'Garbled Circuits: Basic Scheme and Applications' vitalik cryptography
are a quite old, and surprisingly simple, cryptographic primitive; they are quite possibly the simplest form of general-purpose "multi-party computation" to wrap your head around.Suppose that there are two parties, Alice and Bob, who want to compute some functionf
Bob runs the encrypted circuit on the encrypted data and gets the answer, and passes it along to Alice. Now, for every gate in the circuit, we do the following. For every combination of inputs, we include in the "garbling" that Alice provides to Bob the label of the output encrypted with a key generated by hashing the input labels that lead to that output together. For simplicity, our encryption algorithm can just beis the index of the gate .
All in all, Alice sends to Bob four ~256 bit numbers for each gate in the circuit. It turns out that four is far from optimal; seefor some optimizations on how to reduce this to three or even two numbers for an AND gate and zero for an XOR gate. Note that these optimizations do rely on some changes, eg. using XOR instead of addition and subtraction, though this should be done anyway for security.
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