The leakage profile in our construction of practical order revealing encryption (ORE). Like all known practical ORE schemes, our scheme leakes more than just the order of plaintexts. Unlike other leakage profiles, however, this leakage is invariant under multiplying all plaintexts by 2. With some additional processing, this allows us to construct parameter-hiding ORE, which hides the scale and shift of the underlying plaintext distribution. Parameter hiding is the only known semantically meaningful privacy notion achieved by practical ORE schemes. See .
Property Preserving Encryption (PPE) deliberately preserves certain relations on the plaintext data (e.g. equalities in the case of deterministic encryption, or order in the case of order revealing encryption). In addition to applications such as encrypted databases, PPE also has other interesting connections, such as security under bad randomness and differential privacy. The question is then: how to reveal such information without revealing other sensitive data, and what security, if any, remains.

On ELFs, Deterministic Encryption, and Correlated-Input Security
By Mark Zhandry
In EUROCRYPT 2019

Parameter-Hiding Order Revealing Encryption
By David Cash, Feng-Hao Liu, Adam O'Neill, Mark Zhandry and Cong Zhang
In ASIACRYPT 2018

Impossibility of Order-Revealing Encryption in Idealized Models
By Mark Zhandry and Cong Zhang
In TCC 2018

Order-Revealing Encryption and the Hardness of Private Learning
By Mark Bun and Mark Zhandry
In TCC 2016-A

Semantically Secure Order-Revealing Encryption: Multi-Input Functional Encryption Without Obfuscation
By Dan Boneh, Kevin Lewi, Mariana Raykova, Amit Sahai, Mark Zhandry and Joe Zimmerman
In EUROCRYPT 2015