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.
Decoy (Dummy) Utxos.
5
Decoy outputs will also be spent eventually.
Lelantus
A one kernel indicates that a transaction was not merged with any other transactions. Grin does not have many of them because there are not a lot of transactions in the Grin network.
By creating decoy, aka Dummies, UTXO’s.
The minimum number is five (5).
The decoy transactions are eventually spent, therefore not creating any permanent clutter on the blockchain.
Lelantus
1.) A trx that has not been merged with others = one kernel
Grins Network isn’t saturated → not enough trx’s to be merged
2.) Decoy UTXO’s. Every merged trx needs atleast 5 outputs
3.) 5
4.) Decoys are eventually spent and not saved forever
5.) Lelantus-MW
As stated in Grin’s response and repeated by Beam, a large percentage of blocks in Grin’s blockchain have only 1 transaction occurring in them, while a significant number of blocks have zero transactions. In this environment, linking inputs and outputs is not even necessary. Without saturation, single kernels can be intercepted in the stem phase before aggregating with other transactions, as well.
Beam’s first solution is that in every step of the Dandelion stem, Beam nodes check that there are at least 5 outputs, and if there are not, the node adds decoy outputs. At a random later stage, that node adds decoy inputs to a random transaction. This method turns definite links into probabilistic links. The next solution is to implement Lelantus-mw, which will increase the anonymity set to 100K’s.
Five.
Nodes which add decoy a decoy output later add a decoy input as well. These transactions eventually get removed with the cut-through process.
Lelantus-mw.
What is a ‘one-kernel transaction’, and why does Grin have so many of them?
A one-kernel transaction means a transaction that is not merged with any other transaction, so inputs are linked to its outputs.
Grin has so many one-kernel transaction because the network is not saturated and there are not enough transactions to be merged in the stem phase of Dandelion protocol. As the usage grows, the anonymity will improve.
What is Beam’s solution to linkability?
Beam’s solution to linkability is through 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.
What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
At least 5
How does Beam prevent dummy transactions from cluttering up the blockchain?
At a later stage 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.
What protocol will increase the anonymity set of Beam to 100,000+?
Lelantus-MW
one kernel transaction is basically a TX that have not been merged with others. This is due to low usage of the blockchain.
Dummy UTXO’s prevent one kernel transactions.
5 outputs required to re-broadcast
prevent dummy UTXO’s from clogging the blockchain by spending them at a later date.
lelantus-MW
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 network is not saturated and there are not enough transactions to be merged in the stem phase of Dandelion protocol.
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.
Minimum 5.
The decoy outputs are eventually spent and removed from the blockchain.
Lelantus-MW will dramatically increase the anonymity set (100K outputs).
One-kernel transactions are transactions where linkability is possible because inputs match outputs with only one kernel. This transactions have not yet been aggregated with other txs outputs with other kernels.
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.
Beam’s solution to linkability are decoy signatures (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.
Each one of the dummy outputs has a value of zero, but it is completely indistinguishable from regular outputs — all outputs look like random numbers. 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. Since those decoy outputs are eventually spent, the mechanism doesn’t create any permanent clutter on the blockchain.
The anonymity set of Beam to 100,000+ will be increased by Lelantus MW
‘One-kernel transaction’ refers to a transaction was not merged with any other transactions. Grin has so many of them because Grin network is not saturated and there are not enough transactions to be merged in the stem phase of Dandelion protocol.
Beam uses the concept of decoy (aka Dummy) UTXOs.
Seven is the minimum number of outputs required.
The mechanism does not create any permanent clutter on the blockchain. 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.
Lelantus-MW will increase the anonymity set of Beam to 100,000.
One kernel indicates it was not merged with any other transactions, thus the inputs are linked to it’s outputs.
By adding decoy UTXO’s.
5
The decoy outputs are eventually spent.
Lelantus-MW
1.) A “one-kernel transaction” is a transaction that isn’t merged with any others, which means the inputs and outputs of the transaction are linked. A connection between two parties can be shown with enough of these links by constructing a graph of different wallets. GRIN has many of these “one-kernel” transactions because its network isn’t saturated enough, and the stem phase of the Dandelion protocol use don’t have enough transactions to merge together (anonymity set is low).
2.) BEAM’s solution to linkability is implementing decoy UTXO’s. BEAM nodes constantly check if transactions are merging at the stem phase of Dandelion, and that these transactions contain at least 5 outputs for sufficiency.
3.) The minimum number of outputs required for BEAM nodes to re-broadcast a transaction is 5 outputs.
4.) BEAM prevents dummy transactions from cluttering up the blockchain by adding them as inputs to other random transactions. Since these transactions are most likely carried out by a different user, they are spent and removed from the blockchain completely.
5.) The protocol that will increase the anonymity set of BEAM to 100,000+ is Lelantus-Mimblewimble. The implementation of Lelantus will make it almost impossible for observers to build the transactions graph if the user chooses Lelantus-MW transactions here-and-there.
What is a ‘one-kernel transaction’, and why does Grin have so many of them?
A one-kernel transaction is one which has not been merged and referenced with other transactions, effectively exposing the parties of a given transaction.
The single-kernel transactions is a result of limited network usage.
What is Beam’s solution to linkability?
Beam makes sure that there are at least 5 outputs added to a transaction, and if not - decoys are added where possible to buff up the ‘anonymity set’.
What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
In order to re-broadcast a transaction, the transaction must have 5 outputs.
How does Beam prevent dummy transactions from cluttering up the blockchain?
A Bean node will add dummy UTXOs as inputs into a random transaction, which spends them and removes them from the blockchain. This also has the effect of making a relation between users that are actually unrelated, bolstering up the anonymity set of transactions on the Beam network.
What protocol will increase the anonymity set of Beam to 100,000+?
Beam states that Lelantus-MW will increase the anonymity set to 100,000+, which would make it almost impossible to build the transactions graph, as recognised in the original ‘attacker’ blog post.
What is a ‘one-kernel transaction’, and why does Grin have so many of them?
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.
What is Beam’s solution to linkability ? : Through the concept of decoy (aka Dummy) UTXOs.
What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction ? : At least 5 outputs.
How does Beam prevent dummy transactions from cluttering up the blockchain? By Adding random UTXOs to spend the dummy transactions.
What protocol will increase the anonymity set of Beam to 100,000+? : Lelantus-MW dramatically increases the anonymity set to (100K outputs) making it pratically impossible to build a transactions graph
if the user choses to use Lelantus-MW.
A ‘one-kernel transaction’ is a transaction on the Grin blockchain that involves only one output, meaning that the funds being transferred are being sent to a single destination. Grin has a high number of one-kernel transactions because the Grin blockchain uses a unique transaction fee structure that incentivizes users to create one-kernel transactions in order to minimize fees.
Beam’s solution to linkability is to use a technique called “off-chain aggregation,” which allows multiple transactions to be bundled together and treated as a single transaction on the blockchain. This helps to obscure the specifics of individual transactions and make it more difficult to link them to specific parties.
The minimum number of outputs required for Beam nodes to re-broadcast a transaction is 5.
Beam prevents dummy transactions from cluttering up the blockchain by using a “burn” mechanism that destroys excess funds that are not needed for a transaction. This helps to reduce the overall size of the blockchain and prevent it from being bogged down by unnecessary data.
The “Dandelion++” protocol will increase the anonymity set of Beam to 100,000+ by randomly selecting a small number of nodes to propagate transactions to, rather than broadcasting them to the entire network. This helps to obscure the source of a transaction and increase the number of potential parties involved, making it more difficult to trace the transaction back to a specific individual.
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.
What is Beam’s solution to linkability?
BEAMs solution to linkabilty is via using decoy (aka Dummy) UTXOs.
What is the minimum number of outputs required for Beam nodes to re-broadcast a transaction?
At least 5 outputs.
How does Beam prevent dummy transactions from cluttering up the blockchain?
Since those decoy outputs are eventually spent, the mechanism doesn’t create any permanent clutter on the blockchain.
What protocol will increase the anonymity set of Beam to 100,000+?
Lelantus-MW will dramatically increase the anonymity set (100K outputs) and will make it almost impossible to build the transactions graph if the user choses to use Lelantus-mw transactions from time to time.