistant and will be obsoleted in the coming years following completion of NIST's post-quantum cryptography competition. Indeed, OpenSSH recently enabled PQC by default (NTRU Prime over X25519) [1]. ECC has, at best, a short-to-medium term lifespan right now. 1. https://www.zdnet.com/article/openssh-now-defaults-to-protec...
Depends on how quickly quantum computer size grows? We don't seem to have anything resembling a Moore's Law yet
https://cloudsecurityalliance.org/press-releases/2022/03/09/...
As some others have pointed out, this is very basic stuff, but a good introduction. I have found this series of blog posts [0] as a super useful explanation of ECC that starts with the basics but covers the math and underlying group theory well, building up to an intermediate-level understanding of the matter. [0] https://andrea.corbellini.name/2015/05/17/elliptic-curve-cry...
Is ECC at all mathematically related to Kepler's equation? (although now that i look at it, I'm not confident that is a trapdoor function because while its much easier to code one way than the other, the sin function itself needs an iterative approximation).
Usually need lossless integer math for cryptography to work. So the form might be similar, but you’re working over finite fields (ie of integers mod some number), not real numbers. (Okay, I have only a tenuous understanding of this myself. I’m a physicist, not a mathematician! Mathematicians are intimidating.)
Earlier quoted context omitted.
Depends on how quickly quantum computer size grows? We don't seem to have anything resembling a Moore's Law yet
The Cloud Security Alliance is assuming something powerful enough shall exist in under 8 years. https://cloudsecurityalliance.org/press-releases/2022/03/09/...