Did you already break the Elliptic Curve, Satoshi, you there?

[omnicreor]

I have been exploring the intricacies of Elliptic Curve Cryptography (ECC) for several years. My interest stems from a skepticism about the ubiquitous use of ECC, which, while currently deemed secure, is susceptible to the relentless advancement of time and technology that historically challenges cryptographic methods.

During my research, I analyzed a collection of public keys attributed to Satoshi Nakamoto. Upon plotting these keys on an elliptic curve, I observed a curious pattern, as shown here: https://ibb.co/zrsDy6c

What struck me as extraordinary was the apparent orderly generation of these public keys. They seem to follow a sequential arrangement along the X-axis, with corresponding values on the Y-axis that collectively form a discernible shape on the curve. This discovery is baffling, as generating public keys in such a precise and ordered manner on an elliptic curve is, to my knowledge, an incredibly challenging, if not impossible feat. I have thoroughly investigated this phenomenon but have yet to find an explanation.

This pattern has led me to ponder several possibilities:
- Could it be possible that Satoshi had found a way to 'break' the elliptic curve as early as 2009?
- Is there a chance that these public keys represent a puzzle, intentionally designed by Satoshi, awaiting a solution?

As of today, these public keys are associated with an estimated value of $72 billion, adding another layer of intrigue to this cryptographic enigma.

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[TamariskDigitalAssetRecov]

Do you have the data behind this plot available? Are the clusters by date? If so, do you know what are the date ranges for each cluster and are the clusters plotted in a sequential order?

[omnicreor]

I've attached the data related to our discussion here: https://file.io/yG3ub34oQqTB.

Regarding the elliptic curve model, it's interesting to note its similarity to models used in the telecom industry, particularly in the context of public key distribution on elliptic curves. This approach focuses on extracting relevant data by targeting the center of each cluster.

This method's resemblance to techniques used in companies like Ericsson leads me to wonder if Satoshi might have a background in the telecom sector. 😊

[NotATether]

I don't think it's part of any larger "puzzle" but that he's just damn good at math.

[moonie]

The distribution of public keys on an elliptic curve might naturally exhibit certain patterns or clusters. This is not indicative of any weakness or manipulation but rather a consequence of how these keys are mathematically generated and distributed across the curve. The specific characteristics of the elliptic curve used in ECC (e.g., curve parameters) might influence the distribution of public keys in a certain manner. This influence might manifest as an observable pattern when a large set of keys is plotted graphically.

In any large set of data, especially cryptographic data, there can be statistical anomalies that appear significant but are actually coincidental.

[omnicreor]

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[snuffman8]

Whoa, this is some next-level crypto detective work! Plotting Satoshi's public keys on an elliptic curve and spotting that sequential pattern is mind-blowing. The puzzle aspect has me hooked – could it be Satoshi's way of leaving a trail for future cryptographers? $72 billion worth of intrigue right there. Any fellow crypto sleuths here with thoughts on cracking this enigma?

[jpbh81]

Jack the Ripper in person.

i hope you solve it.

[citb0in]

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Let me give you an example, just try it on normal calculator, subtract 1 from the following and then
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Digaran, stop creating mass fake accounts and spreading around. You're even using your signature ~dig OMG
This is really getting ridiculous.

In a bid to keep my research and efforts transparent and accessible, I have decided to share the GitHub repository containing my work on elliptic curve cryptography (ECC). Here's the link to the repository:
https://github.com/ecc-r/ECC-Vulnerability-Research

your python program yields following error:

line 122, in is_point_odd
    point_exponent = point_exponent(point, scalar)
                     ^^^^^^^^^^^^^^
UnboundLocalError: cannot access local variable 'point_exponent' where it is not associated with a value

The name of the function is used as a variable in the function itself, which leads to an UnboundLocalError. To fix that bug, here's a patch...

Create a new file bugfix.patch inside your local git folder with following content:

Code:

diff --git a/ecc_analysis.py b/ecc_analysis.py
index d216974..7307f5a 100644
--- a/ecc_analysis.py
+++ b/ecc_analysis.py
@@ -119,7 +119,7 @@ def is_point_odd(point):
 
     scalar = CURVE_MAX - 2
 
-    point_exponent = point_exponent(point, scalar)
+    result = point_exponent(point, scalar)
     modulo_2_result = point_multiplication(point, point_exponent)
 
     if modulo_2_result == get_first_point():

and then apply the patch

Code:

git apply bugfix.patch

or just merge in your branch, I created a pull-request in your git repo, feel free to check and update. I have included the patch in the forked repository here.

[omnicreor]

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[omnicreor]

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[jpbh81]

Thank you for your insights and the shared script. Firstly, the assertion that "we can not multiply a point by another point" in ECC is contextually accurate in the realm of today's cryptographic applications. However, we must remember that the field of mathematics and cryptography is in a constant state of evolution. What we "currently can not do" is precisely what paves the way for future breakthroughs. My work is dedicated to investigating these unexplored potentials.

By sharing my research on GitHub, I aim to open the doors to collaborative innovation, inviting others to join in pushing the boundaries of ECC. This is not just about challenging the status quo but about expanding our collective understanding and capabilities in cryptography.

Let’s continue to advance the field, keeping in mind that today's theoretical explorations could be the foundation of tomorrow's cryptographic realities.

Props, dont listen to  the Karens theres quite of them over here!!

The ecc its so intresting and mind-blowing at te same time

[omnicreor]

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[vjudeu]

My main problem is not "It can't be done", I clearly see it can be done, I just could not realized it yet..

What about this topic? https://bitcointalk.org/index.php?topic=5460766.0

I think this proof is sufficient to say, that it cannot be done, if you use only one public key as your argument. You actually need two public keys: the one you want to reveal the private key for, and the generator. Then, the distance between them is unique. But if you work on your public key alone, without thinking about the generator, then you won't get the proper answer, which was well explained by Garlo Nicon in the topic above.

And I think if you want to break any keys, then you should start with lower numbers, before trying secp256k1 directly. Just to confirm, that your method is "mathematically correct".

[mamuu]

- Is there a chance that these public keys represent a puzzle, intentionally designed by Satoshi, awaiting a solution?

Hello

Can a public key be generated without knowing the private key? yes

https://doc.sagemath.org/html/en/reference/arithmetic_curves/sage/schemes/elliptic_curves/ell_generic.html#

Can the coordinate of a desired number in the curve be generated pubkey at the same time? yes.

After creating the curve, it is possible to create it with the "lift_x" function.
If the source you mentioned has private keys
and if the diagram you show is produced, we can talk about a security vulnerability.
However, it is possible to calculate the points that will form this diagram without private keys.

Thank you.

[omnicreor]

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