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In this paper authors extend Asmuth–Bloom and Kaya schemes to bipartite access structures and further investigate how SSSs realizing multipartite access structures can be conducted with the CRT.

The authors, also, written Secret Construction procedure is same in Unipartite Secret Construction, Bipartite Secret Construction and Multipartite Secret Construction.

Unipartite(Asmuth–Bloom) Secret Construction

Assume $C$ is a coalition of $t$ participants to construct the secret. Let $M_C =\prod_{i=1}^{C}m_i$ $y ≡ y_ i \mod m_ i $

for $i ∈ C$, solve y in $GF(M_C )$ uniquely using the CRT. Compute the secret as K = y mod p

According to the CRT, y can be determined uniquely in $GF(M_ C)$ . Since $y < M ≤ M_C$ , the solution is also unique in $GF(M)$.

Bipartite Secret Construction:

Assume $C$ is a coalition of $\tau$ participants to construct the secret. Let $M_C =\prod_{f(y_i) ∈ C}m_i$

$y \equiv y_i \mod m_ i $

for $f(y_i) ∈ C$, solve y in $GF(M_C )$ uniquely using the CRT.
Compute the secret as K = y mod p

Multipartite Secret Construction

Assume $C$ is a coalition of $\tau$ participants to construct the secret. Let $M_C =\prod_{f(y_i) ∈ C}m_i$

$y \equiv y_i \mod m_ i$

for $f(y_i) ∈ C$, solve y in $GF(M_C)$ uniquely using the CRT.

Compute the secret as K = y mod p

I am getting confusion regarding the difference between Unipartite Secret Construction, Bipartite Secret Construction and Multipartite Secret Construction to .

Could you please explain the intuitive difference between Unipartite Secret Construction, Bipartite Secret Construction, and Multipartite Secret Construction.

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