Redefining Privacy & solving Double-Spending
In the traditional banking system, the transactions or the business between two parties happens through a third party or a trusted entity which is the Bank. The access to the business or transaction is very limited, not available for a third-party audit, it requires permission to conduct an audit, which is a time-consuming process.
Further, the business between two parties in the traditional system is not that private as the intermediary(Bank) still has all the information about the business, so the corrupt individuals of a Bank can still have that sensitive information of the businesses between two individuals/entities.
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all the transactions are publicly available in the distributed ledger (making it auditable by any third party without seeking permission from anyone), yet making it anonymous, respecting the privacy of the peers, as the public keys are not attached to the identity of any person, they are anonymous.
So you have the flow of business information, but you won't be able to know who the person behind the public key is. However, repeated transactions from the same address could help to establish the owner of the public key by little social engineering. To shield you from that probability, it enables you to create a new key pair for each new transaction you go for.
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