Threshold Fully Homomorphic Cryptosystems
A new paper by Steven Myers, Mona Sergi, and Abhi Shelat on eprint, &quot;Threshold Fully Homomorphic Encryption and Secure Computation&quot;, claims a threshold fully homomorphic encryption scheme.
From their abstract:

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Gentry [Gen09a] shows how to combine both ideas with fully homomorphic encryption in order to construct secure multi-party protocol that allows evaluation of a function $f$ using communication that is independent of the circuit description of $f$ and computation that is polynomial in $|f|$. This paper addresses the major drawback's of Gentry's approach: we eliminate the use of non-black box methods that are inherent in Naor and Nissim's compiler.
To do this we show how to modify the fully homomorphic encryption construction of van Dijk et al. [vDGHV10] to be threshold fully homomorphic encryption schemes.
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Altogether, we construct the first black-box secure multi-party computation protocol that allows evaluation of a function $f$ using communication that is independent of the circuit description of $f$.