Breaking Beam - Reading Assignment

Privacy Coins - Ultimate Course
#21

  1. What is a ‘one-kernel transaction’, and why does Grin have so many of them?
    The reason for a large amount of such one-kernel transactions being broadcast to the network is that Grin network is not saturated and there are not enough transactions to be merged in the stem phase of Dandelion protocol.

  2. What is Beam’s solution to linkability?
    Beam creates 4 additional decoy transactions with are merged with a real transaction.

  3. What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
    At least 5 outputs.

  4. How does Beam prevent dummy transactions from cluttering up the blockchain?
    By getting the nodes to add dummy UTXOs as inputs to a random transaction, most likely belonging to a different user, thus spending them and removing them from the blockchain, but also by creating a relation between users that are in fact unrelated.

  5. What protocol will increase the anonymity set of Beam to 100,000+?
    Lelantus-MW

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#22

  1. A “one-kernel transaction” is a transaction that has not been merged with any other transactions. There are many of them on GRIN because the blockchain is new and there are currently not many users.

  2. Beams solution is to employ decoy or “dummy” outputs.

  3. The minimum number of outputs required for a BEAM transaction to re-broadcast is 5. If it does not have 5 outputs, “dummy” outputs are added.

  4. The are of zero actual value so they are later added to a randomly chosen future transaction and “spent”, effectively removing them from the blockchain.

  5. BEAM plans to activate Lelantus-MW, which will increase the anonymity set (all outputs) to 100,000.

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#23

  1. What is a ‘one-kernel transaction’, and why does Grin have so many of them?
    One kernel transaction indicates that was not merged with any other transactions, and thus the inputs are linked to its outputs.
    Grin has so many because the network is not saturated and there are not enough transactions to be merged in the stem phase of Dandelion protocol.

  2. What is Beam’s solution to linkability?
    Adding decoy (Dummy) UTXOs in the transactions.

  3. What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
    Five.

  4. How does Beam prevent dummy transactions from cluttering up the blockchain?
    Adding the dummy UTXOs at a later stage as inputs to a random transaction, thus spending them and removing from the blockchain; and also creating a relation between users that are in fact unrelated.

  5. What protocol will increase the anonymity set of Beam to 100,000+?
    Lelantus-MW.

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#24

1 - What is a ‘one-kernel transaction’, and why does Grin have so many of them?

Grin, having one kernel indicates that a transaction was not merged with any other transactions, and thus the inputs of this transaction are linked to its outputs. The reason why there are so many one-kernel transactions being broadcast to the network is because the Grin network is not saturated and there are not enough transactions to be merged in the stem phase of Dandelion protocol. As the usage increases, the anonymity set will become more effective.

2 - What is Beam’s solution to linkability?

Beam decided to use a concept of decoy (aka Dummy) UTXOs. At every step of the Dandelion Stem Phase, Beam nodes check whether the merged transactions (might be only one transaction) have at least 5 outputs. If not, decoy outputs are added to the merged transactions, making sure that the number of outputs is at least 5.

3 - What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?

If needed, decoy outputs are added to the merged transactions, to ensure that the number of outputs is at least 5

4 - How does Beam prevent dummy transactions from cluttering up the blockchain?

Permanent clutter on the blockchain is not possible because at some later point a randomly chosen block height for each output, the node adds dummy UTXOs as inputs to a random transaction, most likely belonging to a different user, thus spending them and removing them from the blockchain, but also creating a relation between users that are in fact unrelated. Hence the “decoys” name.

5 - What protocol will increase the anonymity set of Beam to 100,000+?

The Lelantus-MW will dramatically increase the anonymity set (100K outputs), and will make it almost impossible to build the transactions graph, if the user chose to use Lelantus-mw transactions from time to time.

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#25
  1. “In Grin, having one kernel indicates that a transaction was not merged with any other transactions, and thus the inputs of this transaction are linked to its outputs.”
  2. The usage of at decoy transactions with value 0
  3. 5 at least one real and 4 decoys
  4. “At a later stage (a randomly chosen block height for each output), the node adds dummy UTXOs as inputs to a random transaction, most likely belonging to a different user, thus spending them and removing them from the blockchain, but also creating a relation between users that are in fact unrelated .”
  5. Lelantus-MW
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#26

#1 - What is a ‘one-kernel transaction’, and why does Grin have so many of them?
low usage of GRIN

#2 - What is Beam’s solution to linkability?
usage of decoy UTXOs

#3 - What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
five (5)

#4 - How does Beam prevent dummy transactions from cluttering up the blockchain?
the decoy outputs are eventually spent

#5 - What protocol will increase the anonymity set of Beam to 100,000+?
Lelantus-MW

1 Like
#27

  1. A one kernel transaction indicates that a transaction was not merged with other transactions and consequently the inputs are linked to its outputs. Until now the Grin network is too small which means there are not enough transactions to be merged in the stem phase of Dandelion protocol.

  2. They use a concept of decoy (aka Dummy) UTXOs. When there are less than five outputs decoy outputs are added.

  3. 5 outputs are needed

  4. In later transactions a node adds dummy UTXOs as inputs to random transactions which then are spend and removed from the blockchain. With this “spend” mechanism cluttering up the blockchain is prevented

  5. Lelantus-MW

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#28

  1. A one kernel transaction is where the input is connected to the output. Grin has so many as there has not been enough of an adoption of Grin to be able to mix transactions in the STEM phase.

  2. Beam’s solution to linkability it to have dummy UTXO’s.

  3. 5

  4. Beam prevents clutter on the blockchain by spending the dummy tx’s.

  5. The Lelantus-MW protocol will increase the anonymity set of Beam.

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#29

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#30

1. What is a ‘one-kernel transaction’, and why does Grin have so many of them?
It’s a transaction that was not merged with any other transaction since there is not enough transaction volume for it to be merged in the stem phase of the Dandelion protocol.This means that sender and receiver are linkable, but as it grows, so will the levels of anonymity.

2. What is Beam’s solution to linkability?
Use of decoy/dummy UTXO’s

3. What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
5

4. How does Beam prevent dummy transactions from cluttering up the blockchain?
Since decoy outputs are eventually spent, the mechanism doesn’t create any permanent clutter on the blockchain

5. What protocol will increase the anonymity set of Beam to 100,000+
Lelantus-MW

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#31

  1. What is a ‘one-kernel transaction’, and why does Grin have so many of them?
    A one-kernal transaction is a transaction which is not merged with other transactions. Which means that inputs and outputs of transactions are not clearly linked.

  2. What is Beam’s solution to linkability?
    Beam nodes check wether the merged transactions have at least 5 outputs.

  3. What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
    3 -5

  4. How does Beam prevent dummy transactions from cluttering up the blockchain?
    Decoys are eventually spent, preventing cluttering of the network.

  5. What protocol will increase the anonymity set of Beam to 100,000+?
    Lelantus

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#32

• One Kernel transaction means that is not merged with any other Tx, and thus the inputs are linked to the outputs. The network is not saturated, basically not enough users
• Decoys (aka Dummy) UTXOs.
• At every step of the stem Dandelion phase beam nodes check for a minimum of 5 outputs. If not, decoys are added.
• If I understand correctly is by adding real UTXOs from other users, that will be at certain point of time spend them.
• Lelantus MW

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#33

  1. A “one-kernel” transaction is a transaction which has not been mixed with another one. Grin has so many because it is not currently processing many transactions.

  2. Beam’s solution to link-ability is to use decoy (dummy) UTXO’s to increase the number of outputs.

  3. I may be missing something here, but according the Beam blockexplorer, explorer.beam.mw the minimum number of outputs required to re-broadcast a transaction is; 1 output for a block with 1kernel, and 7 outputs for a block with two or more kernels. Hmm…

If I am wrong on this, is there some confusion regarding the term “outputs”?

  1. Beam prevents dummy transactions from cluttering-up the blockchain by later adding dummy UTXO’s as inputs to a random transaction, thereby spending them and removing them from the blockchain.

  2. The protocol which will increase the anonymity set of Beam to 100,000+ is Lelantus-MW.

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#34
  1. A “one-kernel transaction” is a non-aggregate transaction, which means that you can see the link between inputs and outputs. Unfortunately Grin has many because it is not yet much used.
  2. To solve the linkability problem Beam uses decoy transactions (Dummy). It’s a step that is done at every step of the Dandelion Stem Phase. If the transactions have less than 5 outputs, decoys are added to reach 5 outputs.
  3. 5 outputs.
  4. Beam has been set up so that decoy transactions are spent after being used, so that they are eliminated and do not clog the blockchain.
  5. Lelantus-MW.
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#35

  1. A “one-kernel” transaction is a transaction which has not yet been mixed with another one. Grin has so many because it is not currently processing many transactions.

  2. Beam’s solution to link-ability is to use decoy (dummy) UTXO’s to increase the number of outputs.

  3. According to this article the minimum number of outputs required for Beam nodes to re-broadcast a transaction is 5.

  4. Beam prevents dummy transactions from cluttering-up the blockchain by later adding dummy UTXO’s as inputs to a random transaction, thereby spending them and removing them from the blockchain.

  5. The protocol which will increase the anonymity set of Beam to 100,000+ is Lelantus-MW.

#36
  1. In Grin, having one kernel indicates that a transaction was not merged with any other transactions, and thus the inputs of this transaction are linked to its outputs. The reason for a large amount of such one-kernel transactions being broadcast to the network is that Grin network is not saturated and there are not enough transactions to be merged in the stem phase of Dandelion protocol.
  2. Decoy (aka Dummy) UTXOs.
  3. 5 outputs.
  4. The decoy outputs are eventually spent, the mechanism doesn’t therefore create any permanent clutter on the blockchain.
  5. Lelantus - MW
#37
  1. A kernel tx is one that was not merged with any other tx, meaning that inputs and outputs of such transactions are clearly linked. Grin has many of them because it is still not popular.
  2. Beam creates 4 additional decoy transactions that are merged with a real transaction.
  3. At least 5 outputs.
  4. Decoys are eventually spent, preventing cluttering of the network.
  5. Lelantus-MW
#38

1: A 1 kernel TRx is where the TRx is not mixed with any other TRx and therefore the inputs and outputs can be linked together.
2:BEAM adds 4 additional decoy TRXs to the real TRXx merging them together making it very difficult to identify the corresponding inputs to outputs link
3: A minimum of 5 outputs are required
4: Spending the decoys removes them form the BC
5:Lelantus

#39
  1. A one kernel transaction indicates that a transaction was not merged with any other transactions, and thus the inputs of this transaction are linked to its outputs.

Grin has so many one kernel transactions because Grin’s network is not saturated and there are not enough transactions to be merged in the stem phase of Dandelion protocol.

  1. Using decoy (dummy) UXTO’s.

  2. 5 outputs.

  3. By adding dummy UTXOs as inputs to a random transaction, thus spending them and removing them from the blockchain, but also creating a relation between users that are in fact unrelated.

  4. Lelantus-MW

1 Like
#40

  1. What is a ‘one-kernel transaction’, and why does Grin have so many of them?
    that is a transaction that has not yet been aggregated. The Grin network is as of now rather small with a low transaction volume therefore there are not a lot of transactions to aggregate. The anonymity set is small.

  2. What is Beam’s solution to linkability?
    Beam deploys decoy UTXOs. so during the stem phase of the dandelion at least 5 UTXOs need to be present if not an amount is added to create at least 5 outputs. Basically creating a synthetic anonymity set.

  3. What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
    5

  4. How does Beam prevent dummy transactions from cluttering up the blockchain?
    At a later stage (a randomly chosen block height for each output), the node adds dummy UTXOs as inputs to a random transaction, most likely belonging to a different user, thus spending them and removing them from the blockchain, but also creating a relation between users that are in fact unrelated . Hence the “decoys” name.
    It’s important to note that since those decoy outputs are eventually spent, the mechanism doesn’t create any permanent clutter on the blockchain.

  5. What protocol will increase the anonymity set of Beam to 100,000+?
    The release of Lelantus -MW will have that effect.