Security of verifiable shamir secret share

sy flag

Let us consider the following verification protocol based on Feldman. Assume, $c_0,\cdots,c_k$ represent the coefficients of the polynomial $p()$ in $\mathbb{Z}_q$. For verifying share $(i,p(i))$ and public parameters group $G$ of prime order $p, q|p-1$ and generator $g$, the share generator provides $(g,d_0,\cdots,d_k)$ where $d_j=g^{c_j}, j \in\{0,1,\cdots,k\}$. The receiver of the share $s$,checks whether $g^s = \prod_j d_j^{i^j}$. Is this scheme secure (based on the hardness of discrete logarithm)?

Aman Grewal avatar
gb flag
Haven't looked closely at this scheme, but keep in mind that whenever you introduce verifiability, you're moving from information-theoretically secure to computationally secure. Granted, whatever you're doing with the secret might mean you're already relying on being computationally secure.

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