BITCOIN: A MATHEMATICAL CRAFTWORK WITH POLITICAL OVERTONES
Tags: History, Cryptocurrency, Bitcoin Mining, History Of Technology, Bitcoin

One of the most influential abstractions to have had been educed by human brain is the concept of Money. Its transmuting capacity in the utilitarian aspects of human life had the accentuating effect that was required for the sapiens to overwhelm some of the unvitiated spheres of nature that were otherwise insurmountable. The ability of humans to subjugate other species in this planet is a consequence of the cooperation between a vast number of individuals from various philosophical predilections due in part to the efficacy of money. It accelerated the cultural revolution to a degree unrivalled by other factors. Without the inclusion of its influence, the characterization of technological and civilizational development that is achieved by humans would be incomplete. Albeit undergoing multiple adaptations during various stages of our cultural evolution, money had retained most of its basic attributes intact until the introduction of the Fractional reserve banking system. The negative repercussions of this centralized banking system were profound enough to precipitate a discovery, prepossessing mathematical intricacies and revolutionary political overtones, called as Cryptocurrency.

CENTRALISED FRACTIONAL RESERVE BANKING SYSTEM

As the European wealth was proliferating during the years of Enlightenment era, a new form of Banking system sprang to life from the accumulation of this affluence in the form of Gold units. When people deposited their golds into safe vaults, the authorities inferred an expedient usage for them. Their experience had taught, at any point in time only a negligible fraction of it is getting transacted. They started to lend a portion of the deposited gold as loan to other customers and started collecting interest out of it. This way, they devised a framework to put each unit of deposited gold into multiple use, sourcing multiple incomes. The procedure was refined in the later years and the central banks in United states and Europe developed a fractional reserve banking system. Under their jurisdiction, any bank can lend 90% of their reserves as loans to people. This increased the amount of money in an economy by creating new units of money from the existing reserves and it is called as Money multiplier effect.

Notwithstanding the digression to Quantum Mechanics, the crude analogy of the nature of Bank reserves to the famous Quantum property of Superposition cant be refrained from being stated: reserve deposits in the banks are in a state of super-position, simultaneously between an ideal presence in the vaults and as loans granted to customers .

THRASHED HUBRIS OF CENTRALIZED BANKS

In the last hundred years, the banking institutions became increasingly ubiquitous in the countries that witnessed substantial growth in their economic activities. Coupled with centralization, their pervasiveness enabled Banks to effectively control and exploit the economic activities of every individual. This helped stake holders to manipulate the collective behavior of citizens to align with effectuated policies should people construe them as irrational. The fractional reserve banking systems thrive only on the confidence of the people regarding its stability. If a significant proportion of the population feel apprehensive about these banks, their collapse is inevitable. This was evident from the great depression of the early 1930s which was caused by the successive breakdown of such banks.

To circumvent this arbitrary third-party presence (Banks) for every transaction undertaken in the international financial network, people can either retreat to a medieval era economic model on the basis of trust or build a parallel currency system that respects the privacy of individuals. With the former being an untenable suggestion, the determination to invent a currency that is independent of influences from Governments and banks was pursued by some of great minds in mathematics and economics for several years and it gained momentum with the invention of internet, as digital currency was deemed to be a proficient alternative.

When United states economy plunged into a crisis in 2008 due to the collapse of Lehman brothers Holdings and subsequent incidents, the European economy saw one of its adverse culminations. This led to the imminence of Greece declaring bankruptcy, an event that could have crashed the financial stability of Eurozone currency. As the world was contemplating about the fragility of the centralized Fractional reserve banking system, a ground breaking mathematical research paper was published anonymously about the feasibility of crypto-currencies in 2009.

A LEGACY SPANING VAST EXPANSES OF HISTORY

Humans have always been captivated by the effectiveness of Cryptic messages during exceptional circumstances. It is the reason we see its continued relevance from the encoded texts in the ancient artefacts of Giza Plateau to various operations for securing communications in today’s digital networks. Yet, the improvements in cryptography were prosaic until the industrial revolution due to the lack of resources for mechanizing the process. First real mechanized cryptography was accomplished by the Nazis during second world war through their enigma devices. The challenges posed by those Enigma machines persuaded the allied forces to increase their research in mathematical tools required for the cryptanalysis of such highly complex ciphers. The conception of theoretical computer science was also the result of such strenuous undertakings during the second world war. With the development of digital computers and the emergence of internet, the need for secured communications initiated unconstrained research in the esoteric field of number theory.

TACKLING THE DOUBLE SPENDING PROBLEM

In a centralized trivial financial network, the double spending problem is prevented by the monitoring mechanisms such as banks (ironic indeed) and other bodies. But this problem was hassling the implementation of a viable decentralized digital currency for years. In simple words, the possibility of using a unit of a digital currency more than once has all the ramifications of the problematic counterfeits of the physical currencies. While the cryptographic tools for a digital currency were discovered decades ago, this problem was thwarting the digital currencies attempts for widespread recognition until an anonymous mathematical paper propounded a solution using some mathematical finesses.

The common attributes to both centralized and decentralized currencies are the cash accounts, a secure communication channel, and the recognition of every transaction by all the concatenated entities of the currency network. Elements of cryptography is ubiquitous in all these phases, as a secure digital currency transaction considerably abrogates the dimensions of trust with mathematical properties. Intricate mathematical contrivances like digital signature, Asymmetric keys, hash functions, block chains constitute the innards of secure digital transactions of crypto currencies.

To perform transactions in digital currency, a sender and receiver is required to possess a unique account. The authentication of these accounts is performed by digital signatures which use Public key and Private key cryptography (Asymmetric key cryptography). An account should have a unique Public key attached to it and a unique private key is entangled with that public key. A facile explanation about the transaction process is, the hash function (Hash function is a mathematical function that converts inputs of arbitrary length into a random unique output of fixed length) takes the transaction value and public key as an input to create a digital signature as an output, that is unique to every sender and receiver. The cryptocurrency system only allows transaction between signed and verified (verification of digital signatures involve private keys, thus prohibiting any fraudulent attacks to impersonate by copying one’s public key) digital signatures. Decentralization being the motive behind such a crypto currency, there is no authority to monitor the necessity of sufficient balance in individual accounts to prevent defaulting transactions. Hence, an ingenious idea of replacing currency’s intrinsic value with its transaction history was invented to negate this requirement for monitoring authority. In cryptocurrency, every transaction is transmitted to every account in the network and all those accounts retain their own copy of the transaction history. The net value of all transactions carried out from a particular account compensates for the intrinsic value of the currency’s balance in that particular account. But there must have been some unit of currency in an account to initiate a transaction in the first place. This is problem was solved through a process called Mining, which enabled every account with the ability to create currency.

DISTRIBUTED CURRENCY CREATION

The crypto currency transactions have to be recorded by every component (termed as Nodes) in the network in the same order for it to be legitimized. Since the information about transactions passes through the network in a way that some components receive a particular transaction in advance relative to the rest, due to physical constraints, it becomes impossible to time order every transaction accurately, considering the potential for the vastness of transactions occurring concurrently. Thus, they are grouped into a block, with each block containing the previous block’s transaction history in the form of a hash function. A sort of time order emerges from the consecutive placements of such blocks and this technique is famously known as Block chain. To produce a new block, one has to solve a particular mathematical problem to find a unique hash value with current block’s transactions and hash function of the previous block as input. Once the problem is solved and a new value is generated for a block, that block is added to the chain. The creation of such new blocks is called as Mining, and each successful attempt is entitled for a particular unit of currency as reward. In the world of crypto currency, thus the sovereignty to create currency is also distributed equally to all participants.

A CREDIBLE ALTERNATIVE?

The real-life applications of the concept of crypto currency, at least in the case of Bitcoin, is proving to be an overwhelming success if the astounding endorsement it has received is any tangible indication. The Bitcoin tackled the major problem that hindered the application of crypto currencies through a deft method. The original bitcoin paper introduced a scrutiny, called as Proof of work, whereby the block chain with maximum number of authenticated blocks is selected to be the reliable one.

Since any individual can add blocks to the chain, it is probable for a particular person to carry out fraudulent transactions (ones not communicated with others) and insert them to a block and add this reclusive block containing the fraudulent transaction to the existing block chain. Through this maneuver that person creates a branch in the existing block chain, because of the fact that the block created by that person contains a different transaction list as opposed to the transactions verified by others. The only thing that could prevent an individual from doing this is the time it takes to solve the mathematical problems for creating hash functions to add new blocks. Therefore, even if a person is able to create a block with fraudulent transaction, it is computationally infeasible for them to subsequently produce new blocks at a pace ahead of the others in the network to sustain the validity of the fraudulent transaction. The bitcoin block chain only validates the chain with maximum proof of work (efforts to add a new block as explained above). It was estimated that for a person to create such a fraudulent block and maintain the veracity of it effectively for a sufficient amount of time, one has to control more than 50% of the network’s resources. Though it could seem highly improbable for any one entity to acquire such vast resources, it was almost achieved by a particular mining body during 2014, propelling the entire Bitcoin community into a crisis situation.

Crypto-currencies are firmly establishing themselves as a credible alternative to the common currencies and their future lies dependent on the acuity of the future mathematical research. The increasing intensity of the research venturing into the once abstract areas of mathematics are escalating the inevitability of the Crypto currencies in the near future.