Cryptography has the concept of homomorphic encryption.
Homomorphic encryption lets you transform binary values into an encoded form, put them through a circuit and then decode the bits, getting the same value as if the plain text bits were put through an equivelant digital circuit. (A write up of a very simple implementation in my blog: http://blog.demofox.org/2015/09/05/super-simple-symmetric-leveled-homomorphic-encryption-implementation/)
This type of encryption was sought for 30 years before someone found an answer. While improvements have been made, its still impractical - on the order of 15 minutes to AND two encoded bits.
Throwing out the security concerns that come with cryptography, are there known methods for homomorphic computation?
I'm hoping that the security portion of homomorphic encryption is what was so elusive, but that homomorphic computation itself has known methods which are quicker or easier to execute even compared to turning off the security of HE schemes.
Thanks for any info you can provide!