M2 Technology Instance
Conceptual Whitepaper
Conceptual Whitepaper The Abacus Coin is an M2-based 2nd-generation Cryptocurrency.1
Glendon Klassen
Oliver Hafner
1 Please note that this technology is constantly under development and the details of the framework and or instance coins
and definitions are subject to change at any time, and this is by no means a final version.
Abstract
Crypto currencies are gaining traction as financial instruments traded as monetary instruments, the recent
issuing of bitcoin with an official ISO currency code XBT. This recognition validates the concept of a proof of
work based currency as a monetary system and paves the way for the next generation of Cryptocurrency with
proof of work based systems built using the M2 Framework allowing for work of scientific value to act as the
proof of work system for digital currencies. The purpose being to create a monetary system on whose value is
based on the inherent value of the scientific work being carried out by the proof of work system.
Keywords
Proof of Work Proof of Stake Cryptcurrency Hadamard Matrices
M2 Technology Instance
Conceptual Whitepaper
1. Background
M2 is a technology which allows for the distributed computing of specific mathematical and
scientific problems. It was designed to replace 1st-generation coins which use man-made
cryptographic algorithms to demonstrate proof-of-work. M2 uses the innate difficulty of scientific
and mathematical problems to do so.
2. Mechanism
Abacus Coin uses the search for large and unknown Hadamard Matrices as its proof of work.
Hadamard matrices are an n by n matrix where n is the order of the matrix. The matrix is comprised
entirely of ones and negative ones. Hadamard matrices have the property that the matrix times its
transform result in the identity matrix of order n times n. These are useful as they are the optimal
weighing matrices of size n. These can be used for signal filtering and a number of other scientific
purposes. They also draw a great deal of interest in the academic community. Abacus is a coin based
on the search for these matrices as its proof-of-work algorithm.
Hadamard Matrix
In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a
square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. In
geometric terms, this means that every two different rows in a Hadamard matrix represent two
perpendicular vectors, while in combinatorial terms, it means that every two different rows have
matching entries in exactly half of their columns and mismatched entries in the remaining columns.
It is a consequence of this definition that the corresponding properties hold for columns as well as
rows. The n-dimensional parallelotope spanned by the rows of an n×n Hadamard matrix has the
maximum possible n-dimensional volume among parallelotopes spanned by vectors whose entries
are bounded in absolute value by 1. Equivalently, a Hadamard matrix has maximal determinant
among matrices with entries of absolute value less than or equal to 1 and so, is an extremal solution
of Hadamard's maximal determinant problem.
Properties
Let H be a Hadamard matrix of order n. The transpose of H is closely related to its inverse. The
correct formula is:
M2 Technology Instance
Conceptual Whitepaper
where In is the n × n identity matrix and HT is the transpose of H. To see that this is true, notice that
the rows of H are all orthogonal vectors over the field of real numbers and each have length \sqrt n.
Dividing H through by this length gives an orthogonal matrix whose transpose is thus its inverse.
Multiplying by the length again gives the equality above. As a result,
where det(H) is the determinant of H.
Suppose that M is a complex matrix of order n, whose entries are bounded by |Mij| ≤1, for each i, j
between 1 and n. Then Hadamard's determinant bound states that
Equality in this bound is attained for a real matrix M if and only if M is a Hadamard matrix.
The order of a Hadamard matrix must be 1, 2, or a multiple of 4.
3. Value
Since Abacus is a member of the 2nd generation of cryptocurrencies, the work involved in the
blockchain is innately useful. This innate value allows Abacus to be valuable without the necessity
for rarity. SHA-256 algorithms find rare series of numbers that result in a special string at the end of
a cryptographic block. Though these are rare, they are not useful. This is where the basic difference
in technologies lies. As Abacus is mined even more value will be accrued as trading and speculation
occurs. This is where Abacus dominates the 2nd generation currency market.
4. Security
Abacus is based on the innate security of mathematical problems. If the mathematical problems
were easy to solve, they would have been. This contrasts with 1st generation cryptocurrencies which
are based on man-made and therefore potentially fallible. Therefore, Abacus innately has more
security than first generation cryptocurrencies. This may sound astonishing, but the secuirty behind
SHA2 and other cryptographic algorithms was designed to transmit signals and store data whereas
the security behind Abacus (innate mathematical security) was not designed at all and is merely a
pervasive rule of nature.
Each Abacus coin is secured cryptographically to preserve its uniqueness using AES-512 encryption,
which is currently approved by the U.S. Department of Defense for protecting classified materials.
This ensures the near-impossibility of coin fraud or theft by cryptographic or implementational
means.
M2 Technology Instance
Conceptual Whitepaper
5. Support & Due Dilligence
Abacus is supported by BitEX's M2 technology meaning any flaw in implementation can be dealt
with as soon as it is noticed. BitEX also supports mining software, hardware, and firmware (i.e. VHSIC
FPGA bitstreams) to aid in the mining and therefore proliferation of this currency.
6. Coin Specifics
Total Coins: 1,000,000
Coins per Block: 10
Difficulty Adjustment: 0.0001% of the total search field for Hadamard Matrices up to order 39
increasing in size every block by n/n+1e5 percent of the entire search field
*Please note these parameters have been determined as preliminary figures and may be changed
upon review by mathematicians on call to BitEX.
www.theabacuscoin.com
