Threshold Fully Homomorphic Encryption Sample Clauses

Threshold Fully Homomorphic Encryption. For our protocol we require a threshold (compact) fully homomorphic encryption (TFHE) scheme. Our definitions follow prior work [25, 41, 9, 2, 6]. Definition 33 A threshold fully homomorphic encryption (TFHE) scheme consists of the following algorithms: • The key-generation algorithm KGen takes as input the security parameter along with integers t, N. It outputs an encryption key ek and decryption keys dk1, . . . , dkN . • The encryption algorithm Enc takes as input the encryption key ek and a message m. It outputs a ciphertext c. • The (deterministic) homomorphic evaluation algorithm Eval takes as input the encryp- tion key ek, an n-input circuit C, and n ciphertexts c1, . . . , cn; it outputs a ciphertext c. • The (deterministic) partial decryption algorithm Dec takes as input a decryption key dki and a ciphertext c. It outputs a decryption share di. • The reconstruction algorithm Rec takes as input decryption shares {di} and outputs a message m. We require: Correctness: For any integers n, t, N, messages {mi}i∈[n], n-input circuit C, and set I ⊆ [N ] with |I| = t, if we run (ek, {dki}i∈[N]) ← KGen(1κ, 1t, 1N ) followed by c := Evalek(C, Xxxxx(m1), . . . , Encek(mn)), then Rec({Decdki (c)}i∈I) = C(m1, . . . , mn).
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Threshold Fully Homomorphic Encryption. The following definitions are adapted from Xxxxxx’x thesis [22]. Definition 25 A fully homomorphic encryption scheme (FHE) consists of four algorithms: • Key generation: (ek, dk) = KGen(1κ), where ek is the public encryption key and dk is the decryption key. • Encryption: c = Encek(m; r) denotes an encryption with key ek of a plaintext m with ran- domness r, to obtain ciphertext c. • Decryption: m = Decdk(c) denotes a decryption of ciphertext c with key dk to obtain plaintext
Threshold Fully Homomorphic Encryption. For our protocol we require a threshold (compact) fully homomorphic encryption (TFHE) scheme. Our definitions follow prior work [25, 41, 9, 2, 6].

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