Explore property preserving symmetric encryption in this 27-minute conference talk from Eurocrypt 2012. Delve into traditional cryptography and new goals for computations on encrypted data. Examine order-preserving encryption, left or right security, and find then guess security. Understand definitional relationships and separation proofs. Learn about constructions using pairings in composite order groups and orthogonality. Discover an explicit construction for setup, encrypt, and test operations. Gain insights into new directions in this field presented by authors Omkant Pandey and Yannis Rouselakis.