------------------------------------------------------------
commit e9175a66746049e1a29bbe99fe23f608a9429a33
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:29:00 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 0cf8028..e485e34 100644
--- a/index.scroll
+++ b/index.scroll
@@ -40,17 +40,17 @@ The problem of course is the payee can't verify that one of the owners did not d
The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.
-We need a way for the payee to know that the previous owners did not sign any earlier transactions. For our purposes, the earliest transaction is the one that counts, so we don't care about later attempts to double-spend. The only way to confirm the absence of a transaction is to be aware of all transactions. In the mint based model, the mint was aware of all transactions and decided which arrived first. To accomplish this without a trusted party, transactions must be publicly announced^[1], and we need a system for participants to agree on a single history of the order in which they were received. The payee needs proof that at the time of each transaction, the majority of nodes agreed it was the first received.
+We need a way for the payee to know that the previous owners did not sign any earlier transactions. For our purposes, the earliest transaction is the one that counts, so we don't care about later attempts to double-spend. The only way to confirm the absence of a transaction is to be aware of all transactions. In the mint based model, the mint was aware of all transactions and decided which arrived first. To accomplish this without a trusted party, transactions must be publicly announced^dai, and we need a system for participants to agree on a single history of the order in which they were received. The payee needs proof that at the time of each transaction, the majority of nodes agreed it was the first received.
# 3. Timestamp Server
-The solution we propose begins with a timestamp server. A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post^[2-5]. The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each additional timestamp reinforcing the ones before it.
+The solution we propose begins with a timestamp server. A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post^massias^haber^bayer^haber2. The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each additional timestamp reinforcing the ones before it.
figure2.png
# 4. Proof-of-Work
-To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof-of-work system similar to Adam Back's Hashcash^[6], rather than newspaper or Usenet posts. The proof-of-work involves scanning for a value that when hashed, such as with SHA-256, the hash begins with a number of zero bits. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash.
+To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof-of-work system similar to Adam Back's Hashcash^back, rather than newspaper or Usenet posts. The proof-of-work involves scanning for a value that when hashed, such as with SHA-256, the hash begins with a number of zero bits. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash.
For our timestamp network, we implement the proof-of-work by incrementing a nonce in the block until a value is found that gives the block's hash the required zero bits. Once the CPU effort has been expended to make it satisfy the proof-of-work, the block cannot be changed without redoing the work. As later blocks are chained after it, the work to change the block would include redoing all the blocks after it.
@@ -89,7 +89,7 @@ The incentive may help encourage nodes to stay honest. If a greedy attacker is a
# 7. Reclaiming Disk Space
-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^[7][2][5], 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.
+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^merkle^massias^haber2, 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.
figure4.png
@@ -125,7 +125,7 @@ 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.
-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^[8]:
+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^feller:
code
p = probability an honest node finds the next block
@@ -231,11 +231,11 @@ The network is robust in its unstructured simplicity. Nodes work all at once wit
# References
-- [1] W. Dai, "b-money," http://www.weidai.com/bmoney.txt, 1998.
-- [2] 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.
-- [3] S. Haber, W.S. Stornetta, "How to time-stamp a digital document," In Journal of Cryptology, vol 3, no 2, pages 99-111, 1991.
-- [4] 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.
-- [5] 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.
-- [6] A. Back, "Hashcash - a denial of service counter-measure," http://www.hashcash.org/papers/hashcash.pdf, 2002.
-- [7] R.C. Merkle, "Protocols for public key cryptosystems," In Proc. 1980 Symposium on Security and Privacy, IEEE Computer Society, pages 122-133, April 1980.
-- [8] W. Feller, "An introduction to probability theory and its applications," 1957.
\ No newline at end of file
+^dai W. Dai, "b-money," http://www.weidai.com/bmoney.txt, 1998.
+^massias 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.
+^haber S. Haber, W.S. Stornetta, "How to time-stamp a digital document," In Journal of Cryptology, vol 3, no 2, pages 99-111, 1991.
+^bayer 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.
+^haber2 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.
+^back A. Back, "Hashcash - a denial of service counter-measure," http://www.hashcash.org/papers/hashcash.pdf, 2002.
+^merkle R.C. Merkle, "Protocols for public key cryptosystems," In Proc. 1980 Symposium on Security and Privacy, IEEE Computer Society, pages 122-133, April 1980.
+^feller W. Feller, "An introduction to probability theory and its applications," 1957.
\ No newline at end of file
------------------------------------------------------------
commit 6f9e3a6fef45152398eaf9521c2cc6ae45a9430e
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:25:07 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 1096ba6..0cf8028 100644
--- a/index.scroll
+++ b/index.scroll
@@ -133,14 +133,11 @@ code
qz = probability the attacker will ever catch up from z blocks behind
katex
- \[
- q_z =
+ q_z =
\begin{cases}
- 1 & \text{if } p \leq q, \\[10pt]
- \left(\frac{q}{p}\right)^z & \text{if } p > q.
+ 1, & \text{if } p \leq q \\[8pt]
+ \left(\frac{q}{p}\right)^z, & \text{if } p > q
\end{cases}
- \]
-
Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.
------------------------------------------------------------
commit 1b832b85414d30b3723f10023d8e60aba042574c
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:24:31 2024 +0000
Reverted to cabec0431db8420a44aef04cd9f848f6545644bb
diff --git a/.requests.scroll b/.requests.scroll
new file mode 100644
index 0000000..e6f528f
--- /dev/null
+++ b/.requests.scroll
@@ -0,0 +1,34 @@
+title Traffic Data
+metaTags
+homeButton
+buildHtml
+theme gazette
+
+printTitle
+
+container
+
+Real time view
+ /globe.html?folderName=blank_template
+
+button Refresh
+ link /summarizeRequests.htm?folderName=blank_template
+ post
+ // Anything
+
+.requests.csv
+ <br><br><span style="width: 200px; display:inline-block; color: blue;">Readers</span><span style="color:green;">Writers</span><br><br>
+ sparkline
+ y Readers
+ color blue
+ width 200
+ height 200
+ sparkline
+ y Writers
+ color green
+ width 200
+ height 200
+ printTable
+
+tableSearch
+scrollVersionLink
diff --git a/.stats.json b/.stats.json
new file mode 100644
index 0000000..0e3f975
--- /dev/null
+++ b/.stats.json
@@ -0,0 +1,23 @@
+{
+ "files": [
+ ".gitignore",
+ "bitcoin.pdf",
+ "figure1.png",
+ "figure2.png",
+ "figure3.png",
+ "figure4.png",
+ "figure6.png",
+ "figure7.png",
+ "index.scroll"
+ ],
+ "stats": {
+ "folder": "satoshi",
+ "folderLink": "https://hub.scroll.pub/satoshi",
+ "created": "2024-12-20T22:23:47.000Z",
+ "revised": "2024-12-20T22:23:47.000Z",
+ "files": 9,
+ "mb": 1,
+ "revisions": 35,
+ "hash": "8043477c96"
+ }
+}
\ No newline at end of file
diff --git a/figure5.png b/figure5.png
new file mode 100644
index 0000000..377f49f
Binary files /dev/null and b/figure5.png differ
diff --git a/index.scroll b/index.scroll
index 35c60c7..1096ba6 100644
--- a/index.scroll
+++ b/index.scroll
@@ -133,11 +133,13 @@ code
qz = probability the attacker will ever catch up from z blocks behind
katex
+ \[
q_z =
\begin{cases}
1 & \text{if } p \leq q, \\[10pt]
\left(\frac{q}{p}\right)^z & \text{if } p > q.
\end{cases}
+ \]
Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.
------------------------------------------------------------
commit 8043477c9648e32213731e4f4552e05201df6620
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:23:47 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 9be66c1..35c60c7 100644
--- a/index.scroll
+++ b/index.scroll
@@ -133,13 +133,11 @@ code
qz = probability the attacker will ever catch up from z blocks behind
katex
- [
q_z =
\begin{cases}
1 & \text{if } p \leq q, \\[10pt]
\left(\frac{q}{p}\right)^z & \text{if } p > q.
\end{cases}
- ]
Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.
------------------------------------------------------------
commit 87196898cede38854e4d185929a4881c00c143e5
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:23:36 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 1096ba6..9be66c1 100644
--- a/index.scroll
+++ b/index.scroll
@@ -133,13 +133,13 @@ code
qz = probability the attacker will ever catch up from z blocks behind
katex
- \[
+ [
q_z =
\begin{cases}
1 & \text{if } p \leq q, \\[10pt]
\left(\frac{q}{p}\right)^z & \text{if } p > q.
\end{cases}
- \]
+ ]
Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.
------------------------------------------------------------
commit cabec0431db8420a44aef04cd9f848f6545644bb
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:23:30 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 57aa097..1096ba6 100644
--- a/index.scroll
+++ b/index.scroll
@@ -133,11 +133,14 @@ code
qz = probability the attacker will ever catch up from z blocks behind
katex
- q_z =
+ \[
+ q_z =
\begin{cases}
- 1 & \text{if } p \leq q \\
- \left(\frac{q}{p}\right)^z & \text{if } p > q
+ 1 & \text{if } p \leq q, \\[10pt]
+ \left(\frac{q}{p}\right)^z & \text{if } p > q.
\end{cases}
+ \]
+
Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.
------------------------------------------------------------
commit 663d2299639bd89b1904084bab0805b0db769279
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:22:49 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 450774a..57aa097 100644
--- a/index.scroll
+++ b/index.scroll
@@ -133,13 +133,11 @@ code
qz = probability the attacker will ever catch up from z blocks behind
katex
- \[
q_z =
\begin{cases}
1 & \text{if } p \leq q \\
\left(\frac{q}{p}\right)^z & \text{if } p > q
\end{cases}
- \]
Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.
------------------------------------------------------------
commit 51ca4682f421ac384ec8660e64f1c4bda8624379
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:22:31 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 8a8a24b..450774a 100644
--- a/index.scroll
+++ b/index.scroll
@@ -133,10 +133,13 @@ code
qz = probability the attacker will ever catch up from z blocks behind
katex
- q_z = \begin{cases}
- 1 & \text{if } p \leq q\\
- (q/p)^z & \text{if } p > q
+ \[
+ q_z =
+ \begin{cases}
+ 1 & \text{if } p \leq q \\
+ \left(\frac{q}{p}\right)^z & \text{if } p > q
\end{cases}
+ \]
Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.
------------------------------------------------------------
commit ec8ad0edba9133db7b3072761a8d799e9bbccbe9
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:20:59 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 723362b..8a8a24b 100644
--- a/index.scroll
+++ b/index.scroll
@@ -160,9 +160,7 @@ katex
Rearranging to avoid summing the infinite tail of the distribution:
katex
- z
- 1 - ∑ λk e-λ / k! * (1 - (q/p)^(z-k))
- k=0
+ 1 - \sum_{k=0}^{z} \frac{\lambda^k e^{-\lambda}}{k!} \cdot (1-(q/p)^{z-k})
code
#include <math.h>
------------------------------------------------------------
commit 1673f700b38093ce223e73edde59351610f71ecf
Author: ffff:12.186.22.250 <ffff:12.186.22.250@hub.scroll.pub>
Date: Fri Dec 20 22:20:51 2024 +0000
updated index.scroll
diff --git a/index.scroll b/index.scroll
index 823f530..723362b 100644
--- a/index.scroll
+++ b/index.scroll
@@ -152,10 +152,11 @@ katex
To get the probability the attacker could still catch up now, we multiply the Poisson density for each amount of progress he could have made by the probability he could catch up from that point:
katex
- ∞
- ∑ λk e-λ / k! * { (q/p)^(z-k) if k≤z
- k=0 { 1 if k>z }
-
+ \sum_{k=0}^{\infty} \frac{\lambda^k e^{-\lambda}}{k!} \cdot \begin{cases}
+ (q/p)^{z-k} & \text{if } k\leq z\\
+ 1 & \text{if } k>z
+ \end{cases}
+
Rearranging to avoid summing the infinite tail of the distribution:
katex