I was thinking of this since yesterday. Imagine, a secret is split into its resp

Question

I was thinking of this since yesterday. Imagine, a secret is split into its respective shares (using any secret sharing scheme) with threshold t and total n. Can we find out given any random string if it is a valid share of the secret ?

Of course without brute force approach, i.e splitting the secret into its shares and matching the string with each of its member to find out if its legitimate member.

Is it possible at all ? for any secret sharing mechanism ? So to summarize, given a string si ,a secret string secret and any configuration parameters needed (say t,n values etc) to share secret.

Can we identify if si is valid secret without brute force approach described above ?

Explanation / Answer

Just to be specific we are talking about information theoretically secure secret sharing, e.g. Shamir sharing. Lets say a secret secret is shared in n shares S={s1,

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