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Do “Shamir Secret Sharing” schemes have a limitation for the amount of data that can be split up between each share, or a maximum number of data that can be shared within one secret?

I believe there is a relationship between the maximum data that can be shared the prime and the number of shares, or am I mistaken?

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In principle, the secret is a single field element. Thus, this is exactly what you can store. However, there is a notion called "packed secret sharing" that enables you to store more than a single value. However, it cannot always be used, and it depends on the required thresholds. For example, assume that you wish that no less than $t$ parties will be able to learn anything about the secrets, but you can assume that $t+\ell$ parties will be able to come together to reconstruct. Then, in this case, you can share $\ell$ values using a single polynomial of degree $d=t+\ell-1$. In order to do this, you can define $p(-i)=s_i$ for $i=0,\ldots,\ell-1$ for secrets $s_0,\ldots,s_{\ell-1}$, and then use other points for the parties' shares (use $p(i)$ for party $i$'s share). Of course, in this case, you also need the field to be larger than $n+\ell$ where $n$ is the number of parties.

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The secret and its shares all are elements of the chosen finite field (need not be a prime field). If the field has $q$ elements, then the secret (and the shares) all can be represented as vectors of $\lceil log_2 q\rceil$ bits.

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