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Then, at least t of these parties are required for a successful decryption.
However, threshold homomorphic encryption requires cooperation between parties for a successful decryption.
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Then, the probability of a successful decryption without knowing all the 2 + 1 4 N = 1152 parameters correctly is 1/2561152.
Threshold homomorphic encryption: It is a special type of homomorphic encryption, which distributes the knowledge of a private key among n parties and at least t of the parties are required for successful decryption.
If the value m+t·(g+sf−ue) does not wrap around mod q (i.e., all errors R∋e,f,g,u←χ must be sufficiently small), we have [!langle mathsf{ct}, vec{s} rangle]_{q} = m + t cdot (g + sf -ue) in the ring "R" (see also Lemma 2 below for the condition of successful decryption).
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