Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private,...

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Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra [email protected] November 21, 2016 1 / 50

Transcript of Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private,...

Page 1: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble: Private, Massively-PrunableBlockchains

Andrew Poelstra

[email protected]

November 21, 2016

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Page 2: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

04:30 UTC, August 2nd, 2016: “Tom Elvis Jedusor” posts a.onion link to a text file on IRC, titled MIMBLEWIMBLE anddated July 19.

Next morning: myself and Bryan Bishop verify it’s actuallyjust text and rehost it.

Following week: discussion on Reddit with Greg Sanders andothers leads to understanding Mimblewimble’s trust model,and hints that the new crypto has merit.

September: myself and Avi Kulkarni develop an extension,“sinking signatures”, to greatly improve its scaling properties.

October 8th: released a paper showing Avi’s and my work forScaling Bitcoin Milan

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Page 3: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

04:30 UTC, August 2nd, 2016: “Tom Elvis Jedusor” posts a.onion link to a text file on IRC, titled MIMBLEWIMBLE anddated July 19.

Next morning: myself and Bryan Bishop verify it’s actuallyjust text and rehost it.

Following week: discussion on Reddit with Greg Sanders andothers leads to understanding Mimblewimble’s trust model,and hints that the new crypto has merit.

September: myself and Avi Kulkarni develop an extension,“sinking signatures”, to greatly improve its scaling properties.

October 8th: released a paper showing Avi’s and my work forScaling Bitcoin Milan

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Page 4: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

04:30 UTC, August 2nd, 2016: “Tom Elvis Jedusor” posts a.onion link to a text file on IRC, titled MIMBLEWIMBLE anddated July 19.

Next morning: myself and Bryan Bishop verify it’s actuallyjust text and rehost it.

Following week: discussion on Reddit with Greg Sanders andothers leads to understanding Mimblewimble’s trust model,and hints that the new crypto has merit.

September: myself and Avi Kulkarni develop an extension,“sinking signatures”, to greatly improve its scaling properties.

October 8th: released a paper showing Avi’s and my work forScaling Bitcoin Milan

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Page 5: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

04:30 UTC, August 2nd, 2016: “Tom Elvis Jedusor” posts a.onion link to a text file on IRC, titled MIMBLEWIMBLE anddated July 19.

Next morning: myself and Bryan Bishop verify it’s actuallyjust text and rehost it.

Following week: discussion on Reddit with Greg Sanders andothers leads to understanding Mimblewimble’s trust model,and hints that the new crypto has merit.

September: myself and Avi Kulkarni develop an extension,“sinking signatures”, to greatly improve its scaling properties.

October 8th: released a paper showing Avi’s and my work forScaling Bitcoin Milan

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Page 6: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

04:30 UTC, August 2nd, 2016: “Tom Elvis Jedusor” posts a.onion link to a text file on IRC, titled MIMBLEWIMBLE anddated July 19.

Next morning: myself and Bryan Bishop verify it’s actuallyjust text and rehost it.

Following week: discussion on Reddit with Greg Sanders andothers leads to understanding Mimblewimble’s trust model,and hints that the new crypto has merit.

September: myself and Avi Kulkarni develop an extension,“sinking signatures”, to greatly improve its scaling properties.

October 8th: released a paper showing Avi’s and my work forScaling Bitcoin Milan

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Page 7: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

At 23:47 UTC, October 20, “Ignotus Peverell” appeared onIRC announcing a project to implement MimbleWimble.

A few minutes later, Bryan Bishop called me to tell me to jointhe conversation. I pointed out that aggregate signatures givespace savings on top of the Voldemort scheme, even withoutnew crypto.

Other Harry Potter characters arrived over the next few weeks;the project continues to move forward. Though I’ve beeninvolved with the project, I have not contributed any code.

I am not Ignotus Peverell.

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Page 8: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

At 23:47 UTC, October 20, “Ignotus Peverell” appeared onIRC announcing a project to implement MimbleWimble.

A few minutes later, Bryan Bishop called me to tell me to jointhe conversation. I pointed out that aggregate signatures givespace savings on top of the Voldemort scheme, even withoutnew crypto.

Other Harry Potter characters arrived over the next few weeks;the project continues to move forward. Though I’ve beeninvolved with the project, I have not contributed any code.

I am not Ignotus Peverell.

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Page 9: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

At 23:47 UTC, October 20, “Ignotus Peverell” appeared onIRC announcing a project to implement MimbleWimble.

A few minutes later, Bryan Bishop called me to tell me to jointhe conversation. I pointed out that aggregate signatures givespace savings on top of the Voldemort scheme, even withoutnew crypto.

Other Harry Potter characters arrived over the next few weeks;the project continues to move forward. Though I’ve beeninvolved with the project, I have not contributed any code.

I am not Ignotus Peverell.

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Page 10: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

History

At 23:47 UTC, October 20, “Ignotus Peverell” appeared onIRC announcing a project to implement MimbleWimble.

A few minutes later, Bryan Bishop called me to tell me to jointhe conversation. I pointed out that aggregate signatures givespace savings on top of the Voldemort scheme, even withoutnew crypto.

Other Harry Potter characters arrived over the next few weeks;the project continues to move forward. Though I’ve beeninvolved with the project, I have not contributed any code.

I am not Ignotus Peverell.

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Page 11: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

What is Mimblewimble?

Mimblewimble is a design for a blockchain-based ledger that isvery different from Bitcoin.

It can be implemented as a sidechain, or softforked intoBitcoin (as an extension block).

In Bitcoin transactions, old outputs sign new outputs; outputshave “script pubkeys” that are independent of each other. InMimblewimble transactions, outputs have only EC pubkeys,and the difference between new outputs’ keys and old ones’ ismultisigned by all transacting parties.

Mimblewimble transactions are inherently scriptless.

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Page 12: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

What is Mimblewimble?

Mimblewimble is a design for a blockchain-based ledger that isvery different from Bitcoin.

It can be implemented as a sidechain, or softforked intoBitcoin (as an extension block).

In Bitcoin transactions, old outputs sign new outputs; outputshave “script pubkeys” that are independent of each other. InMimblewimble transactions, outputs have only EC pubkeys,and the difference between new outputs’ keys and old ones’ ismultisigned by all transacting parties.

Mimblewimble transactions are inherently scriptless.

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Page 13: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

What is Mimblewimble?

Mimblewimble is a design for a blockchain-based ledger that isvery different from Bitcoin.

It can be implemented as a sidechain, or softforked intoBitcoin (as an extension block).

In Bitcoin transactions, old outputs sign new outputs; outputshave “script pubkeys” that are independent of each other. InMimblewimble transactions, outputs have only EC pubkeys,and the difference between new outputs’ keys and old ones’ ismultisigned by all transacting parties.

Mimblewimble transactions are inherently scriptless.

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Page 14: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

What is Mimblewimble?

Mimblewimble is a design for a blockchain-based ledger that isvery different from Bitcoin.

It can be implemented as a sidechain, or softforked intoBitcoin (as an extension block).

In Bitcoin transactions, old outputs sign new outputs; outputshave “script pubkeys” that are independent of each other. InMimblewimble transactions, outputs have only EC pubkeys,and the difference between new outputs’ keys and old ones’ ismultisigned by all transacting parties.

Mimblewimble transactions are inherently scriptless.

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Page 15: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

A Mimblewimble transaction is the following data:

Inputs (references to old outputs).

Outputs: confidential transaction outputs (group elements,which blind and commit to amounts), plus rangeproofs.

Excess: difference between outputs and inputs (groupelement), plus signature (for authentication and to provenon-inflation)

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Page 16: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

A Mimblewimble transaction is the following data:

Inputs (references to old outputs).

Outputs: confidential transaction outputs (group elements,which blind and commit to amounts), plus rangeproofs.

Excess: difference between outputs and inputs (groupelement), plus signature (for authentication and to provenon-inflation)

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Page 17: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

A Mimblewimble transaction is the following data:

Inputs (references to old outputs).

Outputs: confidential transaction outputs (group elements,which blind and commit to amounts), plus rangeproofs.

Excess: difference between outputs and inputs (groupelement), plus signature (for authentication and to provenon-inflation)

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Page 18: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

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Page 19: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

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Page 20: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

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Page 21: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

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Page 22: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Blocks

Blocks consist of:

A merkle tree of transaction inputs.

A merkle tree of transaction outputs and rangeproofs.

A list of excess value(s) and signature(s)

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Page 23: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Blocks

Blocks consist of:

A merkle tree of transaction inputs.

A merkle tree of transaction outputs and rangeproofs.

A list of excess value(s) and signature(s)

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Page 24: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Blocks

Blocks consist of:

A merkle tree of transaction inputs.

A merkle tree of transaction outputs and rangeproofs.

A list of excess value(s) and signature(s)

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Page 25: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

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Page 26: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

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Page 27: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

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Page 28: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Mimblewimble Transactions

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Page 29: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Transactions

A transaction is valid if:

It is non-inflationary (total input amount equals total outputamount)

The owner of the input(s) has signed off on it.

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Page 30: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Transactions

A transaction is valid if:

It is non-inflationary (total input amount equals total outputamount)

The owner of the input(s) has signed off on it.

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Page 31: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Transactions

A transaction is valid if:

It is non-inflationary (total input amount equals total outputamount)

The owner of the input(s) has signed off on it.

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Page 32: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Blockchain

It should be verifiable that

A transaction, once committed to a block, cannot be reversedwithout doing enough work to rewrite the block (and all itsdescendants).

The current state of all coins reflects zero net theft andinflation.

The exact historical sequence of transactions does not need tobe publicly verifable.

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Page 33: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Blockchain

It should be verifiable that

A transaction, once committed to a block, cannot be reversedwithout doing enough work to rewrite the block (and all itsdescendants).

The current state of all coins reflects zero net theft andinflation.

The exact historical sequence of transactions does not need tobe publicly verifable.

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Page 34: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Blockchain

It should be verifiable that

A transaction, once committed to a block, cannot be reversedwithout doing enough work to rewrite the block (and all itsdescendants).

The current state of all coins reflects zero net theft andinflation.

The exact historical sequence of transactions does not need tobe publicly verifable.

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Page 35: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Blockchain

It should be verifiable that

A transaction, once committed to a block, cannot be reversedwithout doing enough work to rewrite the block (and all itsdescendants).

The current state of all coins reflects zero net theft andinflation.

The exact historical sequence of transactions does not need tobe publicly verifable.

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Page 36: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Block Verification

It is possible to verify the blockchain with only the following data:

Block headers

Unspent outputs from each block

Excess values and signatures.

Rangeproofs for the above (witness data)

Full blocks near the tip should be kept to handle reorgs

In Bitcoin there are 150 million transactions and 40 millionunsigned transaction outputs: 21.6Gb of historic data, 2Gb ofUTXOs and 100Gb of UTXO rangeproofs.

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Page 37: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Block Verification

It is possible to verify the blockchain with only the following data:

Block headers

Unspent outputs from each block

Excess values and signatures.

Rangeproofs for the above (witness data)

Full blocks near the tip should be kept to handle reorgs

In Bitcoin there are 150 million transactions and 40 millionunsigned transaction outputs: 21.6Gb of historic data, 2Gb ofUTXOs and 100Gb of UTXO rangeproofs.

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Page 38: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Block Verification

It is possible to verify the blockchain with only the following data:

Block headers

Unspent outputs from each block

Excess values and signatures.

Rangeproofs for the above (witness data)

Full blocks near the tip should be kept to handle reorgs

In Bitcoin there are 150 million transactions and 40 millionunsigned transaction outputs: 21.6Gb of historic data, 2Gb ofUTXOs and 100Gb of UTXO rangeproofs.

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Page 39: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Block Verification

It is possible to verify the blockchain with only the following data:

Block headers

Unspent outputs from each block

Excess values and signatures.

Rangeproofs for the above (witness data)

Full blocks near the tip should be kept to handle reorgs

In Bitcoin there are 150 million transactions and 40 millionunsigned transaction outputs: 21.6Gb of historic data, 2Gb ofUTXOs and 100Gb of UTXO rangeproofs.

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Page 40: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Block Verification

It is possible to verify the blockchain with only the following data:

Block headers

Unspent outputs from each block

Excess values and signatures.

Rangeproofs for the above (witness data)

Full blocks near the tip should be kept to handle reorgs

In Bitcoin there are 150 million transactions and 40 millionunsigned transaction outputs: 21.6Gb of historic data, 2Gb ofUTXOs and 100Gb of UTXO rangeproofs.

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Page 41: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Trust Model: Block Verification

It is possible to verify the blockchain with only the following data:

Block headers

Unspent outputs from each block

Excess values and signatures.

Rangeproofs for the above (witness data)

Full blocks near the tip should be kept to handle reorgs

In Bitcoin there are 150 million transactions and 40 millionunsigned transaction outputs: 21.6Gb of historic data, 2Gb ofUTXOs and 100Gb of UTXO rangeproofs.

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Page 42: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Next Steps

Development, development, development!

Nail down chain parameters

Sidechain / asset support

More crypto ;)

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Page 43: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Next Steps

Development, development, development!

Nail down chain parameters

Sidechain / asset support

More crypto ;)

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Page 44: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Next Steps

Development, development, development!

Nail down chain parameters

Sidechain / asset support

More crypto ;)

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Page 45: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Next Steps

Development, development, development!

Nail down chain parameters

Sidechain / asset support

More crypto ;)

45 / 50

Page 46: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Open Problems

Unconditionally sound commitments and rangeproofs

Smaller rangeproofs? Aggregation of rangeproofs?

Peer-to-peer protocol that can handle transaction merging

Quantum resistance

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Page 47: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Open Problems

Unconditionally sound commitments and rangeproofs

Smaller rangeproofs? Aggregation of rangeproofs?

Peer-to-peer protocol that can handle transaction merging

Quantum resistance

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Page 48: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Open Problems

Unconditionally sound commitments and rangeproofs

Smaller rangeproofs? Aggregation of rangeproofs?

Peer-to-peer protocol that can handle transaction merging

Quantum resistance

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Page 49: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Open Problems

Unconditionally sound commitments and rangeproofs

Smaller rangeproofs? Aggregation of rangeproofs?

Peer-to-peer protocol that can handle transaction merging

Quantum resistance

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Page 50: Mimblewimble: Private, Massively-Prunable Blockchains · 2018-10-08 · Mimblewimble: Private, Massively-Prunable Blockchains Andrew Poelstra grindelwald@wpsoftware.net November 21,

Thank You

Andrew Poelstra <[email protected]>

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