Limitations of Secret Sharing Schemes
Several secret sharing schemes are said to be information theoretically secure and can be proved 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 128-bits of entropy each, since each share would be considered enough to stymie any conceivable present-day adversary, requiring a brute force attack of average size 2127.
Common to all unconditionally secure secret sharing schemes, there are limitations:
- 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 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.
- All secret sharing schemes use random bits. To distribute a one-bit secret among threshold t people, t-1 random bits are necessary. To distribute a secret of arbitrary length entropy of (t-1)*length is necessary.
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