隐藏的证明

“Effective zero knowledge” beats long-standing cryptographic impossibilities IN MATHEMATICS, PROOFS CAN BE written down and shared. In cryptog- raphy, when people are trying to avoid revealing their secrets, proofs are not always so simple—but a new result sig- nificantly closes this gap. Zero-knowledge proofs are the closest cryptography gets to magic. They promise to let one person con- vince another of the truth of some fact—say, that they know the solution to a sudoku puzzle—without giving away any information about it. Such proofs can help people authenticate identities virtually, make online bank- ing transactions, build blockchains, and more. Cryptographers, however, have long understood that zero-knowledge proofs can’t safely be written down like a typical mathematical proof. …