Quote from: kTimesG on Today at 09:20:08 AM

Quote from: tifosi87 on May 10, 2024, 08:19:01 PM

hi all i read the post since one year sorry for my english i found a interesting think but i does takes me further. in every elliptic curve like y^2= x^3+7 there is something interesting like :
if P(1,y1) - k times--> Q(-29/3 ,y2)
P(2,y3) --k times--> Q(-3,y2)
so on there is a simple math here where k is always too know independent from whcih curve we work .
i don't want to give more information this operation is 10 times faster then k*G= and find the x value

Too bad the points need to be on the curve. We already know about the endomorphisms.

I'd say any attempt to break a private key that involves more than a constant amount of scalar multiplications (no matter how well optimized by precomputed tables), has very few chances of success.
Any multiplication means, by definition, more than one addition, more time.

Random key -> multiply and match -> good luck waiting.

First level of magnitude reduction: don't do scalar multiplications.

Second wall to break is then the point addition (and there's one more after that, and finally one more after). I already said too much, but I believe there's something that can run around 20x in less time (fewer computations) if we know the public key and simplify the question. Some known details around secp256k1 help a lot.

Yeah I endorse what is kTimeG is saying.
the problems is way more deep than I even expected, honestly

I'm not specialist in secp256, not even close, but the sheer amount of calculation is above my capacities. Besides my Jupyter and R have an absolutely collapse trying to do the statistics

a simple example, for the puzzle 65 the coordinates are
X: 21769406468394979245979020739332080729679479243955596515614749275274212371227
Y:102907830890434238525231690377346540046672568029169549965500018466490455252476

you will understand very quick floating point problems, if you come from scientific field like me
besides all the shenanigans around binary calculation Huh

One website I found fantastic is https://learnmeabitcoin.com/
This person need a award because the site is amazing.
Have a lot of calculator and they try to simplify the max possible but honestly is absurdly convoluted.
But I admire their effort, is worth it to take a look

Another stuffs I was reading is this week was

https://pure.tue.nl/ws/portalfiles/portal/128510960/BEP_BSA_298_299_300_301.pdf
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3367674
https://engineering.purdue.edu/kak/compsec/NewLectures/Lecture7.pdf

On this papers you may can guess why K3ntina is trying to push this idea of the circle: its because of the nature of the calculation, sometimes they have a sqrt(2) have on the pi series expansion in the 3order almost the same decimals where some of the addresses can be build on it.
But again, correlation is not causation: k3ntina is suffering of apophenia... very common in conspiracy theorist

again I'm not bitcoin specialist, i'm scientist so I went to my route what is: statistics
Apparently even if is a HD and this are child wallets, the reality hass one detail: the onwer FORCED to have this structure.
This reminds me a lot of the case of the Profanity (article: https://medium.com/@rebryk/how-to-hack-a-vanity-address-generated-with-profanity-ffad61ecacd2).
Beside my cpu almost meltdown of trying to run that code, the idea from this case is is very simple, but on bitcoin has one caveat: we dont have the extended public key and is essential on this case.
so my best next guess is to try to see if the pseudo-random numbers interfere in the wallet construction beside the owner own interference.... and Im still learning but looks like has something on that could be use to reduce the range of the search

Btw, on the k3ntina offer, I also offer a zoom meeting to discuss about it Grin