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## RPOW Theory

## Tokens

Tokens in the RPOW system are of two types: proof of work (POW) tokens, and reusable proof of work (RPOW) tokens. The POW tokens used in the RPOW system are pieces of hashcash, invented by Adam Back and well described at that link.

## Hashcash

Hashcash is a textual string in a particular format which has a special property: when run through the SHA-1 hash algorithm (the same algorithm used in the sha1sum utility often used to validate downloaded files) the result has the first N of its initial bits equal to zero, where N is typically around 20-30. The terminology used for hashcash describes the number of leading zero bits as the size of its "collision". Because of SHA-1's properties, the only way to find a string with a large collision size is by exhaustive search: trying one variation after another, until you get lucky.

Here, for example, is a hashcash token with a 28 bit collision (or we might say it is "worth 28 bits"):

1:28:040727:halmail1@finney.org::1c6a5020f5ef5c75:63cca52

And here is the SHA-1 hash of that text string:

0000000a86d41df172f177f4e7ec3907d4634b58

See? It starts with 7 digits of 0, which in this hexadecimal representation means 7*4 or 28 bits.

The chance of any bit being a zero is 1/2, so the chance of finding the first N bits being zero is one in two to the Nth power. This means that you must try, on the average, about one million test strings before finding one with a 20 bit collision; or about a billion test strings before finding a 30 bit collision. These calculations can take from seconds to hours on modern computers. In general, finding a one bit longer collision will take twice as long.

This means that if you think of a piece of hashcash as having a "value" which is the size of the bit collision, then a piece of hashcash with a value one higher is in effect twice as rare and twice as "valuable". A piece of hashcash with a value of 30 is actualy 1024 times more valuable (in terms of difficulty of creation) as one of value 20, because it is 10 bits higher value and 2 to the 10th power is 1024.

What makes hashcash useful is not just that it is relatively time-consuming to produce, but that it is quick to verify. Once a hashcash token is created, it can be verified by running the string through the SHA-1 algorithm and counting the leading zeros. This is almost instantaneous, despite the fact that it may have taken a long time to produce the hashcash.

Hashcash therefore provides a means by which someone can prove very easily and quickly that they spent (on average) some specified amount of computer cycles to create the token. In particular, it can be used to show that the sender spent a lot of time to create the token. Hashcash therefore serves as evidence of effort, and in many contexts can be used to demonstrate a level of importance or significance to a message or some other kind of data.

## Reuse

One of the problems with hashcash tokens is that they cannot be reused. The risk is that someone could perform an extensive calculation and produce a high-value hashcash token, one with a large collision of, say, 36 bits. On my present-day laptop computer this would take about one day. But if, having created the token, they could use it as many times as they wanted, this would provide misleading evidence to the recipient of the attention that they were receiving. That one-day effort could be spread over thousands or millions of recipients, making the per-message effort negligible. Under these circumstances, users would have no way of knowing the true value of hashcash tokens, and they would not be useful.

To avoid this, hashcash tokens have embedded within them a "resource string". This is supposed to identify the particular use for which the token is intended, and should be sufficient to allow the recipient to make sure the token could not be used for any other purpose. For the case of email, the resource might be the email address of the recipient. When a hashcash token is received for such a purpose, the receiver (i.e. his software) must check the hashcash resource string and make sure it matches the expected value.

In addition, recipients of hashcash need to keep a local record of all of the hashcash tokens they have received recently, so that they can detect the case where someone tries to send them the same piece of hashcash more than once. In order to keep this local hashcash database from growing indefinitely, hashcash also embeds the time and date of its creation within the text string that gets hashed. This allows hashcash recipients to expire old values from their database and only keep the hashcash tokens they have seen within recent days.

## RPOW Tokens

Reusable proof of work (RPOW) tokens extend on hashcash to provide a limited form of reuse. As explained above, allowing hashcash to be freely reused would make the tokens effectively worthless, as there would be no limits to how many times a given token could be shown. RPOW tokens provide a limited form of reuse called sequential reuse. In essence, once a POW token is created in the form of a piece of hashcash, it can be exchanged at an RPOW server for an RPOW token of equal value. The RPOW token can then be exchanged, sent, or otherwise used similarly to a hashcash token. However, rather than being effectively discarded after use, the RPOW token can be exchanged by the recipient at the RPOW server for a new, equal-value, RPOW token. This token can be used exactly like the first one. It can be sent to a recipient, who can verify and exchange it at an RPOW server, just as they might do for a POW token. And that new recipient can, after exchanging the RPOW token at the server and receiving a new one in exchange, retain the new RPOW token and use it again in the future.

In this way, a single POW token is the foundation for a chain of RPOW tokens. The effect is the same as if the POW token could be handed from person to person and retain its value at each step.

Security researcher Nick Szabo has coined the term bit gold to refer to a similar concept of tokens which inherently represent a certain level of effort. Nick's concept is more complex than the simple RPOW system, but his insight applies: in some ways, an RPOW token can be thought of as having the properties of a rare substance like gold. It takes effort and expense to mine and mint gold coins, making them inherently scarce. Gold coins can then be passed from person to person, and each recipient can verify the authenticity of the coinage.

In a similar way, RPOW tokens take a certain level of effort and expense to be created. They all start with a hashcash collision which, at the higher levels, will take hours or even days of computing time to create. RPOW tokens can be validated and verified upon receipt by exchanging them at the RPOW server for a new RPOW token. This allows them to be passed from person to person much like coins.

Most importantly, the RPOW system is architected with one overriding goal: to make it impossible for anyone, even the owner of the RPOW server, even the developer of the RPOW software, to be able to violate the system's rules and forge RPOW tokens. Without such a guarantee against forgeability, RPOW tokens would not credibly represent the work that was done to create them. Forgeable tokens would be more like paper money than bit gold. My goal in this project was to bring to life a simple realization which demonstrates the power of the bit gold concept. This requires resistance to forgeability, and this goal has dominated every part of the design.

See the security page for more detail on how the system is designed to resist forgery, and the World of RPOW page for information on the potential for a worldwide network of RPOW servers.

## RPOW Format

An RPOW token is composed of several parts:

- value
- keyid
- id
- bignum
The most important are the

idand thebignum. Theidcontains 20 random bytes, along with some extra data to be described later. Thebignumis an RSA signature on a value created by extending theidwith repeated hashing to add redundancy:___________________________________________________________________ | SHA1(id) | 2 | SHA1(bytes 0-20) | SHA1(bytes 0-40) | ... | -------------------------------------------------------------------- 0 - 19 20 21 - 40 41 - 59 ... 127 Byte numbers (MSB first)This value is interpreted as a 1024 bit bignum value, and exponentiated with the secret exponent of an RSA signing key. The result is the

bignumfield of the RPOW. The RPOW can be mathematically verified by raising thebignumvalue to the appropriate public exponent, and comparing the result to the extendedidvalue, created using the pattern shown above.RPOWs can be of different values, just as POWs can. The value of an RPOW is stored in its

valuefield and is equivalent to the number of bits in a POW collision. Each RPOW value corresponds to a public exponent, according to the following rule. The lowest RPOW value, which corresponds to a 20 bit POW collision, is mapped to an RSA public exponent of 65537. Successively increasing values are then mapped to consecutive primes above 65537, leading to the following table:

RPOW

ValueRSA

Exponent20 65537 21 65539 22 65543 23 65551 24 65557 25 65563 26 65579 27 65581 28 65587 29 65599

RPOW

ValueRSA

Exponent30 65609 31 65617 32 65629 33 65633 34 65647 35 65651 36 65657 37 65677 38 65687 39 65699

RPOW

ValueRSA

Exponent40 65701 41 65707 42 65713 43 65717 44 65719 45 65729 46 65731 47 65761 48 65777 49 65789 50 65809 The RSA key which signed the RPOW is indicated by the

keyidfield. Thekeyidis a SHA-1 hash of the RSA modulus and exponent, each preceded by a four-byte byte count field. Initially there is only one RPOW signing key and only onekeyid, but over time there may be more RPOW signing keys created, as described on the World of RPOW page. To verify an RPOW it is necessary to know which RSA key signed it. Thekeyidimplicitly identifies the RSA modulus, and thevalueidentifies the RSA exponent; together they define the RSA verification key.## No Inflation Principle

Unlike with POWs, it takes no longer to create high valued RPOWs than low valued ones. Nevertheless, RPOWs are considered to have the same value as equivalent POWs. The reason is that the only way that an RPOW server will sign a bignum with an exponent of a certain value, is if it receives in exchange an equal-value POW or RPOW token. The RPOW server thus enforces conservation of value, also called the no-inflation principle. RPOWs will only be created when POWs or RPOWs of equal value are exchanged for them.

To enforce the no-inflation rule, the RPOW server must make sure that no POW or RPOW can be used more than once as part of an exchange. Each one is created, and then exchanged at the server for a new RPOW, and after that, the old one can never be used again. The RPOW server enforces this rule primarily by keeping a record of all of the RPOWs and POWs that it has seen in the past. Whenever one is offered for exchange, the RPOW server compares it against this database of previously-seen RPOWs. If it is on the list, this is an attempt to reuse the POW or RPOW, and the exchange request is rejected. If the POW or RPOW is not on the list, it is added to the list, and then the RPOW server will sign the bignum value supplied as part of the exchange, creating a new RPOW.

Initially, a POW is created of a certain value, represented by the size of the hash collision (number of leading zeros in the hash value). This can then be exchanged for an RPOW whose signing exponent represents the same value. This RPOW can be transferred and further exchanged for equal value RPOWs. Each RPOW can only be used at one step, but as it is destroyed it allows a new RPOW of equal value to be created in the exchange operation. The result is as though the original POW could be handed from person to person while retaining its value.

## Time to Split?

In addition to allowing straight one-for-one exchanges of equal value, the RPOW server allows exchanges where tokens are split or combined in various ways. The rule is that the combined value of the new RPOWs must equal the combined value of the incoming POWs and RPOWs which are being exchanged.

When calculating these values it is important to take into consideration the property of POWs described above, that one with a value of one greater is actually worth twice as much (in terms of expense to create). This means that you can, for example, exchange a single token worth 21 for two with values of 20. Or you could go the other way and exchange two tokens worth 24 for a single one worth 25. The general formula is to add two to the power of the

valuefield for each incoming POW and RPOW, and do the same thing with the requested outgoing RPOWs. Only if the results are equal will the RPOW server allow the exchange.More examples of some legal exchanges would be two 24's, a 25, and two 29's for a 26 and a 30; or a 32 exchanged for a 31, a 30, a 29 and four 27's. Using these rules, an RPOW server will allow you to split or combine your existing RPOW tokens in a variety of ways.

This creates a great deal of flexibility in how RPOWs are used, as you don't have to calculate in advance the exact sizes or values you will need. You could keep a few relatively large RPOWs around and then split them into smaller values to give to someone else. Or if you receive a large number of RPOWs, you can combine them and store just a few higher valued ones.

It also means that you can generate large RPOWs in a more systematic way than simply trying to find a really large POW hashcash collision. You can create smaller collisions, exchange them for RPOWs, and combine them. Suppose you wanted to create, say, a 36 bit RPOW and on your machine that would take a day of compute time. Instead, you could create 30 bit RPOWs, each one taking only about half an hour on average, and then combine 64 (2 to the 6th power) of those to create your 36 bit RPOW. It's the same amount of compute time on average, but by splitting it up into smaller pieces you decrease the randomness and make the time to create a certain size RPOW more predictable.