Confidential Transactions - Reading Assignment

[Joeyj007]

1. What piece of information to Confidential Transactions obscure?
   They obscure the amounts sent in a transaction to only participants in the transaction.

2. What is the ‘commutative property’ and how does it relate to Confidential Transactions?
   The basic tool that CT is based on is a Pedersen commitment.

A commitment scheme lets you keep a piece of data secret but commit to it so that you cannot change it later. A Pedersen commitment works with an additional property: commitments can be added, and the sum of a set of commitments is the same as a commitment to the sum of the data. The commitment preserves addition, and the commutative property applies.

3. What is the ‘scanning key’ and what important function does it enable?
   The scanning key is used to establish the shared secret used by the rewindable range proofs and users can share these keys with auditors to enable them to view their transaction amounts.

4. What do ‘range proofs’ do and why are they necessary in Confidential Transactions?
   Range proofs are only required in cases where there are multiple confidential value outputs (including fees).

5. How does Confidential Transactions affect the size of a blockchain?
   They increase the size of each block in a blockchain.

[PaulS96]

1. What piece of information to Confidential Transactions obscure?
Transaction values can only be seen by participants.
2. What is the ‘commutative property’ and how does it relate to Confidential Transactions?
The commutative property is a mathematical property which states the changing of the order of the operands does not change the result. With Pedersen commitments commitments can be added, and the sum of a set of commitments is the same as a commitment to the sum of the data.
3. What is the ‘scanning key’ and what important function does it enable?
It allows you to share and verify transactions privately with other parties.
4. What do ‘range proofs’ do and why are they necessary in Confidential Transactions?
They prove that the amount of the transaction is within the specific range without revealing the value itself.
5. How does Confidential Transactions affect the size of a blockchain?
It has some impact in the amount of data stored, but there are also work arounds presented in the article.

[serba]

What piece of information to Confidential Transactions obscure?

Confidential Transactions make the transaction amounts private, while preserving the ability of the public network to verify that the ledger entries still add up.

What is the ‘commutative property’ and how does it relate to Confidential Transactions?

The commutative property deals with the order of mathematical operations. The commutative property states that the numbers which we operate for addition or multiplication can be moved or swapped in their position without changing the result.

Confidential Transactions are based on the Pedersen Commitment which has an additional property. Commitments can be added, and the sum of a set of commitments is the same as a commitment to the sum of the data (with a blinding key set as the sum of the blinding keys). This allows the commitment to preserve addition.

What is the ‘scanning key’ and what important function does it enable?

The scanning key used to establish the shared secret used by the rewindable range proofs, this approach is completely compatible with watching wallets; users can share these keys with auditors to enable them to view their transaction amounts.

What do ‘range proofs’ do and why are they necessary in Confidential Transactions?

The range proofs are only required in cases where there are multiple confidential value outputs (including fees). When there are multiple outputs we must prove that each committed output is within a range which cannot overflow.

How does Confidential Transactions affect the size of a blockchain?

Confidential Transactions are possible due to the cryptographic technique of additively homomorphic commitments. A side-effect of this enables the additional exchange of private “memo” data (such as invoice numbers or refund addresses) without any further increase in transaction size, by reclaiming most of the overhead of the Confidential Transactions cryptographic proofs.

Similar to signatures, the range proofs can be placed on separate tree branches in blocks.

[maddie]

1. What piece of information to Confidential Transactions obscure?
   Confidential Transactions obscure the amounts in the transactions, enhancing privacy by allowing the participants to hide the transaction values from the public blockchain.

2. What is the ‘commutative property’ and how does it relate to Confidential Transactions?
   The commutative property in the context of Confidential Transactions refers to the ability to change the order of the inputs and outputs without affecting the validity of the transaction. This property is important because it allows for the combination of multiple transactions into a single transaction, which can improve privacy and efficiency.

3. What is the ‘scanning key’ and what important function does it enable?
   The scanning key is a cryptographic key that enables the selective disclosure of transaction amounts. It allows the participants of a transaction, or other parties they authorize, to view the obscured amounts while keeping them hidden from the general public.

4. What do ‘range proofs’ do and why are they necessary in Confidential Transactions?
   Range proofs are a cryptographic technique used in Confidential Transactions to prove that the hidden transaction amounts are within a certain range without revealing the actual amounts. They are necessary to prevent the creation of Bitcoin out of thin air and to ensure that the transaction amounts are valid and positive.

5. How does Confidential Transactions affect the size of a blockchain?
   Confidential Transactions increase the size of a blockchain because the range proofs and other cryptographic data required to obscure the transaction amounts and ensure their validity take up additional space. This means that Confidential Transactions can lead to larger transactions compared to those with visible amounts.