H. V. Kumar Swamy
The socio-economics and governance aspects of the genre of cryptocurrencies, including the seminal earlier notions of digital cash, led us to the development of our version of electronic money termed VMcoins and its embedding it in a blockchain like system termed VSKchains. We provide a brief description of this scheme. We discuss the mathematical underpinnings of hash functions, which are the main work-horses of cryptocurrencies and blockchains. Also the digital signature primitive plays an important role in the management of blockchains. In the Appendix, we explain briefly, the basic principles of elliptic curves, an interesting object of mathematics and computer science, which plays a critical role in all functionalities of contemporary cryptographic applications.
The properties of physical money, such as anonymity, privacy, transferability, fungibility, ease and control of use, have made them a way of life for human beings. Rapid technological developments in the context of slowly changing sociological milieux, have prompted human ingenuity to come up with novel solutions to the handling of money matters.
The initial technical developments in the field of cryptography, namely ecash, provide many new ways of handling digital money analogous to the ways of using physical money. These employ the principle of cryptographically secure pseudo-random sequences called hash chains. The seminal results of David Chaum, in 1982, led to a spurt of exciting ideas and potential applications of digital cash during the subsequent two decades. However, all these ideas needed to wait, for blooming, for the coming of the mobile communication and computing platforms. Meanwhile the fiscal instruments of digital commerce and trading (or widely known as e-commerce and m-commerce) had found the convenient solutions of plastic card based transactions.
The digital cash phenomenon made a forceful reappearance in a different form Bitcoin, and its ilk, during the last 7 years. These forms of digital currency, termed cryptocurrencies, which are members of the broader family of digital entities termed blockchains, are current technological torch-bearers. In this article, we trace the technical developments in these two tracks of ideas. We also point to our our works (i) on transferable digital cash, and (ii) on a version of cryptocurrency that seeks to strike a balance between completely, decentralized (or distributed) private fiscal instruments and state-mediated fiduciary instruments.
In both forms of digital cash, the technical aspects get intertwined with other sociological features. Such a situation is prevalent, in any sector, when an innovative, new technology makes appearance. We discuss the salient issues with a view to highlighting the pros and cons and hence forecasting the future of the exciting topic of cryptocurrencies.
In Section 2, we trace the evolution of digital cash, a cryptographic token, analogous to a coin, or a coupon, which can be used as an instrument of exchange for digital payments. Such a digital form of money was a precursor to the contemporary phenomenon of cryptocurrency. We devote Section 3, to a description of a canonical example of this genre of money, the Bitcoin. We also note the wave of alternative cryptocurrencies. In Section 4, we first discuss certain aspects of monetary transactions with physical fiat cash instrument issued by the state. This paves the way for discussions on digital currencies, fiat or private. Then we describe our proposal for a variant of the private currency genre, which could serve as a template for state regulated cryptocurrency, as well. In the closing Section 5, we make a summary examination of the future of blockchains and cryptocurrencies. Finally, in the Appendix, we explain briefly, the basic principles of elliptic curves, an interesting object of mathematics and computer science, which plays a dominant role in contemporary cryptography. Elliptic curves are being used routinely, to provide information security functionalities, in many software products such as SSL, WhatsApp, Bitcoin, Ethereum and other cryptocurrencies.
2. Digital Cash
Money plays a central role in the conduct of human affairs. Money in the form of cash, as a store-of-value and as a medium of exchange, also referred to as currency, takes many forms. These forms have evolved over centuries among civilizations, from physical tokens to state issued denominational, fiat currencies of universal acceptance. The physical instruments co-exist with other non-physical forms of instruments, based on denotational, legal, political, economic and governance principles. The advent of computer, communication technologies in human activities of trade and commerce, brought new perspectives on money matters. The transactions using the physical cash instrument has many useful features such as privacy, anonymity, peer-to-peer, fungibility and ease of use. A notable input from the scientific community was digital or electronic cash (ecash).
Many electronic payment systems using the payment instrument of ecash, were proposed soon after the seminal work of D.Chaum, in 1982, on ecash. They are classified into two types, viz, online and offine. Online e-payment systems are those in which the transfer of electronic money between the payer and payee takes place in the presence of a third party, usually a bank, that guarantees the authenticity of the coins being transferred. In contrast, in offine systems the transaction occurs between the two parties, payer and payee, alone. The money transferred is verified when the payee deposits the coins with a bank.
We briefly review some of the ecash based payment systems. For brevity, we choose only the major systems  ,  Certain other related and interesting systems are ,,,, David Chaum’s ecash is a fully anonymous, secure online electronic cash system. It implements anonymity using blind signature techniques. The ecash system consists of three main entities:
- Banks who issue coins, validate existing coins and exchange real money for ecash.
- Buyers who have accounts with a bank, from which they can withdraw and deposit ecash coins.
- Merchants who can accept ecash coins in payment for information, or hard goods. Merchants can also run a pay-out service where they can pay a client ecash coins.
To withdraw a coin, the user generates a coin(message), m, consisting of a random serial number, r, multiplied by a blinding factor, b, and the denomination. This message, m, is signed by user using his private key and sent to the bank after encrypting the message using the bank’s public key. The bank signs the blinded coin and debits the user’s account. The user un-blinds the coin by dividing by an appropriate blinding factor. Thus the bank cannot link the ecash to the user. While spending, the coins are securely transferred to the merchant. The merchant verifies the coins by sending them to the bank. After ascertaining that the coins are not double spent, the bank credits the merchant’s account and the coin is destroyed. If the coin is double spent the bank sends an appropriate message to abort the transaction. The advantage of ecash is that it is fully anonymous and secure as it uses public key cryptography. The downside is that the database of spent coins gets bigger and new coins have to be issued for every transaction.
Stefan Brands proposed an offline ecash payment system . In this scheme, three participants are involved : the computer at the bank, computer of an Internet service provider and the machine of the user. The user’s machine is interfaced with a tamper resistant device. The tamper resistant device increases the counter at withdrawal time by the amount that is withdrawn and decreases the counter when a payment is made. To make a payment from the user to the Internet service provider and for the latter to verify that the payment is genuine, a secret key is installed in the device. When a specified amount is transferred this key is used to sign the amount. The service provider can now use the bank’s public key to verify the authenticity of the electronic money so transferred. The user does not know the secret key and hence cannot produce the signature. After the digital signature is verified, the service provider accepts and provides the requested service to the user. The advantage of this system is that no transaction requires the presence of a third party for the verification. Thus offline operation provides lesser communication overheads. But if the device is broken by anybody then it would necessitate a change of device for every user of the system.
Transferability of coins is a difficult feature in most of the ecash systems, whether online or offline. This is due to the fact that double-spending by copying digital cash instruments is trivial as opposed to situation with physical cash. In ecash payment systems usually the lifetime of a coin is the lifetime of the transaction it is involved in. This is in contrast to physical cash where the money retains its value over several transactions and merely changes ownership. An obvious advantage of transferable cash is that a coin issuing authority need not issue new coins for every transaction that takes place.
A concern in the early years was the enormous load that would be placed on the central bank or coin-issuing authority that would check the authenticity of coins. This as certainly a bottleneck since each coin in a transaction needed to be verified by a central server. We proposed a scheme  in which we replaced a central verifying server with a set of trusted servers, thereby distributing the load across several entities. We also required a dispute resolving mechanism in place for the electronic payment system. Given the fact that the payer and payee do not know each others’ real identities as they transact over the Internet, the payment system should be able to give guarantees to both the parties in the transaction. We outlined such a dispute resolution protocol as a part of this payment system.
In the next section we describe a current, modern version of digital currency called the Bitcoin. The Bitcoin invention takes advantage of the cryptographic principles of ecash design and combines these with distributed database operations.