I am curious if there are any released standards for homomorphic encryption, or computing on encrypted data. Perhaps by NIST, ANSI, or ISO. If not, are there any that are under development right now? If you have any estimates for a time frame about when a standard might arise, that would be helpful too.
There's an ISO publication currently under development called "Information technology security techniques -- Encryption algorithms -- Part 6: Homomorphic encryption". It is listed under ISO/IEC DIS 18033-6, there is a table of contents available here.
The Computer Security Division's (CSD) Cryptographic Technology Group (CTG) is also following the progress of emerging technologies, such as fully homomorphic encryption (FHE). FHE could potentially solve a large class of problems by allowing computation on encrypted data without decryption. CTG has also shown that the NIST Randomness Beacon (discussed below) can be used as a primitive in secure multi-party computation, such as sealed-bid online auctions, in which losing bids are never opened.
ANSI has nothing so far on homomorphic encryption, neither has the German BSI.
There are no other standards available as far as I know but there is a lot of research going into FHE. What can be said: FHE has not found its way into any major standard yet and if you try to run a standardized production environment you probably should not try to implement FHE or use FHE.
There are currently standards under development by folks in industry, government, and academia, with details and a draft located here: http://homomorphicencryption.org/
This is the current state of the standard:
We are developing a community standard for homomorphic encryption based on three white papers created by the participants at the first standardization workshop hosted by Microsoft Research in Redmond WA on July 13-14 2017; the three white papers addressed Security, API, and Applications of homomorphic encryption.
After being publicly scrutinized and improved further, the security white paper was publicly endorsed by many leading security experts at the second standardization workshop, resulting in the first version of the Homomorphic Encryption Standard.
Today, this document provides scheme descriptions, a detailed explanation of their security properties, and tables for secure parameters. Future versions of the standard may describe a standard API and a programming model for homomorphic encryption.