Editing Secret sharing (section)

==Limitations==
Several secret-sharing schemes are said to be [[Information-theoretic security|information-theoretically secure]] and can be proven to be so, while others give up this ''unconditional security'' for improved efficiency while maintaining enough security to be considered as secure as other common cryptographic primitives.  For example, they might allow secrets to be protected by shares with entropy of 128 bits each, since each share would be considered enough to stymie any conceivable present-day adversary, requiring a brute force attack of average size 2<sup>127</sup>.

Common to all unconditionally secure secret sharing schemes, there are limitations:{{Citation needed|date=April 2023}}
* Each share of the secret must be at least as large as the secret itself. This result is based in [[information theory]], but can be understood intuitively. Given {{nowrap|''t'' − 1}} shares, no information whatsoever can be determined about the secret. Thus, the final share must contain as much information as the secret itself. There is sometimes a workaround for this limitation by first [[Data compression|compressing]] the secret before sharing it, but this is often not possible because many secrets (keys for example) look like high-quality random data and thus are hard to compress.
* All secret-sharing schemes use [[random]] [[bit]]s for constructing the shares.{{Citation needed|date=April 2023}} To distribute a one-bit secret shares with a  threshold of ''t'' shares, {{nowrap|''t'' − 1}} random bits are needed.{{Citation needed|date=April 2023}} To distribute a secret of ''b'' bits, entropy of {{nowrap|(''t'' − 1) × ''b''}} bits is necessary.{{Citation needed|date=April 2023}}