A brief hiatus for my work was because of the launch of the second edition of my collection of essays titled “Essays on the Blockchain: Volume 2” which is now available on Amazon for purchase.
The following paper has one of the clearest mathematical definitions of Zero-Knowledge systems and the background of Zero-Knowledge systems: https://eprint.iacr.org/2013/879.pdf
These class of algorithms called ZK-SNARKs in short – it allows one to validate the existence of information, without revealing more than what needs to be known. For example, in a blockchain transaction, if a receiver (client) has to debit 10 ETH from a particular sender’s (sender’s) wallet, I need to know that the wallet has at least 10ETH. Though such a transaction seems simple, there are many aspects related to security, confidentiality, and privacy that need a more formal treatment.
The three properties of zero knowledge systems:
Firstly, the client has to ascertain that the information he receives is sound. This property is the property of integrity.
Secondly, the server has to ascertain confidentiality of his information e.g. remaining account balance, wallet contents, location, prior transactions that led to the wallet amount, etc. that are not related to his transfer of 10ETH is kept confidential.
Thirdly, another property of this system known as efficiency need for this system of verification is that both the client and the server can possibly need not engage in real-time interactions, and/or intensive computation.
Of course, there are other network-security/communications security challenges here too e.g. security against a man-in-the middle attack if there is data being transmitted, validation against partial availability of data, etc….
An example in the context of the Bitcoin’s Blockchain is that of a Merkle-tree data structure can be used to validate the presence of a transactions, in a block without knowing all other transactions, etc.
There are many technical papers – most of them Eli-Ben-Sassoon’s work. ZCash a crypto-token created based on this algorithm is a widely acclaimed implementation of both the Z-K and the efficiency (SNARKs).
“Essays on the Blockchain: Volume 2” which is now available on Amazon for purchase.