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add end of garbled circuits

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blog/posts/multi-party-computation.md
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@ -31,6 +31,8 @@ Alice and Bob have struck it rich! They're both millionaires, but they want to b
Luckily, we can use MPC to solve this "Millionaire's Problem" this using a method invented by Andrew Yao called *garbled cricuits*. Garbled circuits allow us to use MPC for any problem as long as it can be represented as a boolean circuit i.e. a set of logic gates such as `AND` `OR` `XOR` etc.
## Garbled Circuits
We can split the two parties into an "Evaluator" and a "Generator". The Generator will be responsible for setting up the cryptography that'll be used and the Evaluator will actually perform the computation.
We start by making the truth table for our inputs. In order to hide the values of the truth table, we assign each input a different label. Importantly, we need to assign a different label for each input, so 1 will not be represented by the same label for each. We also need to shuffle the order of the rows so the values can't be inferred from that.
@ -39,4 +41,8 @@ We can still tell what the value is based on knowing the type of logic gate, for
We still have a problem, though: how can the Evaluator put in their inputs? Asking for both labels would allow them to decrypt more than one output, and giving their input would break the whole point. The solution is something called "Oblivious Transfer".
The solution is for the Evaluator to generate two public keys, one of which they have the private key for. The Generator encrypts the two labels for the Evaluator's inputs using the provide public keys and sends them back. Since the Generator only has a private key for one of the labels, they will decrypt the one they want. The Generator puts the labels in order so that the Evaluator can choose which one they want to decrypt. This method relies on the Evaluator not to send multiple keys that can be decrypted.
### Birth of Multi-Party Computation
Multi-Party Computation was solidified with the research of Oded Goldreich, Siltnb Micali, and Avi Wigderson and the GMW paradigm (named after the researchers, similar to how RSA is named).