Assume $d=abc$ and to implement first order threshold implementation , the minimum input and output shares are 4 (1*3+1) , and 4 , calculated using ${4\choose 3}$ , Theorem 2. The new TI equation is: $$d_{0,1,2,3}= (a_0 \oplus a_1 \oplus a_2 \oplus a_3)(b_0 \oplus b_1 \oplus b_2 \oplus b_3)(c_0 \oplus c_1 \oplus c_2 \oplus c_3)$$

breaking out the multiplication results in 64 terms , divinding the terms on 4 output shares , each share will have 16 terms , but how to select the terms for each share?

Q. How do you find the output shares ($d_0$,$d_1$,$d_2$,$d_3$) equations that acheive non-complete , uniform and correctness features ?


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