Chapter 16 Digital Cash – Introduction to Cryptography with Coding Theory, 3rd Edition

Chapter 16 Digital Cash

Suppose Congressman Bill Passer is receiving large donations from his friend Phil Pockets. For obvious reasons, he would like to hide this fact, pretending instead that the money comes mostly from people such as Vera Goode. Or perhaps Phil does not want Bill to know he’s the source of the money. If Phil pays by check, well-placed sources in the bank can expose him. Similarly, Congressman Passer cannot receive payments via credit card. The only anonymous payment scheme seems to be cash.

But now suppose Passer has remained in office for many terms and we are nearing the end of the twenty-first century. All commerce is carried out electronically. Is it possible to have electronic cash? Several problems arise. For example, near the beginning of the twenty-first century, photocopying money was possible, though a careful recipient could discern differences between the copy and the original. Copies of electronic information, however, are indistinguishable from the original. Therefore, someone who has a valid electronic coin could make several copies. Some method is needed to prevent such double spending. One idea would be for a central bank to have records of every coin and who has each one. But if coins are recorded as they are spent, anonymity is compromised. Occasionally, communications with a central bank could fail temporarily, so it is also desirable for the person receiving the coin to be able to verify the coin as legitimate without contacting the bank during each transaction.

T. Okamoto and K. Ohta [Okamoto-Ohta] list six properties a digital cash system should have:

  1. The cash can be sent securely through computer networks.

  2. The cash cannot be copied and reused.

  3. The spender of the cash can remain anonymous. If the coin is spent legitimately, neither the recipient nor the bank can identify the spender.

  4. The transaction can be done off-line, meaning no communication with the central bank is needed during the transaction.

  5. The cash can be transferred to others.

  6. A piece of cash can be divided into smaller amounts.

Okamoto and Ohta gave a system that satisfies all these requirements. Several systems satisfying some of them have been devised by David Chaum and others. In Section 16.2, we describe a system due to S. Brands [Brands] that satisfies 1 through 4. We include it to show the complicated manipulations that are used to achieve these goals. But an underlying basic problem is that it and the Okamoto-Ohta system require a central bank to set up the system. This limits their use.

In Section 16.3, we give an introduction to Bitcoin, a well-known digital currency. By ingeniously relaxing the requirements of Okamoto-Ohta, it discarded the need for a central bank and therefore became much more widely used than its predecessors.