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So I have posted the whitepaper on my upcoming cryptocurrency Nebula. Nebula will be distinct from all other cryptocurrencies since the POW problem for Nebula will incentivize the future development of the reversible computer (which has not been invented yet). You can find the whitepaper on the POW problem for Nebula at https://boolesrings.org/jvanname/2017/07/22/nebula-the-cryptocurrency-that-will-produce-the-reversible-computer/ (https://boolesrings.org/jvanname/2017/07/22/nebula-the-cryptocurrency-that-will-produce-the-reversible-computer/) and you can find previous discussion on how cryptocurrency POW problems will incentivize reversible computation at https://bitcointalk.org/index.php?topic=1985289.msg20247850#msg20247850 (https://bitcointalk.org/index.php?topic=1985289.msg20247850#msg20247850).

So Landauer's principle states that every time a bit of information is erased, ln(2)*k*T energy is used where T is the temperature and k is Boltzmann constant. Landauer's principle amounts to 2.8*10^(-21) J per bit erasure at room temperature. The efficiency of conventional computation is limited by Landauer's principle, but there is no such limit of the efficiency of reversible computation. Reversible computation however has the downside that it usually takes more steps to perform a certain calculation reversibly than it takes to perform the same calculation irreversibly. Therefore, since reversible computation requires some computational overhead, computing machinery manufacturers currently do not have an incentive to research and develop new reversible devices since any gains in efficiency will be dwarfed by the increase in the number of steps required to perform such a calculation.

Nebula will be the first cryptocurrency to incorporate a kind of POW problem which I call an RCO-POW (reversible computation optimized) problem. An RCO-POW problem is a POW problem which can be solved using a reversible computing device just as easily as it can be solved using a conventional computation device. Since RCO-POW problems can be solved using reversible computers in just as many steps as they can be solved using conventional computers, it is advantageous for one to develop energy efficient reversible computing devices to solve these RCO-POW problems. After computational device manufacturers produce devices to solve RCO-POW problems, they will have the knowledge and infrastructure to produce reversible computers for many other purposes and possibly even quantum computers.

The RCO-POW for Nebula, which we shall call R5, consists of five different algorithms. Since R5 relies on several different algorithms, it will be difficult for a single entity to launch a 51% attack against Nebula. Furthermore, since R5 has multiple algorithms to choose from, a reversible device manufacturer can choose the problem which the device will be made to solve. RCO-POW problems are not ASIC resistant since reversible computing devices can be thought of as certain kinds of ASICs and because the same qualities that make an algorithm easy to compute with a reversible device also make it easy to compute using an ASIC. Therefore R5 will be minable by CPUs/GPUs at first but R5 mining will soon be dominated by ASICs.

The problem of wasted energy and wasted resources in POW mining is one of the biggest problems with cryptocurrencies today. I hope that the cryptocurrency community will consider Nebula to be a satisfactory solution to this problem. I hope that either the cryptocurrency community would flock to Nebula or incorporate an RCO-POW into some other cryptocurrency with a high market cap.

-Joseph Van Name Ph.D.
https://boolesrings.org/jvanname (https://boolesrings.org/jvanname)

Good luck! I'm definitely interested in this project.

i'm interested. Though to some extent hasn't POS already solved the energy wastage of POW?

Fatoshi and  bathrobehero. Thanks. I appreciate your interest.

I do not know enough about POS to judge its security, merits, or whether it can completely replace POW as a method of securing the cryptocurrency. However, POW better solves the problem of fairly initially distributing newly minted coins. I do not see POW going away any time soon even for established currencies since cryptocurrencies may want to mint new coins in order to replace lost or destroyed coins and because some altcoins may want steady inflation. A useful POW like an RCO-POW will also give the cryptocurrency a perception of greater value to the cryptocurrency since people will see that the work used to produce the newly minted coins were used for some good purpose.  This positive perception of value is harder to achieve using a POS system. I am simply looking to implement another solution to the wasted energy problem for cryptocurrency POW problems.

R5 - i like that name. i'll give my hash power for it.
Waiting for more info about the project

Hello crypto enthusiasts.

I will take a look in to the whitepaper and if I like, I sure will follow the project closley. Good luck and keep up working on your nebula project.

This looks quite interesting even if I dont think that this sole project will incentize industries to make such computers.

I like the idea of decentraland, it breaks the limits of centralization.
I want to support this project by promoting on social media pages so when will be the lauch of bounty campaigns? I'll keep an eye on this program because I know this would be successful.

This looks quite interesting even if I dont think that this sole project will incentize industries to make such computers.

Although I'm not sure about the concept of this project, but it will be an interesting project, hopefully it can run well and good luck for you

This sounds like a promising project with an important concept. I'll be keeping my eye on it over the next few days!

any bounty dev?

;) The five kinds of algorithms, I like, continue to pay attention    ;)

Very interesting topic. As most people on this forum I also did not know anything about reverse computaion, I'm going to learn about it. BTC mining consumes a lot of electricity and produces a lot of heat, there are just a few coins that are doing something usefull for the science - folding coin and gridcoin research (maybe more?). I'd like to see more projects that will be usefull for science.

interesting project , maybe there is a roadmap and whitepaper to make this project more more interesting

+watchlist , looks promising.

Nebula? Sounds like the name of a planet in a science fiction movie.interesting and waiting for more info about this

it is interesting even just for the sake of environmental argument (and believe me when I enter my mining facilities I do understand the irony in your conclusion section -- unfortunately). Of course I see a big disadvantage in RCO-POW being non ASIC resistant. But wouldn't that RCO-ASIC be in fact a Reverse Computer device by itself? Also how the RCO-POW will perform on non optimized CPU/GPU hardware in terms of hit/energy? Sorry if my questions are obvious I am not a scientist may be missed it in your paper.

I got you man. Hope this great project.

Very interesting white paper, R5 for 5 algos, I like this already, definitely keeping my eye on this. Good luck and everything of the best.

Hi Joseph, I'm watching your project with great interest. Thank you.

All would want the success of this project, I also hope this project will be successful ..

Any news yet ?

Dev last activity 29 07 2017. looks like project closed even before its opened.

Mhmmm or hard at work :)

Hi!
I'm very interested about this project. What's the status? How's everything going?

Hope this succeeds.

Hello everyone,

In addition to cryptocurrencies, I have been simultaneous working on another mathematical research project on Laver tables http://boolesrings.org/jvanname/2017/08/29/generalizations-of-laver-tables-is-posted-140-pages/ (http://boolesrings.org/jvanname/2017/08/29/generalizations-of-laver-tables-is-posted-140-pages/) where among other things I have developed the mathematical structures behind new post-quantum public key cryptosystems from the highest levels of infinity (this project is the only real-world application of these very large levels of infinity). My project on Laver tables is finished after two years of work, so I can now devote all my extra time that I have to Nebula. I apologize for the delay.

-Joseph Van Name Ph.D.
http://boolesrings.org/jvanname

Fantastic news! Thanks for the update!

Very good news. Haven't heard about Laver tables term before. Will try to investigate more and understand your research paper, since it's seems quite interesting concept.

Good luck with Nebula!

Joseph Van Name, take your time to research, we'll be waiting. It's very interesting project, watching this thread!

I am now testing the security of the problem R5 and my observations will be outlined in a paper. The security of R5 is an issue since it typically takes at least a couple of years for major organizations such as the NIST to analyze the security of a symmetric cryptosystem and much longer for public key cryptosystems. I do not have any of these luxuries and since R5 uses 5 problems, I can only give a basic security analysis of each of these problems and show the security report to a few fellow cryptographers to gauge their approval. Nevertheless, at this point, there are two possible things I can do to ensure the security of R5. I can either make sure that the POW problems in R5 have enough rounds in order to ensure that the cryptosystem remains secure beyond any reasonable doubt for the foreseeable future (Solution 1) OR I can put a mechanism into the cryptocurrency that will automatically increase the number of rounds in the POW problem.

Let me list a few pros of each of the solutions.

Pros for Solution 1:

-A large number of rounds for R5 will increase the reversible computer friendliness since a greater portion of the processing power will be spent on computing reversible functions rather than setting up the input or reading the output for every "hash."

-This solution is simpler than Solution 2. Therefore, with this solution Nebula will be launched more quickly and solution 2 may present its own security weaknesses.

Pros for Solution 2:

-The built in mechanism for testing the security of R5 can be thought of as a useful POW problem which will be in the spirit of Nebula and which will advance cryptography.

-Cryptographers will likely have a greater peace of mind with this solution since any security issue with R5 will be resolved automatically by adding more rounds.

-It may be easier to construct reversible machines that solve R5 if there are fewer rounds (especially for problems 3-5).

I wonder if there could be security issues which aren't addressed by any number of additional rounds.

For option 2, how would the number of rounds be increased?  How can an algorithm detect the security is at risk?

I have just posted the security report on http://boolesrings.org/jvanname/2017/11/09/security-report-for-r5-the-pow-problem-for-nebula. I now have the functions for R5 ready and coded in c++, but I need to get the thing launched (at this point, I am pretty sure that I will need some help from professional cryptocurrency developer in exchange for unobfuscated code access that will allow for quicker mining for problems 1-3, and a short period of pre-mining).

jukKas. I appreciate your interest in the Laver tables. They are truly unique and profound mathematical structures that arise from the highest levels of infinity (and they can be understood and calculated by just about anyone too).

I doubt that there will be any security issue for R5 that cannot be remedied by simply increasing the number of rounds since R5 is a symmetric cryptosystem rather than a public key cryptosystem (symmetric cryptography gains its security through the number of rounds while public key cryptography is another story since the Merkle-Hellman knapsack cryptosystem has been broken overnight and it cannot be improved by increasing the  number of rounds.). Each problem in R5 employs many Toffoli gates and Fredkin gates and both the Toffoli gates and the Fredkin gates are universal for reversible computation. Furthermore, any permutation of {0,1}^n can be computed by Toffoli gates with at most 3 ancilla bits.

I have ultimately decided that having a mechanism in R5 that automatically increases the number of rounds in case there is any insecurity of R5 is unnecessary since the security requirements for R5 do not seem too demanding. For R5, recall that the POW is simply to find a 256 bit hash k along with 68 bit string x so that f_i(k#x)<1/d where d is the difficulty. A miner will have little control over k since a miner can only try many different hashes until he finds a good one. A miner can only control the 68 bit string x, and it will be difficult for an attacker to break R5 when he only has control over the 68 bit string x. By the nature of R5, the attacker does not have much room to work with. Therefore, since attackers do not have much room to work with, the functions f_1,...,f_5 only need to be OK randomizing functions in order for R5 to be secure. Most of the work has already been done for me since we already have secure hash functions. In essence, for all i, a one bit change to the input for f_i will result in a completely different output even after going through 1/4 of all rounds.

For option 2, the mechanism to increase the number of rounds will have an additional POW problem which for our purposes we shall call weak R5. Weak R5 will be like strong R5 except that weak R5 will only employ 1/3 as many rounds as strong R5, and weak R5 may employ other features that make it less secure. If weak Problem i is solved too often in proportion to strong Problem i, then the number of rounds in both weak and strong Problem i will automatically increase. Therefore, strong R5 will remain secure since an attacker cannot break strong R5 unless someone is able to break weak R5.

P.S. Since I have posted the original whitepaper on Nebula, I have changed each of the problems R5 slightly in order to increase the level of security.

It is an interesting project.
I look forward to next information.

Hello Dev, quite an interesting project you have got here. Nebula isn't connected to Nebulas (NAS) in any way right?

Nebulas Token (NAS) is completely unrelated.

jukKas. I am actually using an image that arises from the Laver tables as the logo for Nebula.

I remember this posted a while ago. I'm super interested in Nebula to be released

Hmm. Interesting.

Princa. dvyanc.

This post is not related to Nebule Cash in any way or any other cryptocurrency or token. The purpose of my upcoming coin is to use a POW that will incentivize the development of the reversible computer. I am trying to solve the problem of "useless" POW problems by introducing a coin with a useful POW problem. No other cryptocurrency is incentivizing reversible computation (I currently resist the urge to change the name of this coin at this point because I am pretty sure that the scamcoin Nebule Cash will probably fail pretty soon. I apologize for any confusion, but the confusion will go away once those scamcoins fall by the wayside).

People will take you seriously when you stop posting like that. I already have you ignored because goddamn is that fucking annoying.

This coin looks incredible though, can't wait to see how it all works.

That sounds freaking Interesting, cant wait so see more and the whole Project, nice Job.

"Slimeland"-Incentivizing an energy efficient implementation of the CNOT gate-A complement to Nebula.

The purpose of Nebula is the make it as easy as possible for the corporations to develop reversible computers by giving them a return on their investment on new technologies as soon as possible. I have an idea for another kind of POW problem that can together with Nebula achieve this goal much better than Nebula can alone. For this post, let me temporarily call this new POW and its corresponding cryptocurrency Slimeland (I promise to come up with a more professional sounding name later on). To describe this kind of POW, I have to now talk some computer science.

Computer science background: Recall that the CNOT gate is the function from Z_{2}^{2} to Z_{2}^{2} defined by (x,y)->(x,x+y mod 2). The CNOT gate is a reversible gate. It should be easier to construct a reversible device solely out of CNOT gates that it would be to construct any other kind of reversible device for several reasons:

1. The CNOT gate only acts on 2 bits rather than 3 like the Toffoli and Fredkin gates do.

2. The CNOT gate is not universal for reversible computation. In fact, no reversible gate on 2 bits is universal for reversible computation.

3. The CNOT gate is linear.

The purpose of Slimeland is to incentivize the construction of a reversible computer consisting of as many CNOT gates as possible in the same way the Nebula incentivizes a more general purpose reversible computer.

Problem description: Suppose that f is a suitable function composed of CNOT gates. Then the POW Slimeland is to find an N bit hash k along with an M bit string x such that f(k||x)<2^(m+n)/D where D is the difficulty of the problem. Now, the way that I have stated Slimeland should raise some red flags to anyone who is familiar with any linear algebra or cryptography. Slimeland as I have stated is trivially breakable since one can solve for x in
f(k||x)<2^(m+n)/D simply by doing a little bit of linear algebra. Therefore, to remedy this problem, the function f shall be composed mainly of CNOT gates with a few non-linear gates such as Toffoli gates or Fredkin gates to give Slimeland the required non-linearity. For example, the function f could be a composition A_{n+1}L_{n}...A_{1}L_{1}A_{0} where each A_{i} is a non-singular linear transformation of {0,1}^{m+n} and where each L_i is a very thin layer of non-linear gates.

Security issues: As stated Slimeland should still raise some major security concerns since the function f is still nearly linear. Of course, one can make Slimeland secure simply by making f composed of an extreme number of gates (for example, if f contains 1,000,000 gates and 10,000 of these gates are non-linear and the rest are CNOT gates, then Slimeland should be secure). However, this solution brings with itself a few of its own problems. First of all, if f is composed of too many gates, then the security of Slimeland will be reduced since fewer entities will be willing to validate the Slimeland POW. Second of all, as the number of gates in Slimeland increases, there is a greater chance of an experimental reversible device making an error in calculation. We want Slimeland to make it as easy as possible for corporations to construct reversible computing devices, so we therefore want to not burden these corporations with extra error correction and accuracy issues. I do not have any intuition about the number of non-linear gates that we need to ensure the security of Slimeland, and I do not know if this minimal non-linearity issue has been studied in cryptography elsewhere.

Another possible security issue of Slimeland stems from the fact that various circuits may be used to calculate the function f. Suppose that Alice has a circuit A that computes the function has a circuit B that computes f, and suppose that B has twice as many gates as A. Then since A has much fewer gates than B, Alice will have an advantage over Bob (we shall call this problem with f the "possible optimizability" of the function f). I do not have much of an intuition about whether Slimeland is possibly optimizable but I do not want to rule out the possibility just yet.

A proposed solution to these security issues:

So the solution which I propose to these issues shall be called the "internal testing technique." The internal testing technique uses two versions of the POW Slimeland which we shall call Secure Slimeland and Testing Slimeland. Slimeland will therefore have two different POW problems. Secure Slimeland is the POW which is used to incentivize the development of the reversible computer while Testing Slimeland is a POW that tests the cryptographic security of Secure Slimeland without compromising the security of Slimeland.

Suppose that N is a natural number (N will change over time). Then Secure Slimeland will require the function f to run for 3N rounds while Testing Slimeland will only require the function f to run for N rounds. If Slimeland becomes to insecure N will automatically increment by 1 in order to ensure that Secure Slimeland remains secure.

Slimeland will only allow Testing Slimeland to be solved for about 1 percent of all blocks. Furthermore, if Testing Slimeland is solved for Block R and for Block S for distinct R,S then we will require that |R-S|>25. This requirement will ensure that an attacker is not able to use Testing Slimeland to launch an attack against Slimeland. If the difficulty of Testing Slimeland grows too high because an entity has an algorithm that breaks Testing Slimeland, then N will increment by 1.

Testing Slimeland will also be weakened in the sense that a miner will have the option of slightly modifying the circuit that computes the N round version of the function f, and therefore Testing Slimeland will be easier to break than Secure Slimeland even if both problems only had N rounds.

Of course, since Testing Slimeland must be solved for only 1% of all problems, the outputs for the hashes for Testing Slimeland must be 100,000 times lower than they are required to be for Secure Slimeland (otherwise the Testing Slimeland problems will be solved all the time).

As I have mentioned before, the internal testing technique will in itself be a useful POW problem since testing the security of a new cryptosystem is in itself a useful problem (and hence the internal testing technique will help Slimeland obtain a strong perception of value).

The internal testing technique guarantees that Secure Slimeland will remain cryptographically secure, but the internal testing technique does not provide any protection against the possible optimization of the circuit for Secure Slimeland. In order to protect Slimeland against any possible optimization for the circuits that compute Secure Slimeland, miners are allowed to submit optimized circuits the Slimeland blockchain in exchange for coins (the miners will first submit the hash of the circuit+their public key and after the hash has been conformed, the miner may post the circuit). The Slimeland miners will then be informed about the best circuits to use to compute the POW, and Slimeland may use this information to automatically improve its POW.

The prognosis of Slimeland: With these security issues of Slimeland and due to the intricacies present with the solutions to these security issues, it will probably take much more resources to research and develop Slimeland than it would to research and develop other cryptocurrency ideas. I will therefore only devote my time to Slimeland once Nebula is up and running. Let me know if you see any insecurities or if you have any other concerns with Slimeland. Slimeland and Nebula will both incentivize reversible computation in different ways, and they are both necessary for the transition from conventional computational devices to reversible computational devices.

-Joseph Van Name Ph.D.
11/16/2017

After computational device manufacturers produce devices to solve RCO-POW problems, they will have the knowledge and infrastructure to produce reversible computers for many other purposes and possibly even quantum computers.

Warning: I has discovered major weaknesses in the following POW problem. Those weaknesses seem non-fatal. I am now working to patch those weaknesses.

-Joseph Van Name Ph.D.


A solution to the Erasure with Faulty Computation Problem

So recall that the objective in the Problem R5 is to find a 256 bit hash k along with a 68 bit string x such that f(k||x)<C where C is some constnat inversely proportion to the difficulty of the POW. One issue with this kind of POW problem is that even though the function f can be computed reversible as well as it can be computed irreversibly, one still has to erase 256 bits in the output f(k||x) after every solution attempt in order to overwrite the first 256 bits in f(k||x) with k so that one can begin a new solution attempt. Therefore R5 does not incentivize the reversible computer, but instead R5 incentivizes a nearly reversible computer or a reversible computer connected to a device that erases bits after every solution attempt. The problem that one has to erase a few bytes of information after ever solution attempt shall be called the Erasure Problem. I now have a solution to the Erasure Problem. In fact, I have a solution to a more difficult problem which I shall call the Erasure with Faulty Computation Problem (EFC Problem). The EFC Problem is to develop a cryptocurrency POW problem that can be solved by a device that does not hav to erase any data after ever solution attempt which is fault tolerant in the following sense: suppose that computing device A has made computational errors in Solution attempt number 5 but these errors do not change the value of the hash k which is used for the POW problem. Then computing device A can still correctly perform Solution attempt number n for n>5 without having to erase any data in order to correct the error that has been made in Solution attempt number 5.

Problem B: Suppose that f_k,T_k are both functions mapping {0,1}^{n} to {0,1}^n that depend on a 256 bit hash k and which can be easily computed using a reversible device. Then the objective of Problem B is to find a string x so that the final bit in the string f_k(x) differs from the final bit in the string f_k(T_k(x)).

Reversible Algorithm for Problem B: Suppose that the state of the device is (y,0) at the beginning of attempt n at solving Problem B.

Step 1: Transition from state (y,0) to state (y,y[last]) where y[last] denotes the last bit in the string y. This step requires one to simply apply a CNOT gate to the state.

Step 2: Transition from state (y,y[last]) to state (f(T(f^(-1)(y))),y[last]).

Step 3: Transition from state (f(T(f^(-1)(y))),y[last]) to state (f(T(f^(-1)(y))),y[last] XOR f(T(f^(-1)(y)))[last]). This step also requires simply a CNOT gate.

Step 4: Suppose that the device is in state (z,i). If z==1, then halt the device since a solution to Problem B has been obtained. Otherwise, continue on to Attempt n+1.

Partially Irreversible Algorithm for Problem B: First compute x,T_k(x),...,T^(n)_k(x) by applying the function T_k to the input x n-different times. Compute f(x),f(T_k(x)),f(T^(2)_k(x)),...,f(T^(n)_k(x)). If f(T^(i)_k(x))[last] is different from f(T^(i+1)_k(x))[last], then we have found our solution to Problem B. Notice how this algorithm is still quite reversible since the functions f,T are reversible.

Suppose that the function f takes j gates to compute while the function T takes k gates to compute. Then the reversible algorithm takes about 2j+k gates per solution attempt while the partially irreversible algorithm takes j+k gates to attempt. Therefore the ratio in the number of gates per solution attempt in irreversible algorithm to the number of gates per solution attempt in the reversible algortihm is (j+k)/(2j+k)=1-1/(2+k/j) and this ratio approaches 1 as k/j approaches infinity. Therefore while the partially irreversible algorithm may be more efficient than the reversible algorithm, by pumping up the value k, one can ensure that the reversible algorithm and the partially irreversible algorithm are almost as efficient as each other; in the case that one pumps the value of k up high, a miner will want to use a completely reversible device as opposed to a partially irreversible device.

The space of all feasible RCO-POW problems is much larger than I had originally imagined since I originally did not know how to make an RCO-POW problem which can be run on a completely reversible faulty computer.

-Joseph Van Name Ph.D.

I am glad that you are still updating this thread jvanname.

Am really excited about this project as it could be truly revolutional.
In your last post you said that the project needs more work than you anticipated. Do you have a timeline or roadmap or sth like that yet?

I would love to follow your work and journey with this project. Is there something else I can follow you except this thread and your blog/homepage http://boolesrings.org/jvanname?

Would be very happy to hear from you.
Keep up the good work!
You will definitely have my hashpower once it is needed.

All that math

*drools*

riderinred. Thanks for the encouragement. At this point, I have C++ programs for the POW problem which I intend to use, but since I am not thoroughly familiar with the source code for Bitcoin and other cryptocurrencies, I will need a cryptocurrency programmer to help me implement the code that I have written and launch the cryptocurrency (I currently only program for mathematical applications). If anyone knows a high quality programmer familiar with the source code of Bitcoin who is willing to help, let me know. Unfortunately, Nebula is currently a completely unfunded project, so my only form of payment is to simply let the programmer privately mine Nebula for a short period of time (which could be a very high level of payment if Nebula achieves a high market cap) and to have access to unobfuscated source code for R5 (the obfuscated source code runs slower so the programmer will have an advantage until someone finally deobfuscates the course code). I am currently working on this project alone, so that is why the development is slow. I apologize for any inconvenience that this delay has caused.

I am now seeking input from tech corporations that make computing devices and researchers about R5 to see their opinions about R5 and how cryptocurrencies could help develop reversible computers (I will even change the RCO-POW R5 if they offer a large sum of money as long as the new POW still incentivizes the construction of the reversible computer just as well).

In the mean time, I am investigating different RCO-POW problems especially those which can be solved by a reversible computer that does not delete information after every solution attempt and by a possibly faulty reversible computer (these sorts of RCO-POW problems appear to be much harder to construct and to verify the security of). I am also interested in RCO-POW problems where almost all of the gates are CNOT gates. The class of RCO-POW problems is much more diverse than I had originally imagined.

Right now, I am mostly just posting on http://boolesrings.org/jvanname (http://boolesrings.org/jvanname).

How many coins do you need for POS-mining?
And where it is better to buy them?

There is no coin yet and so no mining, if I understood jvanname correctly.

Currently it is about setting up/determining the RCO-POW problem to be used and to get more people involved.
Devs to actually write the code and researchers to get their oppinion so we could convince a chip manufacturer to actually create a RCO-Chip.
Am sorry if I messed something up, I only understand the basic principles of this topic.

But the coin is already worth: https://coinmarketcap.com/currencies/neblio/
 :o

That coin is not about reversible computing and it is called "Neblio" not Nebula.
So I don't think this is the project jvanname is writing about here.

rideinred.

I can make the RCO-POW problems myself (I already have made and analyzed these problems, but I am now considering modifying them again), though peer review is always helpful.

I just brought up the idea that a corporation will influence the final version of the RCO-POW problem in the case that such a corporation thinks that it will be easier for them to design a will computer for that RCO-POW problem (I want to make it as easy as possible for those corporations to design the reversible computer). For example, a corporation may think it is easier to construct a circuit using lesser known reversible gates such as the DKG or the Peres gate or they may want the RCO-POW problem to be based upon a 1 dimensional cellular automaton. Of course, they will have to pay in order for their recommendations to be implemented or launch their own corporate altcoin (which people will be skeptical about using) since I am not going to let a specific corporation have an advantage over others unless they pay.

Anyways, since the version of R5 which I have already posted requires one to delete 256 bits after every solution attempt, I am now considering drastically modifying the problems so that a much smaller amount of information is deleted after every solution attempt and so that these new problems have other superior characteristics. I will post my outline of how these new problems will work shortly.

As for implementing the RCO-POW that I have developed, I will write the functions in C++, but it will be better for a cryptocurrency developer to implement the functions which I have written.

This is definitely on my watch list

So here is an outline of the new kinds of POW problems which I am considering. Don't worry. The new POW problems will be modeled after the old R5 problems. So recall that with the old POW R5, we must find a 256 bit hash k along with a 64 bit string x such that f(k||x)<C where C is an adjustable number and where f is designed to be computed reversibly. As I have stated before, one issue with R5 is that after every solution attempt, one must erase 256 bits of output since one must set up a new input k||y for the next solution attempt. Since reversible components may be very difficult to hook up to irreversible components, we want to minimize the amount of data erased. Of course, it is probably too much to ask for a reversible device which solves the POW in just as many steps as an irreversible device but which does not erase any information whatsoever, but we can do better than erasing 256 bits after every solution attempt. Also, the input for the function f is a 324 bit string and if one can shrink the size of the inputs for the function f, then it would be much easier to construct a reversible device for solving the POW problem. Let me now give the details on a new POW that will remedy these issues.

New R5 problem description:

Input: Suppose that for each 256 bit hash k, f is a function from {0,1}^64 to {0,1}^64 designed to be computed using a reversible circuit. Suppose that H is a cryptographic hash function. Suppose that C and D are adjustable numbers.

Problem: Find a 256 bit hash k along with a 64 bit string x such that f_k(x) XOR f(x)<C and H(k||x||f_k(x))<D.

Let me now outline a nearly reversible algorithm for solving New R5. Let E be a natural number with 0<E<65. The number E will specify how many bits shall be deleted after every solution attempt. Of course, if E is smaller, then fewer bits will be deleted. However, if E is smaller, then one has to read and evaluate more false solution attempts. Now let v be a non-zero 64 bit string.

The state of the machine shall be a pair (x,y,z) where x is a 64 bit string and y,z are E bit strings.

Suppose that after attempt N at solving the POW problem, the machine is in state (x,y,0) where y is the first E bits of the string x.

Step 1: Move from state (x,y,0) to state (f_k(x),z,z XOR y) where z is the first E bits of the string f_k(x). This state is completely reversible.
 
Step 2: If z XOR y=0, then the machine halts and one reads the output f_k(x). In this case, one would test whether f_k(x) XOR f(x)<C and H(k||x||f_k(x))<D or not. If
f_k(x) XOR f(x)<C and H(k||x||f_k(x))<D, then k along with x is the desired solution to the POW problem. Otherwise, move to state (f_k(x) XOR v,z,0) and then move to attempt N at solving the POW problem.

Step 3: If z XOR y>0, then move from state (f_k(x),z,z XOR y) to state (f_k(x) XOR v,z,0). This state is irreversible since the E bit string z XOR y. Now move to attempt N+1 at solving the POW problem.

There does not appear to be any security issues with this kind of sort of POW problem.

Remarks:

-The function f_k should not be of the form g^n for easily computable g since if f_k=g^n, then the optimal algorithm for solving the POW problem is not the algorithm that I have stated above and the optimal algorithm will delete E bits of information every time g is computed rather than deleting E bits of information every time f_k is computed.

-Since the input for the function f_k is 64 bits, the reversible device for solving the POW is probably much simpler than it would be for solving Old R5. Furthermore, the function f_k can probably be secure with fewer rounds than it can be for Old R5.

-The optimal algorithm is solving this POW problem is reversible in the sense that in Step 1, one can instead move from state (x,y,0) to state (f_k^(-1)(x),z,z XOR y) where z is the first E bits of the string f_k^(-1)(x).

-Since f_k has a 64 bit input, it is probably feasible to make f_k so that it computes a 1D cellular automaton or a circuit consisting mostly of CNOT gates without compromising the security of efficiency of the POW problem.

-With Old R5, I included a few layers of CNOT gates which I called sigma, mu, and tau in order to increase security and so that all of the logic gates are actually necessary for solving the Old R5 problems. With these new problems, the awkward layers sigma,mu, and tau are not necessary. Therefore, these new problems can be considered more pure than the Old R5 problems.

Hope everything well guys.

What's the news about Nebula?

There are many projects coming...Hope we can do the best!

Am also very excited about this project.
There are more and more ideas about how Blockchain can help in the transition from the now dominant idea of just putting more and more transistors onto one chip to another way of doing it.
Am so excited, Moores Law is coming to an end and we are right here, living in interesting times.

Yeah, that's correct.

I am very glad that we meet the blockchain here.

Hope this next-generation project get the best!

It is a really novel idea and can change things.

Hi there i stumbled here while searching for $nas,

This is a very interesting idea, I wonder whether such reversible computer / crypto will enable an cryptographic algorithm based on cellular automata to create a protocol/system that can self govern itself?

News: There are already cryptocurrencies named "Nebulas" (MARKET-CAP $346,031,635) and "Neblio" (MARKET-CAP $182,594,614). Furthermore, the name "Nebula" is far to generic. I therefore plan on changing the name of the cryptocurrency. The name of the individual coins shall be called CIRCs which stands for Certificate of Innovation in Reversible Computation. I still need to finalize the name of the entire cryptocurrency though instead of the individual coins (I have an idea in mind).

I am looking forward to it.

As an update, I am still working on the security of the POW problem.  A lot of security issues arise because I want to design a POW that incentivizes the construction of the reversible computer in the best possible way. For R5, I will use reversible linear cellular automata of dimensions 1 and 2. However,
I can list several security anomalies that arise from the use of linear cellular automata of dimension 1 including the following:

1. Suppose that f,g are involutions which are related to each other in some way. Then the composition fg is a permutation with cycles of an exceptionally low period. I so far have not been able to explain this phenomenon.

2. Cryptosystems require a large amount of non-linearity in order to thwart linear algebraic attacks. My POW problems however need to have as much linearity as possible since the CNOT gates (which are reversible and linear) will be much easier to construct than other reversible gates.

3. Reversible linear cellular automata over Z_2 of dimensions 1 or 2 over the torus of size 2^n x 2^n or circle of length 2^n have exceptionally low periods.

4. Reversible linear cellular automata over Z_2 of dimensions 1 or 2 have a Sierpinski triangle structure which indicates that these functions are not disorderly enough for cryptographic use.

Of course, I can solve these issues simply by basing my POW problems on something other than reversible linear cellular automata of dimension 1 or 2, but I do not want to do that because these reversible linear cellular automata are literally the simplest reversible objects that I can use, and I need my POW problem to be simple enough so that it will be as easy as possible for reversible computing manufacturers to construct machinery to solve these POW problems.

I hope you are doing fine and keep making progress.
Just wanted to drop by and give you some positive vibes :)
Would love to hear about any new stuff you got.

Hi, Jvanname

How is this project going? I still think that this project will be a very promising one in the future.

The market also needs something new and interesting to attract new comers. Hahaha

Hope everything goes well!

EDIT(Nov 21):  
Here is an official Circcash announcement:

https://bitcointalk.org/index.php?topic=5292018.0;all

---

You can find relevant project updates here:
https://github.com/jvanname/circcash  

I have started the unofficial ANN thread:  

[ANN] Circcash [unofficial :: unmoderated]
https://bitcointalk.org/index.php?topic=5290467.0;all

Now is probably a good time to list some weaknesses of R5 and some of my early ideas of reversible mining algorithms (this in part explains why I did not release any cryptocurrency earlier).

Multiple mining algorithms-Multiple mining algorithms have been largely untested in the cryptocurrency community. From my experience, the Bitcoin community is quite conservative and they would not accept multiple mining algorithms running in parallel each with their own difficulties. The Bitcoin community does not like new ideas that could potentially bring a security risk like having multiple mining algorithms. Furthermore, having multiple algorithms means that each of those algorithms has to be vetted for cryptographic security. Even though cryptocurrency mining algorithms could easily be made secure by adding more rounds (I did this) and there is not much history of broken mining algorithms, this is not a risk that people should be willing to take.

Iterating compositions of involutions-If f,g:X->X are involutions, then you do not want to use an iterate of fg or anything like an iterate of fg in a cryptosystem since such a component presents a security weakness. I originally wanted to use this construction because of its simplicity, but this sort of construction is not very secure (this is why you do not see it in cryptosystems such as AES and SHA-256 despite its simplicity).

Lack of solution lottery technique-Without the solution lottery technique, the reversible mining algorithms look much more like reversible cryptographic hash functions. This presents a security issue. First of all, reversible cryptographic hash functions are a better at incentivizing the development of reversible computation than something like SHA-256d, but they are not optimized for this task. Second of all, the solution lottery technique means that the new portion of the mining algorithm does not have to have much cryptographic security. For example, the reversible portion of Hashspin (Circcash's mining algorithm) only requires 16 bits of security while SHA-256d mining requires about 128 bits of cryptographic security. For this reason, using the solution lottery technique, one can use the security buffer to focus on designing the algorithm to accelerate the development of reversible computing hardware.

I guess the moral of this story is that mathematicians should not trust themselves with more than 16 bits of security.