gokulsan · May 13, 2019 09:29
diff --git a/Blockchain_KeyManagement_Tools_Techniques.txt b/Blockchain_KeyManagement_Tools_Techniques.txt
 Bullet Proofs does not requrie trusted setup like ZK Snarks. Bulletproofs shrink the size of the cryptographic proof from over 10kB to less than 1kB. If all Bitcoin transactions were confidential and used Bulletproofs, then the total size of the UTXO set would be only 17 GB, compared to 160 GB with the currently used proofs. Bulletproofs have many other applications in cryptographic protocols, such as shortening proofs of solvency, short verifiable shuffles, confidential smart contracts, and as a general drop-in replacement for Sigma-protocols - https://crypto.stanford.edu/bulletproofs/

 Decentralized Anonymous Payments - https://blog.acolyer.org/2017/02/21/zerocash-decentralized-anonymous-payments-from-bitcoin/

 Most efficient zero knowledge proofs known are based on Sigma protocols. Informally, Sigma protocols are honest-verifier perfect zero-knowledge interactive proof systems with some very interesting properties.  First, they are three round public-key protocols (meaning
 that the verifier’s single message—or challenge—is just a random string); second, if the statement is not in the language, then for every first prover message there exists just a single verifier challenge that can be answered; third, there exists a simulator that is given the statement and verifier challenge and generates the exact distribution over the prover’s messages with this challenge. 

 https://practice-project.eu/downloads/publications/sigma-to-nizk.pdf

 Pinocchio’s end-to-end toolchain, plus its support for both Boolean and arithmetic circuits, allows us to implement real applications that benefit from verification. In particular, we implement two forms of matrix multiplication, multivariate polynomial evaluation, image matching, all-pairs shortest paths, a lattice-gas scientific simulator, and SHA-1.
	Bullet Proofs does not requrie trusted setup like ZK Snarks. Bulletproofs shrink the size of the cryptographic proof from over 10kB to less than 1kB. If all Bitcoin transactions were confidential and used Bulletproofs, then the total size of the UTXO set would be only 17 GB, compared to 160 GB with the currently used proofs. Bulletproofs have many other applications in cryptographic protocols, such as shortening proofs of solvency, short verifiable shuffles, confidential smart contracts, and as a general drop-in replacement for Sigma-protocols - https://crypto.stanford.edu/bulletproofs/

	Decentralized Anonymous Payments - https://blog.acolyer.org/2017/02/21/zerocash-decentralized-anonymous-payments-from-bitcoin/

	Most efficient zero knowledge proofs known are based on Sigma protocols. Informally, Sigma protocols are honest-verifier perfect zero-knowledge interactive proof systems with some very interesting properties. First, they are three round public-key protocols (meaning
	that the verifier’s single message—or challenge—is just a random string); second, if the statement is not in the language, then for every first prover message there exists just a single verifier challenge that can be answered; third, there exists a simulator that is given the statement and verifier challenge and generates the exact distribution over the prover’s messages with this challenge.

	https://practice-project.eu/downloads/publications/sigma-to-nizk.pdf

	Pinocchio’s end-to-end toolchain, plus its support for both Boolean and arithmetic circuits, allows us to implement real applications that benefit from verification. In particular, we implement two forms of matrix multiplication, multivariate polynomial evaluation, image matching, all-pairs shortest paths, a lattice-gas scientific simulator, and SHA-1.