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@ -70,7 +70,7 @@ The incentive may help encourage nodes to stay honest. If a greedy attacker is a
==== Reclaiming Disk Space
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<p>Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. To facilitate this without breaking the block's hash, transactions are hashed in a Merkle Tree <a href="#7">[7]</a> <a href="#2">[2]</a> <a href="#5">[5]</a>, with only the root included in the block's hash. Old blocks can then be compacted by stubbing off branches of the tree. The interior hashes do not need to be stored.</p>
<p>Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. To facilitate this without breaking the block's hash, transactions are hashed in a Merkle Tree <a href="#ref_seven">[7]</a> <a href="#ref_two">[2]</a> <a href="#ref_five">[5]</a>, with only the root included in the block's hash. Old blocks can then be compacted by stubbing off branches of the tree. The interior hashes do not need to be stored.</p>
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image::images/mbc2_abin04.png["disk"]
@ -104,7 +104,7 @@ We consider the scenario of an attacker trying to generate an alternate chain fa
The race between the honest chain and an attacker chain can be characterized as a Binomial Random Walk. The success event is the honest chain being extended by one block, increasing its lead by +1, and the failure event is the attacker's chain being extended by one block, reducing the gap by -1.
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<p>The probability of an attacker catching up from a given deficit is analogous to a Gambler's Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to try to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the honest chain, as follows <a href="#8">[8]</a>:</p>
<p>The probability of an attacker catching up from a given deficit is analogous to a Gambler's Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to try to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the honest chain, as follows <a href="#ref_eight">[8]</a>:</p>
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p == probability an honest node finds the next block
@ -203,33 +203,33 @@ We have proposed a system for electronic transactions without relying on trust.
==== References
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<p>
<span id="1">[1]</span> W. Dai, "b-money," <a href="http://www.weidai.com/bmoney.txt"><em>http://www.weidai.com/bmoney.txt</em></a>, 1998.
<span id="ref_one">[1]</span> W. Dai, "b-money," <a href="http://www.weidai.com/bmoney.txt"><em>http://www.weidai.com/bmoney.txt</em></a>, 1998.
</p>
<p>
<span id="2">[2]</span> H. Massias, X.S. Avila, and J.-J. Quisquater, "Design of a secure timestamping service with minimal trust requirements," In 20th Symposium on Information Theory in the Benelux, May 1999.
<span id="ref_two">[2]</span> H. Massias, X.S. Avila, and J.-J. Quisquater, "Design of a secure timestamping service with minimal trust requirements," In 20th Symposium on Information Theory in the Benelux, May 1999.
</p>
<p>
<span id="3">[3]</span> S. Haber, W.S. Stornetta, "How to time-stamp a digital document," In Journal of Cryptology, vol 3, no 2, pages 99-111, 1991.
<span id="ref_three">[3]</span> S. Haber, W.S. Stornetta, "How to time-stamp a digital document," In Journal of Cryptology, vol 3, no 2, pages 99-111, 1991.
</p>
<p>
<span id="4">[4]</span> D. Bayer, S. Haber, W.S. Stornetta, "Improving the efficiency and reliability of digital time-stamping," In Sequences II: Methods in Communication, Security and Computer Science, pages 329-334, 1993.
<span id="ref_four">[4]</span> D. Bayer, S. Haber, W.S. Stornetta, "Improving the efficiency and reliability of digital time-stamping," In Sequences II: Methods in Communication, Security and Computer Science, pages 329-334, 1993.
</p>
<p>
<span id="5">[5]</span> S. Haber, W.S. Stornetta, "Secure names for bit-strings," In Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 28-35, April 1997.
<span id="ref_five">[5]</span> S. Haber, W.S. Stornetta, "Secure names for bit-strings," In Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 28-35, April 1997.
</p>
<p>
<span id="6">[6]</span> A. Back, "Hashcash - a denial of service counter-measure," <a href="http://www.hashcash.org/papers/hashcash.pdf"><em>http://www.hashcash.org/papers/hashcash.pdf</em></a>, 2002.
<span id="ref_six">[6]</span> A. Back, "Hashcash - a denial of service counter-measure," <a href="http://www.hashcash.org/papers/hashcash.pdf"><em>http://www.hashcash.org/papers/hashcash.pdf</em></a>, 2002.
</p>
<p>
<span id="7">[7]</span> R.C. Merkle, "Protocols for public key cryptosystems," In Proc. 1980 Symposium on Security and Privacy, IEEE Computer Society, pages 122-133, April 1980.
<span id="ref_seven">[7]</span> R.C. Merkle, "Protocols for public key cryptosystems," In Proc. 1980 Symposium on Security and Privacy, IEEE Computer Society, pages 122-133, April 1980.
</p>
<p>
<span id="8">[8]</span> W. Feller, "An introduction to probability theory and its applications," 1957.
<span id="ref_eight">[8]</span> W. Feller, "An introduction to probability theory and its applications," 1957.
</p>
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