Sentient code: An inside look at Stephen Wolfram's utterly new, insanely ambitious computational paradigm | VentureBeat | Dev | by John Koetsier

Sentient code: An inside look at Stephen Wolfram’s utterly new, insanely ambitious computational paradigm

Next Berlin

November 29, 2013 2:13 PM

John Koetsier

Forum - Patch Notes - 1.0.2 Patch Notes - Path of Exile

Version 1.0.2
Notes:

• This patch contains substantial balance changes to Damage Over Time calculations. If problems are found, we'll follow up rapidly with hotfixes. Please be very careful when playing in the Hardcore or Nemesis leagues after patches of this size.

Major Content/Features:

• Added a new intelligence skill - Storm Call: Sets a marker at a location. After a short duration, lightning strikes the marker, dealing damage around it. When this happens, it will also set off the lightning at any other markers you've cast.
• Storm Call is available to the Shadow, Witch and Templar from the "Breaking some Eggs" quest in Normal Difficulty.
• Added four new Unique items, three of which were designed by supporters.
• Added six new cosmetic microtransactions: Seraph Spectral Throw Effect, Lightning Bat Pet, Orange Portal Effect, Exile's Essentials Back Attachment and two Thanksgiving limited-time items: Pilgrim Hat and Ornate Pilgrim Hat.
• Added two new achievements: Elemental Aegis and Dream Within a Dream.
• One new vendor recipe has been added.
• End-game Maps have been increased in size. Map mods that affect size have been removed. More details are provided in the balance section below.

Minor Content/Features:

• You can now report whisper messages by right clicking on them.
• Our system for rendering effects on game objects has been improved. Multiple effects on the same object can now co-exist without looking bad.
• Several skills have had their effects updated to remove additional lights. This should result in fewer performance issues and frame rate drops when these skills are used.
• A button to view the Path of Exile Credits has been added to the login screen. It doesn't play the awesome music, though.
• Some skills now display average damage per skill use instead of DPS, as DPS would not make sense for them.
• Hailrake now has a couple of new effects.
• Added new visual effects to several unique items: Redbeak, Heartbreaker, Soul Taker, Nycta's Lantern, The Supreme Truth, alternate art Reaper's Pursuit and The Blood Reaper.
• The Scion is now enabled on your account after killing Dominus, even if she has not been rescued from her cage.
• Continued to incrementally improve the sound, art, effects and environments.

End-game Map Balance:

• All maps have been increased in size. All maps will be similar to or larger than they would be if they previously had the Larger or Branchy map mods.
• Removed "Massive" and "Labyrinthine" mods from maps. Existing maps with these mods will grant 20% quantity, but will not change the size of the map. This quantity won't show on the map, but will appear on the world area once it is made.
• The following mods have been added: "of Lightning" (causes shocked ground), "Hexproof" (monsters are immune to curses), "Feral", "Demonic", "Bipedal" (these replace monsters with a specific type).
• The "Villainous" mod has been removed.
• The "Capricious" mod now grants more quantity and larger pack sizes.
• The map mod "of Ice" now grants more quantity. "of Flames" grants less quantity.
• Insect map packs have had their composition changed.
• Added Vaal Fallen and Serpentine Constructs as the signature monsters for the Maze Map.
• Removed Devourers as the signature monster in the Labyrinth Map.
• Added additional large skeleton packs to the signature monsters for the Museum Map.
• Added additional Vaal Construct packs to the signature monsters for the Vaal Pyramid Map.
• The "of the Warlord" mod has been removed (Warlord's Mark Curse).
• The additional quantity granted by the "of Hemomancy" mod has been increased to 25 from 15.
• The "Fleet" mod has been increased from 20-25 attack speed, cast speed and movement speed to 25-35 attack speed, cast speed and movement speed.

Damage Over Time Balance:

• Previously, modifiers to damage dealt applied only to damage on hits unless they specifically said otherwise (for example, Increased Burning Damage).
• Generic modifiers to damage dealt will now apply to damage over time that your character causes. Damage over time is not spell damage, nor attack damage, so modifiers specific to those types will not apply. Non-specific "increased damage" modifiers will apply to damage over time. Type-specific modifiers will apply as well. For example, "increased fire damage" modifiers will apply to fire damage over time.
• Modifiers based on how the damage is dealt will apply as appropriate - for example, increased area damage and increased projectile damage will both apply to the poison clouds from Poison Arrow, as it fills an area and is an effect of a projectile.
• Viper Strike can be supported by Melee Splash, now that the damage penalty also applies.
• Damage conversion does not apply to damage over time.
• The changes in this patch apply to most damage over time in the game (i.e. both players and monsters).
• One exception is that damage increases will not apply to damage over time that you cause on yourself. For example, having 100% increased damage won't make the chaos damage over time from Blood Rage more powerful.
• Note: This is a functional change to Righteous Fire. Previously this skill did increase the burning damage on you by your increased burning damage modifiers. Increased burning damage will still affect the burning on enemies.
• Magic, Rare and Unique monsters have a damage bonus built into their rarity - this will now also apply to any damage over time they cause.
• On hit effects do not apply to damage over time.
• The Ignite status ailment now deals only 20% of the original hit per second for 4 seconds. This has been reduced as it can be increased in more ways with the damage over time changes.
• Several skills have had their scaling adjusted. As these skills now have many more things that can scale them up, their built-in progression has been reduced. They are potentially more powerful if you specialise in them.

General Balance:

• Cast When Stunned now has a 250ms cooldown.
• On the passive tree, the Deadly Draw and Heavy Draw bow group has been changed. It now only has one entry and has been made symmetric. The Heavy Draw arm offers life, while Deadly Draw offers more consistent critical bonuses.
• General Gravicius' Molten Shell now has a 30 second cooldown in all difficulties.
• The Devourer's Emerge skill has had its damage reduced.
• The priorities of several vendor recipes have been reordered. Recipes with multiple components should now take priority over recipes with one component. Some higher value recipes have been moved up in priority relative to others.
• The Endless Ledge now increments one monster level per area after monster level 30, until monster level 60. Areas repeat at level 60s. Only after 100 total Endless Ledge levels do you wrap back to the first area.

Bug Fixes:

• The hybrid flask recipe now correctly gives rarity and itemlevel based on the component flasks and no longer provides quality. This is now consistent with other recipes.
• Fixed a bug where initiating a trade with your stash open would cause the trade to cancel.
• Fixed a bug where right clicking could close the stash panel.
• Fixed a bug in the character selection screen where pressing escape with the options panel open would log out instead of closing the options panel.
• Fixed bugs related to Dominus' charge attack.
• Fixing a bug where flask-use sounds wouldn't play if you had reduced flask charges used.
• Fixed a bug where shield crabs did not drop items in certain situations.
• Fixed a bug where monster outlines disappeared when monsters were on low life.
• Fixed a bug involving spectres and trigger supports.
• Fixed a bug where Lightning Warp cast at the caster's feet would always default to casting in the same direction.
• Fixed a bug where some Nemesis mods with casted effects would not work if the monster was hidden.
• Fixed Cast on Death preventing curse application on hit, which is not a triggered cast.

Bitcoin: A Peer-to-Peer Electronic Cash System

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Bitcoin: A Peer-to-Peer Electronic Cash System

Satoshi Nakamoto satoshin@gmx.com www.bitcoin.org

Abstract. A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power. As long as a majority of CPU power is controlled by nodes that are not cooperating to attack the network, they'll generate the longest chain and outpace attackers. The network itself requires minimal structure. Messages are broadcast on a best effort basis, and nodes can leave and rejoin the network at will, accepting the longest proof-of-work chain as proof of what happened while they were gone.

1. Introduction

Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model. Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions, and there is a broader cost in the loss of ability to make non-reversible payments for non- reversible services. With the possibility of reversal, the need for trust spreads. Merchants must be wary of their customers, hassling them for more information than they would otherwise need. A certain percentage of fraud is accepted as unavoidable. These costs and payment uncertainties can be avoided in person by using physical currency, but no mechanism exists to make payments over a communications channel without a trusted party.

What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party. Transactions that are computationally impractical to reverse would protect sellers from fraud, and routine escrow mechanisms could easily be implemented to protect buyers. In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions. The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes.

1

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2. Transactions

We define an electronic coin as a chain of digital signatures. Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership.

Transaction

Transaction

Owner 1's

Owner 2's Public Key

Public Key

Owner 0's

Owner 1's Signature

Signature

The problem of course is the payee can't verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. 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.

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.

2

Transaction

Owner 3's Public Key

Hash

Hash

Hash

V

e

rify

V

e

rify

Owner 2's Signature

S

ig

n

S

ig

n

Owner 1's

Owner 2's

Owner 3's Private Key

Private Key

Private Key

Hash

Hash

Block

Block

Item Item ...

Item Item ...

---

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.

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.

Block

Prev Hash Nonce

Tx Tx ...

The proof-of-work also solves the problem of determining representation in majority decision making. If the majority were based on one-IP-address-one-vote, it could be subverted by anyone able to allocate many IPs. Proof-of-work is essentially one-CPU-one-vote. The majority decision is represented by the longest chain, which has the greatest proof-of-work effort invested in it. If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes. We will show later that the probability of a slower attacker catching up diminishes exponentially as subsequent blocks are added.

To compensate for increasing hardware speed and varying interest in running nodes over time, the proof-of-work difficulty is determined by a moving average targeting an average number of blocks per hour. If they're generated too fast, the difficulty increases.

5. Network

The steps to run the network are as follows:

1) New transactions are broadcast to all nodes. 2) Each node collects new transactions into a block. 3) Each node works on finding a difficult proof-of-work for its block. 4) When a node finds a proof-of-work, it broadcasts the block to all nodes. 5) Nodes accept the block only if all transactions in it are valid and not already spent. 6) Nodes express their acceptance of the block by working on creating the next block in the

chain, using the hash of the accepted block as the previous hash.

Nodes always consider the longest chain to be the correct one and will keep working on extending it. If two nodes broadcast different versions of the next block simultaneously, some nodes may receive one or the other first. In that case, they work on the first one they received, but save the other branch in case it becomes longer. The tie will be broken when the next proof- of-work is found and one branch becomes longer; the nodes that were working on the other branch will then switch to the longer one.

3

Block

Prev Hash Nonce

Tx Tx ...

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New transaction broadcasts do not necessarily need to reach all nodes. As long as they reach many nodes, they will get into a block before long. Block broadcasts are also tolerant of dropped messages. If a node does not receive a block, it will request it when it receives the next block and realizes it missed one.

6. Incentive

By convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block. This adds an incentive for nodes to support the network, and provides a way to initially distribute coins into circulation, since there is no central authority to issue them. The steady addition of a constant of amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended.

The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free.

The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.

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.

A block header with no transactions would be about 80 bytes. If we suppose blocks are generated every 10 minutes, 80 bytes * 6 * 24 * 365 = 4.2MB per year. With computer systems typically selling with 2GB of RAM as of 2008, and Moore's Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory.

4 Block

Block Header (Block Hash)

Block Prev Hash Nonce

Hash01

Hash0 Hash1 Hash2 Hash3

Block Header (Block Hash)

Prev Hash Nonce

Root Hash

Root Hash

Hash23

Hash01

Hash23

Hash2

Hash3

Tx0 Tx1 Tx2 Tx3

Tx3

Transactions Hashed in a Merkle Tree After Pruning Tx0-2 from the Block

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8. Simplified Payment Verification

It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it's timestamped in. He can't check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it.

Longest Proof-of-Work Chain

Block Header

Block Header

Merkle Root

Merkle Root

Tx3

As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification.

9. Combining and Splitting Value

Although it would be possible to handle coins individually, it would be unwieldy to make a separate transaction for every cent in a transfer. To allow value to be split and combined, transactions contain multiple inputs and outputs. Normally there will be either a single input from a larger previous transaction or multiple inputs combining smaller amounts, and at most two outputs: one for the payment, and one returning the change, if any, back to the sender.

It should be noted that fan-out, where a transaction depends on several transactions, and those transactions depend on many more, is not a problem here. There is never the need to extract a complete standalone copy of a transaction's history.

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Block Header

Prev Hash Nonce

Prev Hash Nonce

Prev Hash Nonce

Merkle Root

Hash01

Hash23

Merkle Branch for Tx3

Hash2 Hash3

Transaction

In Out

In

...

...

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10. Privacy

The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party. The necessity to announce all transactions publicly precludes this method, but privacy can still be maintained by breaking the flow of information in another place: by keeping public keys anonymous. The public can see that someone is sending an amount to someone else, but without information linking the transaction to anyone. This is similar to the level of information released by stock exchanges, where the time and size of individual trades, the "tape", is made public, but without telling who the parties were.

As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner. Some linking is still unavoidable with multi-input transactions, which necessarily reveal that their inputs were owned by the same owner. The risk is that if the owner of a key is revealed, linking could reveal other transactions that belonged to the same owner.

11. Calculations

We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them. An attacker can only try to change one of his own transactions to take back money he recently spent.

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]:

p = probability an honest node finds the next block q = probability the attacker finds the next block q

z

Traditional Privacy Model

Identities Transactions

Trusted Third Party

Counterparty Public

New Privacy Model

Identities Transactions Public

= probability the attacker will ever catch up from z blocks behind

q

z

=

{ q/ 1 p z

if if p≤q pq

}

6

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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.

We now consider how long the recipient of a new transaction needs to wait before being sufficiently certain the sender can't change the transaction. We assume the sender is an attacker who wants to make the recipient believe he paid him for a while, then switch it to pay back to himself after some time has passed. The receiver will be alerted when that happens, but the sender hopes it will be too late.

The receiver generates a new key pair and gives the public key to the sender shortly before signing. This prevents the sender from preparing a chain of blocks ahead of time by working on it continuously until he is lucky enough to get far enough ahead, then executing the transaction at that moment. Once the transaction is sent, the dishonest sender starts working in secret on a parallel chain containing an alternate version of his transaction.

The recipient waits until the transaction has been added to a block and z blocks have been linked after it. He doesn't know the exact amount of progress the attacker has made, but assuming the honest blocks took the average expected time per block, the attacker's potential progress will be a Poisson distribution with expected value:

=z

q p

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:

∑ k=0

{ q/ pz−k 1 ∞ 

k

k! e

−

⋅

if if k≤z kz

}

Rearranging to avoid summing the infinite tail of the distribution...

1−

∑ z

k=0

k k!

e−



1−q/ p

z−k

Converting to C code...

#include

double p = 1.0 - q; double lambda = z * (q / p); double sum = 1.0; int i, k; for (k = 0; k <= z; k++) {

double poisson = exp(-lambda); for (i = 1; i <= k; i++)

poisson *= lambda / i; sum -= poisson * (1 - pow(q / p, z - k)); } return sum; }

7

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Running some results, we can see the probability drop off exponentially with z.

q=0.1 z=0 P=1.0000000 z=1 P=0.2045873 z=2 P=0.0509779 z=3 P=0.0131722 z=4 P=0.0034552 z=5 P=0.0009137 z=6 P=0.0002428 z=7 P=0.0000647 z=8 P=0.0000173 z=9 P=0.0000046 z=10 P=0.0000012

q=0.3 z=0 P=1.0000000 z=5 P=0.1773523 z=10 P=0.0416605 z=15 P=0.0101008 z=20 P=0.0024804 z=25 P=0.0006132 z=30 P=0.0001522 z=35 P=0.0000379 z=40 P=0.0000095 z=45 P=0.0000024 z=50 P=0.0000006

Solving for P less than 0.1%...

P < 0.001 q=0.10 z=5 q=0.15 z=8 q=0.20 z=11 q=0.25 z=15 q=0.30 z=24 q=0.35 z=41 q=0.40 z=89 q=0.45 z=340

12. Conclusion

We have proposed a system for electronic transactions without relying on trust. We started with the usual framework of coins made from digital signatures, which provides strong control of ownership, but is incomplete without a way to prevent double-spending. To solve this, we proposed a peer-to-peer network using proof-of-work to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of CPU power. The network is robust in its unstructured simplicity. Nodes work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can leave and rejoin the network at will, accepting the proof-of-work chain as proof of what happened while they were gone. They vote with their CPU power, expressing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism.

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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.

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