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Ordinary avatar Crypto

Security of verifiable shamir secret share

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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)?

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Aman Grewal avatar
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Aman Grewal
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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