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I'm doing some research about full homomorphic encryption (FHE). As I figured out, algorithms are implemented in circuits. I suppose that they are called circuits because the Holy Grail is to realize a NAND gate and then be able to do any kind of logic with that.

My question is: how does homomorphic encryption deal with conditions and jump operations? How could you calculate the nth item of a Fibonacci series recursively with a circuit?

Most of the manuals of FHE implementations don't talk about conditions and jumps. Is the idea that some instances do some preparation of the circuit before execution?

Patriot
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Robin
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    Might me related [Representing a function as FHE circuit](https://crypto.stackexchange.com/q/63781/18298). Due to the semantic security, you calculate both and combine them since the evaluator cannot know the jump. – kelalaka Feb 17 '20 at 13:02
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    Also related: [Can Fully Homomorphic Encryption do comparisons?](https://crypto.stackexchange.com/questions/57714/can-fully-homomorphic-encryption-do-comparisons/57716#57716) – Geoffroy Couteau Feb 18 '20 at 08:28
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    Unroll all loops, convert into circuit. There's nothing specific about FHE here. – Maeher Mar 01 '20 at 13:30
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    @Robin: since you added a bounty to your question, can you explain why the two other questions linked to in the comments, and their answer, do not already answer your question? – Geoffroy Couteau Mar 03 '20 at 18:28
  • @GeoffroyCouteau: In my opinion it doesn't, but I think the question arose because of a misunderstanding on my side. Jumps are not handled directly within a circuit. – Robin Mar 07 '20 at 10:09

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