I was reading this paper Homomorphic evaluation of the AES Circuit by Gentry et al. when I thought if something similar can be done with DES or 3DES, e.g. it is plausible to decrypt DES homomorphically ?
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$\begingroup$ The multiplicative depth of a DES-round should be similar to an AES-round, but a DES has 16 and a 3-DES 48 rounds, so you would need about 64 rsp. 192 levels for a DES rsp. 3-DES calculation. You might get away without bootstrapping for the single DES, but for 3-DES I'd expect it to be necessary. My rough guess (using the numbers from the AES-paper you cited) is that a 3-DES might take about an hour on one modern CPU core. $\endgroup$– j.p.Oct 12, 2015 at 15:51
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1$\begingroup$ Putting a bit more context into the question would not hurt. Requiring us to read an entire, unnamed paper doesn't help if you want to attract attention to the question. Some people here would have already read it, but they're not likely to download it to find out. $\endgroup$– Maarten Bodewes ♦Dec 10, 2015 at 18:54
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Every algorithm that can be modeled as a Boolean circuit can be homomorphically encrypted. DES/3DES can surely be modeled by a Boolean circuit.
The question is if it is practical to use DES/3DES for homomorphic encryption. I don't think so.
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$\begingroup$ @MaartenBodewes The algorithm doesn't need to be encrypted, but it does need to be realized as a homomorphic circuit... $\endgroup$– ThomasDec 10, 2015 at 19:04