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The Garbled Circuit (GC) is now over thirty years old, and many optimization methodologies have been proposed, including point-and-permute, row-reduction, free-XOR, fixed-key blockcipher, half-and.

But, after Googling papers and forums, I can't find any concrete algorithmic descriptions which includes all of these optimizations. Does anyone know the exact descriptions of optimized GCs?

I ask because I need to implement the algorithm for personal use.

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Not all optimizations of garbled circuits are compatible with each other. Are you interested in implementing all of the different combinations? If not, the Half Gates paper already gives a formal description of the scheme, which includes point-permute, fixed-key block cipher, free-XOR. This should represent the state-of-the-art combination of GC optimizations. There is a good implementation of half-gates in the Ivory project.

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  • $\begingroup$ Thanks for your response. After looking at the paper talking about half-and, it is clear that it deploys almost all optimizations that can be integrated. Indeed, the final scheme of Half-And is really hard to understand for me. Do you have any good explanation on the constructions of its T_Gc and W_Gc as well as T_Ec and W_Ec? $\endgroup$ – alexander Aug 21 '18 at 3:44

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