3 ms·

I've wondered about another system, and perhaps someone here can point me in the right direction. Fully homomorphic encryption (FHE) has total control of two op

I've wondered about another system, and perhaps someone here can point me in the right direction. Fully homomorphic encryption (FHE) has total control of two operations. Partially homomorphic encryption (PHE) has one operation. We can do PHE pretty well, and we're currently very very bad at doing FHE in reasonable amounts of time. In Craig Gentry's FHE schemes (and all current ones that I know of) are all based off of an idea of bootstrapping, where each operation performed introduces some additional noise and every so often one must work to limit the noise and re-extract the signal. But somehow, as more operations are performed, simply too much effort goes into understanding the signal and noise. But let's say that I had a FHE scheme in which I could do a limited (and relatively small, on the order of 100) operations, but no more. I suspect this has a name, but I'm not familiar with it. If I had to name it something, I would give it the confusing name Limited FHE, or perhaps Finite FHE. Then my question is: what sorts of things could we do with Limited FHE? Is this a question that people have thought about?

deleted 11y ago
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roymurdock 11y ago
I don't see this idea of bootstrapping at all in the Enigma whitepaper: http://enigma.mit.edu/enigma_full.pdf http://enigma.mit.edu/enigma_full.pdf Enigma uses secure addition and multiplication protocols to construct a fully secure interpreter. A user throws a problem to a bunch of decentralized nodes running this secure interpreter that are incentivized by fees to perform these computations and then post the results to a public blockchain, where the validity of the computations can be verified by an auditor. It also includes (unlike Bitcoin) a distribution protocol so that the "miners" aren't all solving the same problem in a redundant fashion, although I don't think the "network reduction" protocol is specified in the whitepaper. This is probably the most relevant part to your question: Code evaluated in our system is guaranteed not to leak any information unless a dishonest majority colludes (t ≥ n/2). This is true for the inputs, as well as any interim variables computed while the code is evaluated. An observant reader would notice that as a function is evaluated from inputs to outputs, the interim results generally become less descriptive and more aggregative. For simple functions or functions involving very few inputs, this may not hold true, but since these functions are fast to compute - no additional steps are needed. However, for computationally expensive functions, involving many lines of code and a large number of inputs, we can dynamically reduce the number computing nodes as we progress, instead of having a fixed n for the entire function evaluation process. Specifically, we design a feed-forward network (Figure 5) that propagates results from inputs to outputs. The original code is reorganized so that we process addition gates on the inputs first, followed by processing multiplication gates. The interim results are then secret-shared with N/c nodes, and the process is repeated recursively.
baby 11y ago
This is called Somewhat Homomorphic Encryption (or SHE).

deleted 11y ago

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roymurdock 11y ago

I don't see this idea of bootstrapping at all in the Enigma whitepaper: http://enigma.mit.edu/enigma_full.pdf http://enigma.mit.edu/enigma_full.pdf Enigma uses secure addition and multiplication protocols to construct a fully secure interpreter. A user throws a problem to a bunch of decentralized nodes running this secure interpreter that are incentivized by fees to perform these computations and then post the results to a public blockchain, where the validity of the computations can be verified by an auditor. It also includes (unlike Bitcoin) a distribution protocol so that the "miners" aren't all solving the same problem in a redundant fashion, although I don't think the "network reduction" protocol is specified in the whitepaper. This is probably the most relevant part to your question: Code evaluated in our system is guaranteed not to leak any information unless a dishonest majority colludes (t ≥ n/2). This is true for the inputs, as well as any interim variables computed while the code is evaluated. An observant reader would notice that as a function is evaluated from inputs to outputs, the interim results generally become less descriptive and more aggregative. For simple functions or functions involving very few inputs, this may not hold true, but since these functions are fast to compute - no additional steps are needed. However, for computationally expensive functions, involving many lines of code and a large number of inputs, we can dynamically reduce the number computing nodes as we progress, instead of having a fixed n for the entire function evaluation process. Specifically, we design a feed-forward network (Figure 5) that propagates results from inputs to outputs. The original code is reorganized so that we process addition gates on the inputs first, followed by processing multiplication gates. The interim results are then secret-shared with N/c nodes, and the process is repeated recursively.

baby 11y ago

This is called Somewhat Homomorphic Encryption (or SHE).