Cryptography and privacy computing

In this paper, we first trace the evolution of cryptography from symmetric- and public-key primitives to the emerging paradigm of privacy computing. We systematically examine three pillars, namely, zero-knowledge proofs, fully homomorphic encryption, and secure multi-party computation, by highlighting their models, algorithms, and performance frontiers. The second half narrows the lens to recent deployed systems. In particular, we introduce the Plonk zk-SNARK powering Ethereum layer-2 roll-ups, and present a state-of-the-art privacy-preserving Vickrey auction algorithm. These case studies illustrate how privacy-computing techniques are transitioning from theory to production-grade blockchain applications.