🥸 Oh, look! Another cryptographic revelation! Diffie-Hellman is dead, long live Elliptic Curve Diffie-Hellman! 🤯 Because what the world definitely needed was more #jargon masquerading as progress. 🧙♂️
https://keymaterial.net/2025/05/23/there-is-no-diffie-hellman-but-elliptic-curve-diffie-hellman/ #cryptography #DiffieHellman #EllipticCurve #technews #cybersecurity #HackerNews #ngated
#EllipticCurve
What the hell is an elliptic curve?
https://onlynv.dev/blog/what-the-hell-is-an-elliptic-curve
#HackerNews #ellipticcurve #cryptography #math #education #technology
The #Monero community is excited to announce the launch of the FCMP++ (Full-Chain Membership Proofs) Optimization Coding Competition!
The best solution for each implementation will be awarded 250 XMR (currently ~53k USD) and 100 XMR (~21k USD)
See all contest details here: https://github.com/j-berman/fcmp-plus-plus-optimization-competition
#cryptography #rust #cryptocurrency #privacy #xmr #ellipticcurve
What isn't linked from those four pages above, however, is the one gem I had been pointed to some time ago. And hadn't made the connection that this was the same person!
Michael Driscoll's «The Animated Elliptic Curve» really helped me in understanding Elliptic Curve Cryptography with its wonderful, well-described animations which you can replay until you understand them.
5/6
#ECC #EllipticCurve #EllipticCurveCryptography
https://curves.xargs.org/
#AntiStatusReport: belatedly noticed that #Launchpad now supports #EllipticCurve keys so I no longer need a special #OpenPGP key just to upload to my #Ubuntu #PPA repos!
If you ever struggle to get #vaultwarden to work with your brand new #ellipticcurve #certs, here's the relevant part from my #dockercompose, I just can attach a screenshot, for copy & paste just take the values from there: https://rocket.rs/v0.5-rc/guide/configuration/ (See topic TLS).
#rockettls #selfhosting #homelab #ssl #tls #certificates #passwords #passwordmanager #ec #encryption
It works as expected despite said otherwise.
Observation of today regarding Ed25519. I'm just trying to understand it on some level. Remember how did-keys have 44 significant "characters" in their base 58 encoding. This number 44 can be derived from 58**43 < 2**255 - 19 < 58**4, where 2**255 - 19 is the characteristic of the field the Curve25519 is considered over.
If my mathematical understanding is correct, there are always at most two points for a given y coordinate. So for the purposes of "representations" one can identify each point on Curve25519 with such a 44 character base 58 encoding.
Also please understand that figuring how numbers match is in no way mathematics. It just helps build a picture in my mind.
sharing via https://infosec.exchange/@nhamiel
"In this blog post, we tell a tale of how we discovered a novel attack against ECDSA and how we applied it to datasets we found in the wild, including the Bitcoin and Ethereum networks. Although we didn’t recover Satoshi’s private key (we’d be throwing a party instead of writing this blog post), we could see evidence that someone had previously attacked vulnerable wallets with a different exploit and drained them. We cover our journey, findings, and the rabbit holes we explored. We also provide an academic paper with the details of the attack and open-source code implementing it, so people building software and products using ECDSA can ensure they do not have this vulnerability in their systems.
How Bad Is It?
In simpler words, what our attack means is that every time an ECDSA signature is generated, the signature itself gives us a relation between the nonce and the private key. If the nonces are truly randomly generated, this should never be a problem because the chance that a number of nonces picked at random fit on a low-degree polynomial recurrence relation is negligibly small.
But there is a catch: nonces are usually output by a pseudorandom number generator (PRNG) rather than being really random, and PRNGs are deterministic algorithms with relatively low complexity. #encryption #ecdsa #ellipticcurve #algorithm #algorithms #bitcoin #ethereum
A great article that goes over how the #SIKE algorithm was cracked with a single #PC and high-level #theoretical #mathematics re: the #EllipticCurve. #EllipticCurveCryptography
https://phys.org/news/2022-11-mathematical-theorem-encryption-algorithm.html
Did you know?
"An Elliptic Curve Primality Proving (ECPP) algorithm was used via a primality proving program, Primo 4.3.0 - LX64, to generate a primality certificate which deterministically verifies the primality of p. The certification process took 39 days and 8 hours to complete using an AMD Ryzen Threadripper 2950X (16-Core, 32-Thread, 3.5GHz Base)."
Here's a fun fact: the oldest-known rational point on *any* #ellipticCurve lies on
y(6-y) = x³ - x
This was considered by Diophantus, problem 24 of Book IV of Arithmetica:
"To divide a given number into two numbers such that their product is cube minus its side"
The "given number" is 6, and the cube turns out to have side length 17/9.
The rational point is:
(x,y) = ( 17/9 , 26/27 )
https://mathoverflow.net/questions/360834/why-is-this-the-first-elliptic-curve-in-nature
the probability measure of x is proportional to sin^x.dx
Where x is solution to a given #ellipticcurve
Range (-1,1) makes cos/sin as eigenvalues work
- group of rational points on an #ellipticcurve has a finite basis. This means that for any elliptic curve there is a finite subset of the rational points on the curve, from which all further rational points may be generated.
ISO rejects the NSA's IoT crypto standard, believing it to be backdoored https://boingboing.net/2018/04/24/fool-me-once.html #internetofshit #ellipticcurve #simonandspeck #standards #security #infosec #snowden #spooks #Post #nist #sdos #iot #ISO #nsa
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