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Created February 20, 2013 17:08

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  1. Jeff Garzik revised this gist Nov 2, 2012. 1 changed file with 8 additions and 1 deletion.
    9 changes: 8 additions & 1 deletion ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -2,7 +2,14 @@ This is a review of "Quantitative Analysis of the Full Bitcoin Transaction Graph

    There are some incorrect details and analyses that warrant attention.

    ## tl;dr (the short version)
    ## Oct. 31 UPDATE

    The authors have introduced several revisions to their paper, available at the same URL as before.

    The criticism below may be outdated in part or in full.


    ## tl;dr (the short [edit: old] version)

    The Ron/Shamir paper contains provably-false key assumptions. Further, their data source (website scraping) is a secondary data source known to have served invalid data in the past.

  2. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 13 additions and 4 deletions.
    17 changes: 13 additions & 4 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -2,14 +2,14 @@ This is a review of "Quantitative Analysis of the Full Bitcoin Transaction Graph

    There are some incorrect details and analyses that warrant attention.

    #tl;dr (the short version)#
    ## tl;dr (the short version)

    The Ron/Shamir paper contains provably-false key assumptions. Further, their data source (website scraping) is a secondary data source known to have served invalid data in the past.

    We **do not** claim this wholly invalidates their statistical results, but given the web wallet and cold storage examples, seems likely to introduce statistically significant changes in the results.


    #Appearance of data and conclusions obtained by a web crawl#
    ## Appearance of data and conclusions obtained by a web crawl
    rather than close analysis of the actual bitcoin system.

    Quote #1: _"On May 13th 2012 we downloaded the full public record of this system, which consisted of about 180,000 HTML files."_
    @@ -29,7 +29,7 @@ While the authors do appear be to aware that bitcoin is based on public/private
    Further, while it may not be material for the results of this particular study, web block explorers are not authoritative sources for bitcoin data and have sometimes been known to display wildly false information.


    #Fundamental assumptions of transaction address ownership appear flawed#
    ## Fundamental assumptions of transaction address ownership appear flawed

    Quote #1: _"A very important feature of the Bitcoin network is that a transaction involving multiple sending addresses can only be carried out by the common owner of
    all those addresses, as it is demanded by the Bitcoin system that “Whoever sent
    @@ -61,4 +61,13 @@ Any bitcoins that are permanently lost, due to wallet deletion, also appear with

    Finally, this analysis does not appear to include "change transactions." When someone sends bitcoin, the system will potentially create two outputs: (1) the bitcoin sent to the receipient, (2) bitcoins sent back to yourself. This preserves the rule that 100% of a bitcoin transaction's inputs are spent. You can never spend half of a 100BTC transaction output: you must spend 100BTC... even if that means sending some bitcoins back to yourself.

    The Ron/Shamir paper does mention Deepbit and MtGox as large "users", but does not indicate that these are essentially multi-owner or multi-user sites. Building graphs that ignore the multi-user aspect of MtGox will produce conclusions different from those that take it into account.
    The Ron/Shamir paper does mention Deepbit and MtGox as large "users", but does not indicate that these are essentially multi-owner or multi-user sites. Building graphs that ignore the multi-user aspect of MtGox will produce conclusions different from those that take it into account.

    ## Additional resources

    davout emailed the authors, and got a response:
    https://bitcointalk.org/index.php?topic=118797.msg1280496#msg1280496

    Meni Rosenfeld also emailed the authors:
    https://bitcointalk.org/index.php?topic=118797.msg1281470#msg1281470

  3. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 1 addition and 0 deletions.
    1 change: 1 addition & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -61,3 +61,4 @@ Any bitcoins that are permanently lost, due to wallet deletion, also appear with

    Finally, this analysis does not appear to include "change transactions." When someone sends bitcoin, the system will potentially create two outputs: (1) the bitcoin sent to the receipient, (2) bitcoins sent back to yourself. This preserves the rule that 100% of a bitcoin transaction's inputs are spent. You can never spend half of a 100BTC transaction output: you must spend 100BTC... even if that means sending some bitcoins back to yourself.

    The Ron/Shamir paper does mention Deepbit and MtGox as large "users", but does not indicate that these are essentially multi-owner or multi-user sites. Building graphs that ignore the multi-user aspect of MtGox will produce conclusions different from those that take it into account.
  4. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 1 addition and 1 deletion.
    2 changes: 1 addition & 1 deletion ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -45,7 +45,7 @@ Read the source code, for the canonical signature checking details: https://gith
    This wiki link describes signature checking detail: https://en.bitcoin.it/wiki/Contracts#Theory
    This forum post provides a concrete example of multiple owners coordinating to create a single transaction containing "multiple sending addresses": https://bitcointalk.org/index.php?topic=112007.0

    It is acknowledged that these multi-owner transactions are rare at this time. However, there is an existing use case that is *very* statistically significant:
    It is acknowledged that these multi-owner transactions are rare at this time. However, there is are two existing use cases that are *very* statistically significant: shared coin pools (web wallets) and change transactions.

    *Web wallets* provide an easy counter-example of the "multiple sending addresses == common owner" assumption. Websites dubbed "web wallets" provide a centralized, HTTP-based web interface to the otherwise decentralized P2P bitcoin network. Web wallets typically pool the bitcoins from all their web users into two large pools, a "hot wallet" and a "cold wallet."

  5. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 2 additions and 0 deletions.
    2 changes: 2 additions & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -45,6 +45,8 @@ Read the source code, for the canonical signature checking details: https://gith
    This wiki link describes signature checking detail: https://en.bitcoin.it/wiki/Contracts#Theory
    This forum post provides a concrete example of multiple owners coordinating to create a single transaction containing "multiple sending addresses": https://bitcointalk.org/index.php?topic=112007.0

    It is acknowledged that these multi-owner transactions are rare at this time. However, there is an existing use case that is *very* statistically significant:

    *Web wallets* provide an easy counter-example of the "multiple sending addresses == common owner" assumption. Websites dubbed "web wallets" provide a centralized, HTTP-based web interface to the otherwise decentralized P2P bitcoin network. Web wallets typically pool the bitcoins from all their web users into two large pools, a "hot wallet" and a "cold wallet."

    Transactions sent to web wallet websites, and sent from web wallet websites, will clearly appear as clusters of bitcoins within the blockchain dataset.
  6. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 1 addition and 1 deletion.
    2 changes: 1 addition & 1 deletion ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -37,7 +37,7 @@ this transaction owns all of these addresses”. This legal requirement is also
    nically ensured by the fact that each received amount must have a cryptographic
    digital signature that unlocks it from the prior transaction."_

    This is unconditional equating of "multiple sending addresses" to a "common owner" is false. We may demonstrate this from a theoretical perspective, with practical examples from today's block chain.
    This is unconditional equating of "multiple sending addresses" to a "common owner" is false. We may demonstrate this from a theoretical perspective, and also with practical examples from today's block chain.

    Each bitcoin transaction contains a number of inputs, and a number of outputs. Ron and Shamir assume that "multiple sending addresses can only be carried out by the common owner of all those addresses", when in fact bitcoin is explicitly designed to permit multiple owners, individually and independently adding signatures to a single transaction.

  7. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 1 addition and 1 deletion.
    2 changes: 1 addition & 1 deletion ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -37,7 +37,7 @@ this transaction owns all of these addresses”. This legal requirement is also
    nically ensured by the fact that each received amount must have a cryptographic
    digital signature that unlocks it from the prior transaction."_

    This is false. We may demonstrate this from a theoretical perspective, with practical examples from today's block chain.
    This is unconditional equating of "multiple sending addresses" to a "common owner" is false. We may demonstrate this from a theoretical perspective, with practical examples from today's block chain.

    Each bitcoin transaction contains a number of inputs, and a number of outputs. Ron and Shamir assume that "multiple sending addresses can only be carried out by the common owner of all those addresses", when in fact bitcoin is explicitly designed to permit multiple owners, individually and independently adding signatures to a single transaction.

  8. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 1 addition and 1 deletion.
    2 changes: 1 addition & 1 deletion ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -6,7 +6,7 @@ There are some incorrect details and analyses that warrant attention.

    The Ron/Shamir paper contains provably-false key assumptions. Further, their data source (website scraping) is a secondary data source known to have served invalid data in the past.

    We *do not* claim this wholly invalidates their statistical results, but given the web wallet and cold storage examples, seems likely to introduce statistically significant changes in the results.
    We **do not** claim this wholly invalidates their statistical results, but given the web wallet and cold storage examples, seems likely to introduce statistically significant changes in the results.


    #Appearance of data and conclusions obtained by a web crawl#
  9. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 1 addition and 1 deletion.
    2 changes: 1 addition & 1 deletion ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -4,7 +4,7 @@ There are some incorrect details and analyses that warrant attention.

    #tl;dr (the short version)#

    The Ron/Shamir paper contains provably-false key assumptions. Their data source (website scraping) is a secondary data source known to have served invalid data in the past.
    The Ron/Shamir paper contains provably-false key assumptions. Further, their data source (website scraping) is a secondary data source known to have served invalid data in the past.

    We *do not* claim this wholly invalidates their statistical results, but given the web wallet and cold storage examples, seems likely to introduce statistically significant changes in the results.

  10. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 7 additions and 0 deletions.
    7 changes: 7 additions & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -2,6 +2,13 @@ This is a review of "Quantitative Analysis of the Full Bitcoin Transaction Graph

    There are some incorrect details and analyses that warrant attention.

    #tl;dr (the short version)#

    The Ron/Shamir paper contains provably-false key assumptions. Their data source (website scraping) is a secondary data source known to have served invalid data in the past.

    We *do not* claim this wholly invalidates their statistical results, but given the web wallet and cold storage examples, seems likely to introduce statistically significant changes in the results.


    #Appearance of data and conclusions obtained by a web crawl#
    rather than close analysis of the actual bitcoin system.

  11. Jeff Garzik revised this gist Oct 18, 2012. 1 changed file with 3 additions and 0 deletions.
    3 changes: 3 additions & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -49,3 +49,6 @@ Another common practice seen in the field (and therefore, in any blockchain data
    This is recommended -- and for large sites, necessary -- security practice. The cold wallet of a large exchange will indeed appear as coins that have not been spent in a long time.

    Any bitcoins that are permanently lost, due to wallet deletion, also appear within the data as old, unmoved coins. One cannot distinguish between unspent "coins under the mattress" and lost/destroyed coins.

    Finally, this analysis does not appear to include "change transactions." When someone sends bitcoin, the system will potentially create two outputs: (1) the bitcoin sent to the receipient, (2) bitcoins sent back to yourself. This preserves the rule that 100% of a bitcoin transaction's inputs are spent. You can never spend half of a 100BTC transaction output: you must spend 100BTC... even if that means sending some bitcoins back to yourself.

  12. Jeff Garzik revised this gist Oct 17, 2012. 1 changed file with 2 additions and 0 deletions.
    2 changes: 2 additions & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -47,3 +47,5 @@ Simplified example: Alice, Bob and Carla each deposit 10 BTC in Wallet.Example.
    Another common practice seen in the field (and therefore, in any blockchain data analysis) is "wallet cold storage." Bitcoin exchanges, merchants and users often keep the *majority* of their bitcoins offline, a technique called "cold wallet" or "cold storage." A "hot wallet" connected to the Internet is then used to store the remaining bitcoins. If a thief steals the hot wallet, the damage is limited.

    This is recommended -- and for large sites, necessary -- security practice. The cold wallet of a large exchange will indeed appear as coins that have not been spent in a long time.

    Any bitcoins that are permanently lost, due to wallet deletion, also appear within the data as old, unmoved coins. One cannot distinguish between unspent "coins under the mattress" and lost/destroyed coins.
  13. Jeff Garzik revised this gist Oct 17, 2012. 1 changed file with 3 additions and 0 deletions.
    3 changes: 3 additions & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -44,3 +44,6 @@ Transactions sent to web wallet websites, and sent from web wallet websites, wil

    Simplified example: Alice, Bob and Carla each deposit 10 BTC in Wallet.Example.Com. Wallet.Example.Com now controls a single shared pool of 30 BTC. Anyone who makes a withdrawal from Wallet.Example.Com, including new users David, Rick and James, will receive coins from that 30 BTC pool.

    Another common practice seen in the field (and therefore, in any blockchain data analysis) is "wallet cold storage." Bitcoin exchanges, merchants and users often keep the *majority* of their bitcoins offline, a technique called "cold wallet" or "cold storage." A "hot wallet" connected to the Internet is then used to store the remaining bitcoins. If a thief steals the hot wallet, the damage is limited.

    This is recommended -- and for large sites, necessary -- security practice. The cold wallet of a large exchange will indeed appear as coins that have not been spent in a long time.
  14. Jeff Garzik revised this gist Oct 17, 2012. 1 changed file with 1 addition and 0 deletions.
    1 change: 1 addition & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -34,6 +34,7 @@ This is false. We may demonstrate this from a theoretical perspective, with pra

    Each bitcoin transaction contains a number of inputs, and a number of outputs. Ron and Shamir assume that "multiple sending addresses can only be carried out by the common owner of all those addresses", when in fact bitcoin is explicitly designed to permit multiple owners, individually and independently adding signatures to a single transaction.

    Read the source code, for the canonical signature checking details: https://github.com/bitcoin/bitcoin/blob/master/src/script.cpp#L1064
    This wiki link describes signature checking detail: https://en.bitcoin.it/wiki/Contracts#Theory
    This forum post provides a concrete example of multiple owners coordinating to create a single transaction containing "multiple sending addresses": https://bitcointalk.org/index.php?topic=112007.0

  15. Jeff Garzik revised this gist Oct 17, 2012. 1 changed file with 1 addition and 1 deletion.
    2 changes: 1 addition & 1 deletion ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -13,7 +13,7 @@ proof-of-work system."_

    Quote #3: _"The entire activity in the Bitcoin network is publicly available
    through the internet and is recorded in the form of a block chain, starting at
    block 0 [7] (created back on the 3rd of January 2009). Each block reports on as
    block 0 (created back on the 3rd of January 2009). Each block reports on as
    little as a single transaction to as much as over a thousand transactions, and
    provides hyperlinks to other blocks and to other activities of each address."_

  16. Jeff Garzik revised this gist Oct 17, 2012. 1 changed file with 2 additions and 0 deletions.
    2 changes: 2 additions & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -19,6 +19,8 @@ provides hyperlinks to other blocks and to other activities of each address."_

    While the authors do appear be to aware that bitcoin is based on public/private key cryptographic signatures, these quotes do not seem to indicate that _the_ block chain, singular, is a globally shared binary structure, based on distributed consensus. Blocks are not web pages containing hyperlinks, even though http://blockexplorer.com/ and http://blockchain.info/ present them as such, for display purposes.

    Further, while it may not be material for the results of this particular study, web block explorers are not authoritative sources for bitcoin data and have sometimes been known to display wildly false information.


    #Fundamental assumptions of transaction address ownership appear flawed#

  17. Jeff Garzik revised this gist Oct 16, 2012. 1 changed file with 6 additions and 6 deletions.
    12 changes: 6 additions & 6 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -7,26 +7,26 @@ rather than close analysis of the actual bitcoin system.

    Quote #1: _"On May 13th 2012 we downloaded the full public record of this system, which consisted of about 180,000 HTML files."_

    Quote #2: "Nodes broadcast transactions to this network, which records them in
    Quote #2: _"Nodes broadcast transactions to this network, which records them in
    publicly available web pages, called block chains, after validating them with a
    proof-of-work system."
    proof-of-work system."_

    Quote #3: "The entire activity in the Bitcoin network is publicly available
    Quote #3: _"The entire activity in the Bitcoin network is publicly available
    through the internet and is recorded in the form of a block chain, starting at
    block 0 [7] (created back on the 3rd of January 2009). Each block reports on as
    little as a single transaction to as much as over a thousand transactions, and
    provides hyperlinks to other blocks and to other activities of each address."
    provides hyperlinks to other blocks and to other activities of each address."_

    While the authors do appear be to aware that bitcoin is based on public/private key cryptographic signatures, these quotes do not seem to indicate that _the_ block chain, singular, is a globally shared binary structure, based on distributed consensus. Blocks are not web pages containing hyperlinks, even though http://blockexplorer.com/ and http://blockchain.info/ present them as such, for display purposes.


    #Fundamental assumptions of transaction address ownership appear flawed#

    Quote #1: "A very important feature of the Bitcoin network is that a transaction involving multiple sending addresses can only be carried out by the common owner of
    Quote #1: _"A very important feature of the Bitcoin network is that a transaction involving multiple sending addresses can only be carried out by the common owner of
    all those addresses, as it is demanded by the Bitcoin system that “Whoever sent
    this transaction owns all of these addresses”. This legal requirement is also tech-
    nically ensured by the fact that each received amount must have a cryptographic
    digital signature that unlocks it from the prior transaction."
    digital signature that unlocks it from the prior transaction."_

    This is false. We may demonstrate this from a theoretical perspective, with practical examples from today's block chain.

  18. Jeff Garzik revised this gist Oct 16, 2012. 1 changed file with 3 additions and 2 deletions.
    5 changes: 3 additions & 2 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -2,7 +2,8 @@ This is a review of "Quantitative Analysis of the Full Bitcoin Transaction Graph

    There are some incorrect details and analyses that warrant attention.

    #1) Appearance of data and conclusions obtained by a web crawl, rather than close analysis of the actual bitcoin system.#
    #Appearance of data and conclusions obtained by a web crawl#
    rather than close analysis of the actual bitcoin system.

    Quote #1: _"On May 13th 2012 we downloaded the full public record of this system, which consisted of about 180,000 HTML files."_

    @@ -19,7 +20,7 @@ provides hyperlinks to other blocks and to other activities of each address."
    While the authors do appear be to aware that bitcoin is based on public/private key cryptographic signatures, these quotes do not seem to indicate that _the_ block chain, singular, is a globally shared binary structure, based on distributed consensus. Blocks are not web pages containing hyperlinks, even though http://blockexplorer.com/ and http://blockchain.info/ present them as such, for display purposes.


    #2) Fundamental assumptions of transaction address ownership appear flawed#
    #Fundamental assumptions of transaction address ownership appear flawed#

    Quote #1: "A very important feature of the Bitcoin network is that a transaction involving multiple sending addresses can only be carried out by the common owner of
    all those addresses, as it is demanded by the Bitcoin system that “Whoever sent
  19. Jeff Garzik revised this gist Oct 16, 2012. 1 changed file with 1 addition and 1 deletion.
    2 changes: 1 addition & 1 deletion ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -29,7 +29,7 @@ digital signature that unlocks it from the prior transaction."

    This is false. We may demonstrate this from a theoretical perspective, with practical examples from today's block chain.

    Each bitcoin transaction contains a number of inputs, and a number of outputs. Ron and Shamir assume that "multiple sending addresses can only be carried out by the common owner of all those addresses", then in fact bitcoin is explicitly designed to permit multiple owners, individually and independently adding signatures to a single transaction.
    Each bitcoin transaction contains a number of inputs, and a number of outputs. Ron and Shamir assume that "multiple sending addresses can only be carried out by the common owner of all those addresses", when in fact bitcoin is explicitly designed to permit multiple owners, individually and independently adding signatures to a single transaction.

    This wiki link describes signature checking detail: https://en.bitcoin.it/wiki/Contracts#Theory
    This forum post provides a concrete example of multiple owners coordinating to create a single transaction containing "multiple sending addresses": https://bitcointalk.org/index.php?topic=112007.0
  20. Jeff Garzik revised this gist Oct 16, 2012. 1 changed file with 2 additions and 3 deletions.
    5 changes: 2 additions & 3 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -1,9 +1,8 @@

    This is a review of "Quantitative Analysis of the Full Bitcoin Transaction Graph" by Dorit Ron and Adi Shamir.

    There are some incorrect details and analyses that warrant attention.

    *1) Appearance of data and conclusions obtained by a web crawl, rather than close analysis of the actual bitcoin system.*
    #1) Appearance of data and conclusions obtained by a web crawl, rather than close analysis of the actual bitcoin system.#

    Quote #1: _"On May 13th 2012 we downloaded the full public record of this system, which consisted of about 180,000 HTML files."_

    @@ -20,7 +19,7 @@ provides hyperlinks to other blocks and to other activities of each address."
    While the authors do appear be to aware that bitcoin is based on public/private key cryptographic signatures, these quotes do not seem to indicate that _the_ block chain, singular, is a globally shared binary structure, based on distributed consensus. Blocks are not web pages containing hyperlinks, even though http://blockexplorer.com/ and http://blockchain.info/ present them as such, for display purposes.


    *2) Fundamental assumptions of transaction address ownership appear flawed*
    #2) Fundamental assumptions of transaction address ownership appear flawed#

    Quote #1: "A very important feature of the Bitcoin network is that a transaction involving multiple sending addresses can only be carried out by the common owner of
    all those addresses, as it is demanded by the Bitcoin system that “Whoever sent
  21. Jeff Garzik created this gist Oct 16, 2012.
    43 changes: 43 additions & 0 deletions ron-shamir-review.md
    Original file line number Diff line number Diff line change
    @@ -0,0 +1,43 @@

    This is a review of "Quantitative Analysis of the Full Bitcoin Transaction Graph" by Dorit Ron and Adi Shamir.

    There are some incorrect details and analyses that warrant attention.

    *1) Appearance of data and conclusions obtained by a web crawl, rather than close analysis of the actual bitcoin system.*

    Quote #1: _"On May 13th 2012 we downloaded the full public record of this system, which consisted of about 180,000 HTML files."_

    Quote #2: "Nodes broadcast transactions to this network, which records them in
    publicly available web pages, called block chains, after validating them with a
    proof-of-work system."

    Quote #3: "The entire activity in the Bitcoin network is publicly available
    through the internet and is recorded in the form of a block chain, starting at
    block 0 [7] (created back on the 3rd of January 2009). Each block reports on as
    little as a single transaction to as much as over a thousand transactions, and
    provides hyperlinks to other blocks and to other activities of each address."

    While the authors do appear be to aware that bitcoin is based on public/private key cryptographic signatures, these quotes do not seem to indicate that _the_ block chain, singular, is a globally shared binary structure, based on distributed consensus. Blocks are not web pages containing hyperlinks, even though http://blockexplorer.com/ and http://blockchain.info/ present them as such, for display purposes.


    *2) Fundamental assumptions of transaction address ownership appear flawed*

    Quote #1: "A very important feature of the Bitcoin network is that a transaction involving multiple sending addresses can only be carried out by the common owner of
    all those addresses, as it is demanded by the Bitcoin system that “Whoever sent
    this transaction owns all of these addresses”. This legal requirement is also tech-
    nically ensured by the fact that each received amount must have a cryptographic
    digital signature that unlocks it from the prior transaction."

    This is false. We may demonstrate this from a theoretical perspective, with practical examples from today's block chain.

    Each bitcoin transaction contains a number of inputs, and a number of outputs. Ron and Shamir assume that "multiple sending addresses can only be carried out by the common owner of all those addresses", then in fact bitcoin is explicitly designed to permit multiple owners, individually and independently adding signatures to a single transaction.

    This wiki link describes signature checking detail: https://en.bitcoin.it/wiki/Contracts#Theory
    This forum post provides a concrete example of multiple owners coordinating to create a single transaction containing "multiple sending addresses": https://bitcointalk.org/index.php?topic=112007.0

    *Web wallets* provide an easy counter-example of the "multiple sending addresses == common owner" assumption. Websites dubbed "web wallets" provide a centralized, HTTP-based web interface to the otherwise decentralized P2P bitcoin network. Web wallets typically pool the bitcoins from all their web users into two large pools, a "hot wallet" and a "cold wallet."

    Transactions sent to web wallet websites, and sent from web wallet websites, will clearly appear as clusters of bitcoins within the blockchain dataset.

    Simplified example: Alice, Bob and Carla each deposit 10 BTC in Wallet.Example.Com. Wallet.Example.Com now controls a single shared pool of 30 BTC. Anyone who makes a withdrawal from Wallet.Example.Com, including new users David, Rick and James, will receive coins from that 30 BTC pool.