diff --git a/content/docs/zkdocs/protocol-primitives/shamir.md b/content/docs/zkdocs/protocol-primitives/shamir.md index 820e81a..9347ff9 100644 --- a/content/docs/zkdocs/protocol-primitives/shamir.md +++ b/content/docs/zkdocs/protocol-primitives/shamir.md @@ -28,7 +28,7 @@ $$f(x) = S + r_1 x + \ldots + r_{k-1} x^{k-1} \enspace.$$ {{< hint info>}} **Example:** We want to share our secret number 42 with three players so that any two of them can recover it. We define the degree-1 polynomial over $\field{73}$ as $$f(x) = 42 + 13 \cdot x \enspace,$$ -where 13 was randomly sampled over $\field{73}$. We evaluate the polynomial at different points obtaining the shares $(x_i, f(x_i))$. Then, we can share 1 point of the coefficient to the three players, each getting one of $(1, 55), (2, 68), (3, 8)$. Since the polynomial is a line, any two of them could meet and recover the secret value 42! +where 13 was randomly sampled over $\field{73}$. We evaluate the polynomial at different points obtaining the shares $(x_i, f(x_i))$. Then, we can share 1 point of the coefficient to the three players, each getting one of $(1, 55), (2, 68), (3, 81)$. Since the polynomial is a line, any two of them could meet and recover the secret value 42! {{< /hint >}} This choice has the advantage of relative simplicity; there is no need to use oddball sampling techniques to select the coefficients of $f\left(x\right)$.