the payment protocol, she gives Bob the public key as part of the electronic coin. Any other transactions involving that withdrawal can only be reconstructed with the cooperation of each consecutive spender of that coin. To counter this problem, it is possible to design a system that has an option to restore traceability using an escrow mechanism. Optional features OF OFF-line cash. There are two ways of doing it: the cut-and-choose method and zero-knowledge proofs. _ 3 In the context of electronic cash, the token is usually called an electronic coin. The letter also explains how to use bitcoin to make the payment. If the system is implemented on-line, then multiple spending can be prevented by maintaining a database of spent coins and checking this list with each payment. However, the issue of counterfeiting must be considered here, since the payment protocols contain built-in protections against. We begin by describing these mechanisms, which are based on public-key cryptography. For this kind of signature, we have a signing function S SK using the secret key SK, and a verifying function V PK using the public key. Thus Alice will have to reveal the other piece of the corresponding pair.

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Anonymity can be provided at varying levels, but increasing the level of anonymity also increases the potential damages. Protocol 3: Untraceable On-line electronic payment. If all goes as it should, the identifying information will never point to Alice. But tm was revealed when tn was spent, so sx 1 and hence s will be revealed. This would violate the privacy that anonymous cash was designed to protect. 5.1 Multiple Spending Prevention.3, we explained that multiple spending can be prevented in on-line payments by maintaining a database of spent electronic coins, but there is no cryptographic method for preventing an off-line coin from being spent more than once. Now suppose we have a line y mx b over the field of integers (mod q ). A.00 payment can be made by spending the shaded nodes. For example, the Bank might be a credit card company, or the overall banking system. Proposed OFF-line implementations.1 Including Identifying Information.2 Authentication and Signature Techniques.3 Summary of Proposed Implementations. The above failure scenarios apply, not only to the electronic cash system, but also to the underlying authentication infrastructure.