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!

  • $\begingroup$ Just checking, did you notice that was the link I gave ad well? That is an HE technique called "homomorphic encryption over the integers" where I made the security parameters effectively disappear. I'm asking this question to see what else is out there. $\endgroup$ – Alan Wolfe Feb 13 '16 at 17:49
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    $\begingroup$ No. ​ ​ ​ In that case, why not just use ​ E(b) = b ​ and ​ D(b) = b ​ ? ​ ​ ​ ​ ​ ​ ​ ​ $\endgroup$ – user12859 Feb 13 '16 at 17:53
  • $\begingroup$ Do you mean basically a no-op? Or am I missing the point? $\endgroup$ – Alan Wolfe Feb 13 '16 at 18:01
  • $\begingroup$ Yes. ​ (Are you hoping for "no completely trivial way to break security", or something else?) ​ ​ ​ ​ $\endgroup$ – user12859 Feb 13 '16 at 18:02
  • $\begingroup$ Security isn't a concern at all but I want to be able to transform bits (or numbers) into another form, do logic on them, then untransform them to get the same answer as if I did the operations on the untransformed bits. I also want it to be capable of universal computation in the encoded form so that it can do any operation, even if the number of operations total that can be performed has a limit. That help at all?? Thanks for responding (: $\endgroup$ – Alan Wolfe Feb 13 '16 at 18:16

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