From 7ed95b283b707dac124c4fdc96d9f259e5297621 Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Wed, 14 Mar 2018 10:23:46 -0600 Subject: [PATCH 1/7] Errata 166266 --- code/ec-math.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/code/ec-math.py b/code/ec-math.py index 668fa455..7dcaa9ea 100644 --- a/code/ec-math.py +++ b/code/ec-math.py @@ -23,7 +23,7 @@ def random_secret(): convert_to_int = lambda array: int("".join(array).encode("hex"), 16) # Collect 256 bits of random data from the OS's cryptographically secure - # random generator + # random number generator byte_array = os.urandom(32) return convert_to_int(byte_array) From 6ef0bbcb954f687d9b9445e1ed5f94f6b95486fd Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Wed, 14 Mar 2018 10:32:54 -0600 Subject: [PATCH 2/7] Errata 166177 --- ch10.asciidoc | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/ch10.asciidoc b/ch10.asciidoc index b39879ad..da9edea7 100644 --- a/ch10.asciidoc +++ b/ch10.asciidoc @@ -862,7 +862,14 @@ In the last two years, the ASIC mining chips have become increasingly denser, ap ((("mining pools", id="MACoverpool10")))((("mining pools", "benefits of")))In this highly competitive environment, individual miners working alone (also known as solo miners) don't stand a chance. The likelihood of them finding a block to offset their electricity and hardware costs is so low that it represents a gamble, like playing the lottery. Even the fastest consumer ASIC mining system cannot keep up with commercial systems that stack tens of thousands of these chips in giant warehouses near hydroelectric powerstations. Miners now collaborate to form mining pools, pooling their hashing power and sharing the reward among thousands of participants. By participating in a pool, miners get a smaller share of the overall reward, but typically get rewarded every day, reducing uncertainty. -Let's look at a specific example. Assume a miner has purchased mining hardware with a combined hashing rate of 14,000 gigahashes per second (GH/s), or 14 TH/s. In 2017 this equipment costs approximately $2,500 USD. The hardware consumes 1375 watts (1.3 kW) of electricity when running, 32 kW-hours a day, at a cost of $1 to $2 per day at very low electricity rates. At current bitcoin difficulty, the miner will be able to solo mine a block approximately once every 4 years. If the miner does find a single block in that timeframe, the payout of 12.5 bitcoin, at approximately $1,000 per bitcoin, will result in a single payout of $12,500, which will not even cover the entire cost of the hardware and the electricity consumed over the time period, leaving a net loss of approximately $1,000. However, the chance of finding a block in a 4-year period depends on the miner's luck. He might find two blocks in 4 years and make a very large profit. Or he might not find a block for 5 years and suffer a bigger financial loss. Even worse, the difficulty of the bitcoin Proof-of-Work algorithm is likely to go up significantly over that period, at the current rate of growth of hashing power, meaning the miner has, at most, one year to break even before the hardware is effectively obsolete and must be replaced by more powerful mining hardware. If this miner participates in a mining pool, instead of waiting for a once-in-four-years $12,500 windfall, he will be able to earn approximately $50 to $60 per week. The regular payouts from a mining pool will help him amortize the cost of hardware and electricity over time without taking an enormous risk. The hardware will still be obsolete in one or two years and the risk is still high, but the revenue is at least regular and reliable over that period. Financially this only makes sense at very low electricity cost (less than 1 cent per kW-hour) and only at very large scale. +Let's look at a specific example. Assume a miner has purchased mining hardware with a combined hashing rate of 14,000 gigahashes per second (GH/s), or 14 TH/s. In 2017 this equipment costs approximately $2,500 USD. The hardware consumes 1375 watts (1.3 kW) of electricity when running, 33 kW-hours a day, at a cost of $1 to $2 per day at very low electricity rates. At current bitcoin difficulty, the miner will be able to solo mine a block approximately once every 4 years. How do we work out that probability? It is based on a network-wide hashing rate of 3 EH/sec (in 2017), and the miners rate of 14 TH/sec: + + +P = (14 * 10^12^ / 3 * 10^18^) * 210240 = 0.98 + +...where 21240 is the number of blocks in four years. The miner has a 98% probability of finding a block over four years, based on the global hash rate at the beginning of the period. + +If the miner does find a single block in that timeframe, the payout of 12.5 bitcoin, at approximately $1,000 per bitcoin, will result in a single payout of $12,500, which will produce a net profit of about $7,000. However, the chance of finding a block in a 4-year period depends on the miner's luck. He might find two blocks in 4 years and make a very large profit. Or he might not find a block for 5 years and suffer a bigger financial loss. Even worse, the difficulty of the bitcoin Proof-of-Work algorithm is likely to go up significantly over that period, at the current rate of growth of hashing power, meaning the miner has, at most, one year to break even before the hardware is effectively obsolete and must be replaced by more powerful mining hardware. If this miner participates in a mining pool, instead of waiting for a once-in-four-years $12,500 windfall, he will be able to earn approximately $50 to $60 per week. The regular payouts from a mining pool will help him amortize the cost of hardware and electricity over time without taking an enormous risk. The hardware will still be obsolete in one or two years and the risk is still high, but the revenue is at least regular and reliable over that period. Financially this only makes sense at very low electricity cost (less than 1 cent per kW-hour) and only at very large scale. Mining pools coordinate many hundreds or thousands of miners, over specialized pool-mining protocols. The individual miners configure their mining equipment to connect to a pool server, after creating an account with the pool. Their mining hardware remains connected to the pool server while mining, synchronizing their efforts with the other miners. Thus, the pool miners share the effort to mine a block and then share in the rewards. From e96c5c0dda0cba74d627b252f054fabe24972a00 Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Wed, 14 Mar 2018 10:39:53 -0600 Subject: [PATCH 3/7] Errata 163831 --- ch10.asciidoc | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/ch10.asciidoc b/ch10.asciidoc index da9edea7..196fef38 100644 --- a/ch10.asciidoc +++ b/ch10.asciidoc @@ -867,7 +867,7 @@ Let's look at a specific example. Assume a miner has purchased mining hardware w P = (14 * 10^12^ / 3 * 10^18^) * 210240 = 0.98 -...where 21240 is the number of blocks in four years. The miner has a 98% probability of finding a block over four years, based on the global hash rate at the beginning of the period. +...where 21240 is the number of blocks in four years. The miner has a 98% probability of finding a block over four years, based on the global hash rate at the beginning of the period. If the miner does find a single block in that timeframe, the payout of 12.5 bitcoin, at approximately $1,000 per bitcoin, will result in a single payout of $12,500, which will produce a net profit of about $7,000. However, the chance of finding a block in a 4-year period depends on the miner's luck. He might find two blocks in 4 years and make a very large profit. Or he might not find a block for 5 years and suffer a bigger financial loss. Even worse, the difficulty of the bitcoin Proof-of-Work algorithm is likely to go up significantly over that period, at the current rate of growth of hashing power, meaning the miner has, at most, one year to break even before the hardware is effectively obsolete and must be replaced by more powerful mining hardware. If this miner participates in a mining pool, instead of waiting for a once-in-four-years $12,500 windfall, he will be able to earn approximately $50 to $60 per week. The regular payouts from a mining pool will help him amortize the cost of hardware and electricity over time without taking an enormous risk. The hardware will still be obsolete in one or two years and the risk is still high, but the revenue is at least regular and reliable over that period. Financially this only makes sense at very low electricity cost (less than 1 cent per kW-hour) and only at very large scale. @@ -981,7 +981,7 @@ Once a miner using the new rules mines a block, the mining power and chain will Let's assume, for example, an 80%–20% split, with the majority of the mining power using the new consensus rules. Let's also assume that the fork occurs immediately after a retargeting period. -The two chains would each inherit the difficulty from the retargeting period. The new consensus rules would have 80% of the previously available mining power committed to them. From the perspective of this chain, the mining power has suddenly declined by 20% vis-a-vis the previous period. Blocks will be found on average every 12 minutes, representing the 20% decline in mining power available to extend this chain. This rate of block issuance will continue (barring any changes in hashing power) until 2016 blocks are mined, which will take approximately 24,192 minutes (at 12 minutes per block), or 16.8 days. After 16.8 days, a retarget will occur and the difficulty will adjust (reduced by 20%) to produce 10-minute blocks again, based on the reduced amount of hashing power in this chain. +The two chains would each inherit the difficulty from the retargeting period. The new consensus rules would have 80% of the previously available mining power committed to them. From the perspective of this chain, the mining power has suddenly declined by 20% vis-a-vis the previous period. Blocks will be found on average every 12.5 minutes, representing the 20% decline in mining power available to extend this chain. This rate of block issuance will continue (barring any changes in hashing power) until 2016 blocks are mined, which will take approximately 25,200 minutes (at 12.5 minutes per block), or 17.5 days. After 17.5 days, a retarget will occur and the difficulty will adjust (reduced by 20%) to produce 10-minute blocks again, based on the reduced amount of hashing power in this chain. The minority chain, mining under the old rules with only 20% of the hashing power, will face a much more difficult task. On this chain, blocks will now be mined every 50 minutes on average. The difficulty will not be adjusted for 2016 blocks, which will take 100,800 minutes, or approximately 10 weeks to mine. Assuming a fixed capacity per block, this will also result in a reduction of transaction capacity by a factor of 5, as there are fewer blocks per hour available to record transactions. From 078489e70a75523bf564a641198e45e28496361c Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Wed, 14 Mar 2018 10:47:50 -0600 Subject: [PATCH 4/7] Errata 163600 --- ch05.asciidoc | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ch05.asciidoc b/ch05.asciidoc index 3fc07dda..ffe8db8d 100644 --- a/ch05.asciidoc +++ b/ch05.asciidoc @@ -169,7 +169,7 @@ Mnemonic words are generated automatically by the wallet using the standardized 1. Create a random sequence (entropy) of 128 to 256 bits. 2. Create a checksum of the random sequence by taking the first (entropy-length/32) bits of its SHA256 hash. 3. Add the checksum to the end of the random sequence. -4. Divide the sequence into sections of 11 bits. +4. Split the result into 11-bit length segments. 5. Map each 11-bit value to a word from the predefined dictionary of 2048 words. 6. The mnemonic code is the sequence of words. 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zG=f3QiC$&Z^(}-J%$QHL(;+nG50Yp4JNQLtr3uLL5SNaYsivm^%<>+uN@` zq9b)WmEJde7CC%~87%kK46MKHGtu5EbXk55j`x3I^Ty0NK5Hw!KC2MjHPw{bys(KkwCR~t-d>FILMIxUoBpiU-fsRW1K*?u43=-W zI_Ntk1emaY$?h@PsxIt^YD2WC?&iJyHj~;l+MRYy{J=+R{Yu=Sg75-kTfo|s(-r;5 zUqfqBt!_QtzYc`r@@d|*F1jN|w}{WF4+rPHe)Ghtguci+ay`x+C|Rkm()$%P%qQ zi#F)&!%hB4Vjkio%gfjzRD-^O>WtoBu&~8v{!^5g|JGZnzjUYX-wg^M$U5u;NThuJ uEF>o1ZiYS85MeahH(EHA4hlP&f5#s2_+2HXVz From 79434212d69f1caaaf23bc7d367124255e6225b6 Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Wed, 14 Mar 2018 10:52:52 -0600 Subject: [PATCH 6/7] Errata 163573 --- ch10.asciidoc | 29 ++++++++++++++++++----------- 1 file changed, 18 insertions(+), 11 deletions(-) diff --git a/ch10.asciidoc b/ch10.asciidoc index 196fef38..34b54b0e 100644 --- a/ch10.asciidoc +++ b/ch10.asciidoc @@ -605,33 +605,40 @@ As you can see, there are a lot of zeros at the beginning of that target, meanin The formula to calculate the difficulty target from this representation is: ----- -target = coefficient * 2^(8 * (exponent – 3)) ----- + +target = coefficient * 2^(8*(exponent–3))^ + Using that formula, and the difficulty bits value 0x1903a30c, we get: ----- -target = 0x03a30c * 2^(0x08 * (0x19 - 0x03))^ -=> target = 0x03a30c * 2^(0x08 * 0x16)^ + +target = 0x03a30c * 2^0x08*(0x19-0x03)^ + + +=> target = 0x03a30c * 2^(0x08*0x16)^ + => target = 0x03a30c * 2^0xB0^ ----- + which in decimal is: ----- + + => target = 238,348 * 2^176^ + => target = 22,829,202,948,393,929,850,749,706,076,701,368,331,072,452,018,388,575,715,328 ----- + switching back to hexadecimal: ----- + + => target = 0x0000000000000003A30C00000000000000000000000000000000000000000000 ----- + + This means that a valid block for height 277,316 is one that has a block header hash that is less than the target. In binary that number must have more than 60 leading bits set to zero. With this level of difficulty, a single miner processing 1 trillion hashes per second (1 terahash per second or 1 TH/sec) would only find a solution once every 8,496 blocks or once every 59 days, on average. From 3d22d30685ec2bdc8a3c3a9d307d63766f654e65 Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Wed, 14 Mar 2018 10:58:05 -0600 Subject: [PATCH 7/7] Errata 163567 --- ch07.asciidoc | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/ch07.asciidoc b/ch07.asciidoc index 36dd9a37..b86d6da6 100644 --- a/ch07.asciidoc +++ b/ch07.asciidoc @@ -565,9 +565,10 @@ Using this construct, we can build redeem scripts with tens or hundreds of execu ((("transactions", "advanced", "multisignature scripts")))((("scripting", "multisignature scripts", "import/export example")))((("multisignature scripts")))In this example, Mohammed wishes to construct a company capital account with flexible rules. The scheme he creates requires different levels of authorization depending on timelocks. The participants in the multisig scheme are Mohammed, his two partners Saeed and Zaira, and their company lawyer Abdul. The three partners make decisions based on a majority rule, so two of the three must agree. However, in the case of a problem with their keys, they want their lawyer to be able to recover the funds with one of the three partner signatures. Finally, if all partners are unavailable or incapacitated for a while, they want the lawyer to be able to manage the account directly. -Here's the script that Mohammed designs to achieve this: +Here's the redeem script that Mohammed designs to achieve this: .Variable Multi-Signature with Timelock +[source,linenum] ---- IF IF