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FHE in action
rdancer edited this page Sep 14, 2010
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Following is a sample run of the fhe executable from commit ea9feb264e1691157ff57344e985622aecaa734e.
fhe takes one optional argument: the security parameter λ from which all the bit widths within the encryption scheme are derived. The bit widths are set as certain powers of the security parameter. The choice of the bit width ratios is to a certain degree arbitrary, but ultimately is driven by the need for certain elements of the encryption scheme to be within certain limits compared to other elements.
rdancer@boston:~/code/fhe/libfhe$ ./fhe 8
We have chosen the security parameter λ to be 8 bits. The private key will be λ² = 64 bits wide, and each encrypted bit will be λ⁵ = 32768 bits wide
Private key: 0xdf609dd49b49b2bc
Encrypt TRUE
Encrypted bit (1): 0xdb908fca2c6d325f47538fb94b41a51689a3d83dbc6e37f368ed37f80853823e06a13 02ae3d359817154fcd0a48a61d583d5fee0b9679fa5f8969915f900968715feb8d31dae cf8954f0ccf4225ea347e9456414404abb8f495f8bc6994dc63c00b7e4db8294441c3f4 a47701bc27b919df084802610da723c26a4abf9ef22d626b3595d2ab2a209c31bb01aaa 97568ffdf17b87ecc5bf560faddbbf698ca0b463744296116f75bfa6bc86d82d3e122a1 a648d28a6ca7a27f6dae993799dd6370481b06c5e925d6e02cee95c72e5552135375473 8433dd241306ede0b7da8d8d240a7573691f7e15f77be5f822d4d9cfbd030a48bc3e70d e330a144a79c62389715dba4c43d6b58f27ef1c5ada4f7ee1721c710a937f441df1c8f8 b5a0fcaf56ceec1fd4fc1d4296d73f0bea76b722cc98b4ce96ce266eeac72b7c8f3515c 5ac07e615a2271a91f3979819c581459cdc148a208a083d37493ae83919a177ae9869ee b2f6c0122eeeb81e60916f0b76857e372d37633d91e825f8829db8c5d387c60c76e9049 47872d6610e5a35a45a45f39802f62e69478e0ff553b501456b596ec2302fe74f463bff 0014f3e060093328ac7c84fc5324a304335521c40358df3e2a6ae1c7132f0dd1c3923f6 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And decrypt it again — decryption of TRUE works
Decrypted bit (1): 1
Encrypt FALSE
Encrypted bit (0): 0x79847661aa13511850983babfd6109ade1249f236cc71cb98564a1b024494c21d09b3 01254508442386fa76e4c4e8ac0ae6364d4f9a93cbe919b354cc412bb8f7992bdbcee57 762defdd5d599f1d121c5899722f81fdd58bc4157d5cdc29146d621568de9890f950ba2 5e02ecc17c3d3d5012d48dcd28f24b9d8149ddeb0e7621250291bba29ee87d70d48b96a 281851e41274601c4fb771c5ee1ce4e60931528ee5b1e5b2c17926261d78bd4bbf53d11 0a4d15dd2ca3d2a9feabb47b7619658ba1fc4004a227115146df243bdb5f311d7074eee e2d6984208ab307833448dbe4498c5fe08c027c78b0ab7dd86d00a37991401a661f1275 402fb0789cdee57ef64e290ab44825891c26dc860ef40a4e112728d41b7fc67bfdc5282 98eaf5dfa4bd6223c65c42f59c11a772b73b76b10389f37a7f55afe40c6e6938d2a0721 0209922b53ee95b625e4ed0bc04c8abe22f0e3c8b03d0423aea6a3bd3ddad0ec38facf8 f4251e053cc2fa441d9c9e03f122a31b17363be0392fc94fe30867dc11e247b3281f4a1 1a5711df50088d78a8a6fa05eaff70068432609aeb3819cf73b188a94244c1efca3fc7a 1adfb7f2a92fde541cb0dbca26a99c7739f2fef265a789303e7247e81522f8d50afad08 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And decrypt it again — decryption of FALSE works
Decrypted bit (0): 0
In the following tests, the bits are first encrypted, then the logical operation is performed on the encrypted bits, then the result of that operation is decrypted. The result will be same as if the logical operation would be performed on the original bits.
Decrypt(XOR, Encrypt(bit2)))
0 ⊕ 0 = 0 0 ⊕ 1 = 1 1 ⊕ 0 = 1 1 ⊕ 1 = 0
Decrypt(AND, Encrypt(bit2)))
0 × 0 = 0 0 × 1 = 0 1 × 0 = 0 1 × 1 = 1