Considerable amounts of data accordingly need to be download and stored at decentralized nodes to carry out meaningful validations. For the Bitcoin blockchain.
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Inputs and outputs are therefore uniquely identified by the ID of the transaction which contains them and their index in the input list and output list, respectively.
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The purpose of a transaction is to spend outputs by creating new ones, which represents the money flow. An output can only be referenced once, and the outputs in the blockchain which have not been referenced at any given moment in time is called the set of unspent outputs. Every transaction carries an implicit transaction fee , which is the difference between the sum of the values of the outputs and the sum of the value of the referenced outputs. Transaction fees will be paid to the miners, which thus prioritize transactions based on their fees, i. Since a block can only be 1 MiB in size, miners will usually consider transaction fees as a function of satoshis per byte of the transaction, i.
Transaction fees are an essential economical element of the Bitcoin network and change constantly depending on the number of transactions in the mempool and how much peers are willing to pay the miners. Special transactions without any inputs referencing other outputs are so-called coinbase transactions and are created when a block is mined to reward the miner, which is how Bitcoins are initially created. That is, before a miner mines a block, they will first create a coinbase transaction which will be put in the block and rewards them with Bitcoins.
This reward is a fixed amount, which gets halved every , blocks, plus the fees of all transactions in the block. Transactions in the Bitcoin network are verified by using a small stack-based language, the programs of which are called scripts. These scripts can perform arithmetic, cryptography, flow control and so on. All of these scripts are then evaluated, and for the transaction to be valid, there must be only one element on the stack after evaluation and this element must be equal to true.
The scripting language contains special instructions for elliptic curve cryptography, which is used within this scripting framework to cryptographically secure transactions.
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Bitcoin Addresses. The hash is then serialized using base58 encoding, which is a more human-readability-friendly version of the base64 encoding and removes ambiguous-looking characters e. We omit the technical details here as they are not required for the scope of this paper. This means that if an attacker leaks a secret key, they gain control over the balances of two addresses. We can define the balance of a P2PKH address by using the previously mentioned scripts.
How to Compress Bitcoin
In this section, we will outline the methodology that we use to discover explicit Bitcoin key leaks, i. To this end, we follow the general idea of open source intelligence OSINT , in which an attacker harvests publicly available information to derive sensitive information. Given its popularity, we expect that Bitcoin users accidentally leak secret information there. Examples of such leaks would be users publishing code snippets doing Bitcoin transactions or the debug output of some wallet software which users want to share privately, not knowing that these pastes are then publicly visible in the Pastebin feed.
We monitored all pastes starting from September and scanned each paste for Bitcoin secrets, i. To scan a paste for secret Bitcoin keys, we leverage the observation that Bitcoin keys are serialized using a well-known format. Then, 0x80 is prepended to b and optionally 0x01 is appended if the secret key will correspond to a compressed public key. Then SHA is applied twice on b , and we call the last four bytes of this hash c. The WIF is defined to be the base58 encoding of b c. The last 4 bytes in this format are a checksum for the remaining bytes, which is used in practice to avoid copy and paste mistakes.
However, this checksum also allows a systematic scan for instances of WIF strings in text with a very low probability of false positives. In our Bitcoin monitoring tool, we thus proceed for each new paste as follows. Both of these constraints are a consequence of the base58 encoding and the fact that the fixed byte 0x80 is prepended. For each string which matches these criteria, we compute and verify the checksum as described above. Finally, we check if the secret key is in the valid range cf. To apply our methodology, we monitored and scanned all public pastes on Pastebin since September We identified 21, secret keys, which correspond to 42, addresses, i.
However, most of these addresses are unused, i. As of now, Open image in new window of those addresses held a balance at some point in time. However, for stealing Bitcoins it is not sufficient that an address held a balance at some point in time. Instead, we also have to take into account that the address held a balance after we have seen the corresponding secret key in a paste. If we respect this constraint, we find that Open image in new window addresses held a balance after we have seen their secret key in a paste.
Those keys were scattered among a total of 34 pastes. Summing up those balances gives a total of It should be mentioned, though, that this is still not a guarantee that this number of Bitcoins could have been stolen. This is due to the fact that we determine the balance of an address at some point in time based on the blockchain, not the mempool.
That is, we take the latest block that was mined before the paste was published and check the balance of an affected address up to this block. It could be the case that there was a transaction in the meantime which redeemed outputs from the given address, i.
In this case, an attacker could not easily create a transaction to steal the Bitcoins. Current network rules discourage the distribution of transactions that double-spend outputs unless the transaction is explicitly marked as a replace-by-fee RBF transaction.
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An attacker could try to mine a stealing transaction themselves or try to directly announce the stealing transaction to mining pools which do not follow these network rules. Alternatively, if the blocking transaction has a low fee, the attacker could wait until a significant number of peers do not have the transaction in their copy of the mempool anymore. This would increase the chances that the new stealing transaction will be pushed to more peers, which in turn will increase the chances that the stealing transactions will be mined.
However, none of these methods guarantees success, and therefore the amount of To get a more conservative estimation of the amount of stealable Bitcoins, we have to consider pending transactions. That is, we only considered cases where there was no transaction in between which was not marked as RBF. As it turns out, this was the case for 26 addresses in pastes. For the remaining cases, there was a blocking transaction in between, i. For example, one paste contained an address holding a balance of In total, we found that an attacker could have stolen We excluded transaction fees in this analysis as they are highly dynamic over time and the number of stealable outputs was so small that the resulting fees would not be a significant factor.
This demonstrates that an attacker can cause significant financial loss with relatively simple means. This is amplified by the fact that an attacker could expand this methodology to other cryptocurrencies and OSINT platforms. Seeing that even explicit key leaks pose a problem to Bitcoin users, in this section, we will study how users implicitly leak secrets. We then show how the incorrect use of this primitive opens severe vulnerabilities. That is, we will systematically describe how an attacker monitoring the transactions of the Bitcoin network can use nonce reuse to steal Bitcoins, and what amount of damage could have been caused or was caused in the past by attackers.
The hash h is then interpreted as a number and truncated so that it does not contain more bits than the group order n. In the next step, we need to identify the nodes and edges which can be mapped to a solvable system of linearly independent equations. This can be achieved by finding non-trivial cycles in G , i.
Hence, for all such cycles we can leak the corresponding secrets, and, as before, we can also leak the secrets of the reachable nodes. There is, however, a little twist to the methodology we described here. This is not strictly true, as the r value is only the x -coordinate of Gk. This means that if the r values coincide, we need to take into account that one nonce might be the additive inverse of the other rather than being equal. For each such combination we have to solve the system of linear equations and check if the returned solutions are correct to leak the correct keys and nonces.
The 10 most frequent r values and their number of occurrences. Number of occurrences of the most prominent duplicate r value over time. Inspecting the other duplicate r values a bit more closely reveals further interesting cases.
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The second most used r value also has 16 leading 0 bits, which is also an indication that the corresponding nonce was not chosen randomly. Similarly, we found two other r values where the corresponding nonces where suspiciously small, i. Using this methodology, we managed to leak out of the 1, possible nonces Open image in new window and 2, out of the 4, secret keys that were used in conjunction with these nonces Open image in new window.
In total, this gives us theoretical control over the balances of 5, addresses, i. The final shape of G did not contain any more cycles, which means that we have leaked the maximum number of secrets. Number of Bitcoins an attacker could have stolen based on a balance threshold. To assess how much an attacker could have stolen over time, we consider two scenarios.
First, we assume an attacker which steals the peak balance of each address over time. That is, we take the sum of the peak balances of each address, which gives a total of Here, we implicitly assume that the owner notices the fraud and therefore we ignore all future funds. However, this attack model requires an attacker to know the peak balance in advance, which is unrealistic.
Note that even though one address alone had a balance of Given the current value of Bitcoin, we believe that it is unrealistic for a single individual to hold such a large balance. Additionally, we also did not consider blocking transactions in this case, as an attacker monitoring transactions can create stealing transactions as soon as possible. Comparison of a spike where Bitcoins might have been stolen due to a sudden drop in stealable Bitcoins left and a case where we see a smooth decrease indicating that no coins might have been stolen right.
Regarding the fourth and fifth spike, we did not observe a similar suspicious drop regarding the number of Bitcoins, but only regarding the number of vulnerable addresses. To see the difference, consider Fig. In the former, we can see a sudden drop in the number of stealable Bitcoins, i.
We identified a single transaction which transferred all the stealable Bitcoins, indicating a theft. The fact that the number of vulnerable addresses did not decrease to 0 at the same time can be explained by various reasons. For instance, it could be possible that the attacker was not aware of the remaining vulnerable addresses.
Or, it could be the case that the attacker used a balance threshold and determined that the remaining addresses are not worth stealing from based on this threshold, because as we can see, the 0.