Incognito - Reading Assignment

  1. The user requests a shield transaction via the Bond smart contract. The contract checks everything and provides the user with an address (of a custodian) where they should deposit the coins they wish to shield. Once the money’s in the user gets a proof of deposit which they pass along to Incognito network, which then mints the shielded, private version of that particular coin.

  2. They use linkable ring signatures, a homomorphic commitment scheme (checks that amounts are valid without knowing the amount) and zero-knowledge range proofs.

  3. A trustless custodian.

  4. The money comes from the custodian, so I would say one. But who paid the custodian I think is the question.
    Assuming that we work with set amounts and that the total amount of BTC that was shielded was also sent to Bob, then I would say the anonymity set is the total amount of shielded transactions resulting from deposits of that particular amount at that particular custodian’s address.
    Assuming the amount is variable (any amount can be shielded and portions of the shielded amount can be paid out) I’d say the anonymity set is all the shielded transactions at the custodians address that have a minimum value of the amount sent to Bob.

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  1. How does “shielding” work on Incognito?
    decentralized group of custodian

  2. What privacy technology does Incognito use for shielded transactions?
    lnkable ring, zero knowledge proof, homomorphic commitment

  3. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?
    decentralized group of custodian

  4. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)
    the number of shielded tx with the same amount

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  1. Both shielding and unshielding processes are carried out via a decentralized group of trustless custodians. Once shielded, transactions are confidential and untraceable.

  2. They employed the linkable ring signature scheme , homomorphic commitment scheme , and zero-knowledge range proofs .

  3. A decentralised group of trustless custodians.

  4. Its anonymity set is equal to the number of all the shielding transactions which were performed for the same amount of that same coin.

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  1. Shielding is carried out via a decentralized group of trustless custodians. Once shielded, transactions are confidential and untraceable

  2. Incognito uses linkable ring signature scheme, homomorphic commitment scheme, and zero-knowledge range proofs for privacy

  3. The receiver of Alice’s Bitcoin transaction is the decentralized group of trustless custodians

  4. Bob’s anonymity set is all the shielded transactions for the same amount

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1.) How does “shielding” work on Incognito?
Both shielding and unshielding processes are carried out via a decentralized group of trustless custodians .

2.) What privacy technology does Incognito use for shielded transactions?
Linkable ring signature scheme, homomorphic commitment scheme, and zero-knowledge range proofs.

3.) If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?
A decentralized group of trustless custodians.

4.) Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)
The anonymity set is equal to the number of all the shielded transactions which were performed for the same amount of that same coin.

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  1. How does “shielding” work on Incognito?

The user deposits their coin with a trustless custodian of the Incognito network and receives a deposit proof which they can submit to be verified by the network to mint a privacy coin at a 1:1 ratio. They can then transact with others privately on the Incognito network and burn those privacy coins to withdraw the original network coins from the custodian.

  1. What privacy technology does Incognito use for shielded transactions?

Ring Signatures, Stealth Addresses, and Confidential Txs

  1. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?

One of the decentralized trustless custodians of the Incognito network

  1. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)

Well, I would say the number of addresses that deposited to the custodian address from which Bob receives the BTC. However, couldn’t someone swap between assets on the Incognito network? For example, swap pETH for pBTC? So, I’m not sure how to determine the anonymity set if people can deposit on one chain, swap them privately, and unshield coins on another chain. Also, if Bob accumulates pBTC from multiple people and then unshields them, isn’t it possible he would be receiving BTC from multiple custodian addresses? And if he sent those accumulated pBTC to Carol on Incognito and she unshielded them, she would receive BTC from multiple custodian addresses even though she only received the pBTC from one person. So is the anonymity set the number of users on the Incognito network?

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The anonymity set is actually equal to the number of same denominations of the same coin. Meaning if Bob withdraws 1 BTC his anonymity set is equal to all withdraws from the Incognito network of 1 BTC. :slight_smile:

  1. Shielding on Incognito is a process that allows to take cryptos and make them private through a decentralized group of trustless custodians which employ a number of techniques (linkable ring signatures, commitment schemes and zk-range proofs) to allow untraceability and confidentiality.
  2. As mentioned above, it uses linkable ring signatures, commitment schemes and zk-range proofs, which are all privacy-oriented technologies.
  3. A decentralized group of trustless custodians.
  4. Its anonymity set is equal to the number of all the shielding transactions which were perfomed for the same amount of that same coin.
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1 The shielding mechanism is based on the experience of building our first-generation trustless bridge, between Incognito and Ethereum. In particular, Incognito generalize it to enable a wider range of cryptonetworks to be interoperable with Incognito.

2 The shielding mechanism operates via a general bridge design that connects Incognito to any number of cryptonetworks, allowing for secure bi-directional transfers of cryptocurrencies whenever privacy is needed. In particular linkable ring signature scheme , homomorphic commitment scheme , and zero-knowledge range proofs .

3 The “Bond smart contract”

4 If the case is: Once shielded, privacy coin transactions are confidential and untraceable. A privacy coin enjoys the best of both worlds. It retains the value of its original counterpart and can be transacted confidentially on the Incognito network. The anonymity set must come down to the number of executed transactions. If you know there is a number of decoy does it really change the anonymity set? At some point the decoy matters, but if there are very few participants the AS cannot be very large.

The most popular privacy coins on the Incognito network from November 2019 to January 2020

PRIVACY COINS COUNTERPART NUMBER OF TRANSACTIONS
pBTC BTC 40,720
pUSDT USDT 13,809
pETH ETH 9,109
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Yea, this is a problem with most (or all) ZK currencies around. They are only as good as their usage. I really like the idea of Incognito. Its actually the first interoperable solution between blockchains plus its Zero Knowledge. Beat that Polkadot! :smile:

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  1. Shielding allows BTC, ETH and other cryptocurrencies to go incognito and back
  2. linkable ring signature scheme, homomorphic commitment scheme, and zero-knowledge range proofs
  3. a decentralized group of trustless custodians
  4. the number of people who shielded the same amount of the same coin around the same time
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  1. How does “shielding” work on Incognito?

Any cryptocurrency can now be a privacy coin. Both shielding and unshielding processes are carried out via a decentralized group of trustless custodians . Once shielded, transactions are confidential and untraceable. To provide privacy , we employed the linkable ring signature scheme , homomorphic commitment scheme , and zero-knowledge range proofs .

  1. What privacy technology does Incognito use for shielded transactions?

To provide privacy , we employed the linkable ring signature scheme , homomorphic commitment scheme , and zero-knowledge range proofs .

  1. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?

Incognito as a privacy hub by the Bond Smart contract which selects trustless custodians.

  1. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)

By the number of transactions that have the same amount of private BTC (pBTC) in the previous blocks.

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  1. How does “shielding” work on Incognito?
    Both shielding and unshielding processes are carried out via a decentralized group of trustless custodians.

  2. What privacy technology does Incognito use for shielded transactions?
    Incognito employs linkable Ring Signature scheme, homomorphic commitment scheme, and zero-knowledge range proofs.

  3. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?
    The network of trustless custodians

  4. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)
    It is equal to the amount of the other transactions that are bitcoin and the same size.

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  1. Shielding per the article: linkable ring signature scheme* , homomorphic commitment scheme , and zero-knowledge range proofs

2.Their technology is to scale out a privacy-focused cryptonetwork by implementing SHARDING; also they implement a new consensus based on proof-of-stake , pBFT , and BLS .

3.Apparently a “Trustless Custodian”

4.It would have to be the same amount of transactions that are doing the same thing Alice is trying to achieve. In essence, all other users shielding BTC

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1. How does “shielding” work on Incognito?

Both shielding and unshielding processes are carried out via a decentralized group of trustless custodians.

2. What privacy technology does Incognito use for shielded transactions?

  • linkable ring signature scheme
  • homomorphic commitment scheme
  • zero-knowledge range proofs

3. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?

A decentralized group of trustless custodians.

4. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)

The anonymity set will be equal to the number of shielded transactions that have the same value Alice will have sent to Bob.

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  1. How does “shielding” work on Incognito?

Through Incognito, a public coin can be shielded to obtain its privacy coin counterpart of the same value. The shielding mechanism operates via a general bridge design that connects Incognito to any number of cryptonetworks, allowing for secure bi-directional transfers of cryptocurrencies whenever privacy is needed. This means any coin can now be a privacy coin.

For example, BTC can be shielded to obtain the privacy coin pBTC. pBTC has the same value as BTC, so 1 pBTC can always be redeemed for 1 BTC and vice versa.

  1. What privacy technology does Incognito use for shielded transactions?

To provide privacy, incognito employs the linkable ring signature scheme, homomorphic commitment scheme, and zero-knowledge range proofs.

  1. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?

“Receiver” is a trustless custodian for BTC incognito transactions.

  1. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)

Bob’s anonymity set is equal to the number of all un-shielding transactions which were performed for the same amount of BTC.

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  1. How does “shielding” work on Incognito?

Both processes shielding and unshielding are you minted and burned a coin that represents your locked up external coin on the incognito network by a decentralized trustless custodians.

  1. What privacy technology does Incognito use for shielded transactions?

The linkable ring signature scheme (sender shield), homomorphic commitment scheme (receiver shield), and zero-knowledge range proofs (amount shield)

  1. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?

A trustless decentralized custodians

  1. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)

Its anonymity set = # of all shielding transactions performed for X amount of that coin.

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  1. How does “shielding” work on Incognito?
    Carried out via a decentralized group of trustless custodians. Once shielded, transactions are confidential and untraceable. To provide privacy, they employed the linkable ring signature scheme, homomorphic commitment scheme, and zero-knowledge range proofs.

  2. What privacy technology does Incognito use for shielded transactions?

  3. The linkable ring signature scheme, homomorphic commitment scheme, and zero-knowledge range proofs.

  4. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?
    A decentralized group of trustless custodians.

  5. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)
    Its anonymity set is equal to the number of all the shielding transactions which were performed for the same amount of that same coin.

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  1. How does “shielding” work on Incognito?
    By using the privacy hub called Incognito.
  2. What privacy technology does Incognito use for shielded transactions?
    Linkable ring signature scheme, homomorphic commitment scheme, and zero-knowledge range proofs
  3. If Alice shields BTC with Incognito, who is the ‘receiver’ of her Bitcoin transaction?
    Incognito network
  4. Suppose Alice shields BTC, sends it to Bob on Incognito, and then Bob un-shields the same amount. How do we find Bob’s anonymity set? (How many people he could have received BTC from?)
    its the set of all transactions in the Incognito hub.
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Just the ones of the same coin and denomination. :slight_smile: