Nebula-The cryptocurrency that will produce the reversible computer

So I have just posted the paper outlining the proof-of-work problem for my upcoming cryptocurrency Nebula. Here is the link for the paper. I hope to launch Nebula as soon as possible.

The idea behind Nebula is to use a reversible computing optimized proof-of-work (RCO-POW) problem instead of an ordinary proof-of-work problem (if you do not know what I am talking about, I suggest for you to read the original paper on Bitcoin). An RCO-POW problem is like an ordinary proof-of-work problem except for the fact that the RCO-POW problem can be solved by a reversible computing device just as easily as it can be solved using a conventional computing device.

It is very rare for a problem to be solvable by a reversible computing device using just as many steps as it is solvable using a conventional computing device. In general, it takes more steps to solve a problem using a reversible computation than it takes to solve the same problem using conventional computation. Therefore, since reversible computation has this computational overhead and since reversible computers currently do not exist, chip manufacturers do not have much of an incentive to manufacture reversible computing devices. However, since RCO-POW problems are just as easily solved using nearly reversible computational devices, chip manufacturers will be motivated to produce energy efficient reversible devices to solve these RCO-POW problems. After chip manufacturers know how to produce reversible devices that can solve these RCO-POW problems better than conventional devices, these manufacturers can use their knowledge and technology to start producing reversible devices for other purposes. Since reversible computation is theoretically much more efficient than conventional computation, these reversible computing devices will eventually perform much better than conventional computing devices. Hopefully these reversible computational devices will also eventually spur the development of quantum computers (one can think of reversible computation as simply quantum computation where the bits are not in a superposition of each other).

Nebula shall use the RCO-POW which I shall call R5. R5 is a POW that consists of five different algorithms which range from computing reversible cellular automata to computing random reversible circuits. I use the multi-algorithm approach in order to ensure decentralization and to incentivize the production of several different kinds of reversible devices instead of just one kind of device.

The only thing that will be different between Nebula and one of the existing cryptocurrencies is the POW problem since I did not want to add features which have not been tested out on existing cryptocurrencies already.

Cryptographic applications of very large cardinals-BLAST 2017

In August, I will be giving a contributed talk at the 2017 BLAST conference.

I am going to give a talk about the applications of functional endomorphic Laver tables to public key cryptography. In essence, the non-abelian group based cryptosystems extend to self-distributive algebra based cryptosystems, and the functional endomorphic Laver tables are, as far as I can tell, a good platform for these cryptosystems.

ABSTRACT: We shall use the rank-into-rank cardinals to construct algebras which may be used as platforms for public key cryptosystems.

The well-known cryptosystems in group based cryptography generalize to self-distributive algebra based cryptosystems. In 2013, Kalka and Teicher have generalized the group based Anshel-Anshel Goldfeld key exchange to a self-distributive algebra based key exchange. Furthermore, the semigroup based Ko-Lee key exchange extends in a trivial manner to a self-distributive algebra based key exchange. In 2006, Patrick Dehornoy has established that self-distributive algebras may be used to establish authentication systems.

The classical Laver tables are the unique algebras $A_{n}=(\{1,…,2^{n}-1,2^{n}\},*_{n})$ such that $x*_{n}(y*_{n}z)=(x*_{n}y)*_{n}(x*_{n}z)$ and $x*_{n}1=x+1\mod 2^{n}$ for all $x,y,z\in A_{n}$. The classical Laver tables are up-to-isomorphism the monogenerated subalgebras of the algebras of rank-into-rank embeddings modulo some ordinal. The classical Laver tables (and similar structures) may be used to recursively construct functional endomorphic Laver tables which are self-distributive algebras of an arbitrary arity. These functional endomorphic Laver tables appear to be secure platforms for self-distributive algebra based cryptosystems.

The functional endomorphic Laver table based cryptosystems should be resistant to attacks from adversaries who have access to quantum computers. The functional endomorphic Laver table based cryptosystems will be the first real-world application of large cardinals!