Meaning
Mathematical algorithm used to divide a single secret into multiple unique parts called shares. Under shamir secret sharing, a specific number of these parts must be combined to reconstruct the original information. It governs the distribution of a single secret and does not apply to the management of multiple unrelated passwords.
Fault Tolerance
Distribution of shares across different physical locations prevents a single point of failure from destroying a secret. If a company uses shamir secret sharing, it can lose several shares to fire or theft and still recover the master key. This redundancy is vital for long-term data preservation.
Collaborative Access
Setting a threshold of shares ensures that a majority of the group must agree before a secret is used. This application of shamir secret sharing prevents any one person from acting without oversight while allowing for the absence of some members. It balances the need for security with the practicalities of a working team.
Mathematical Proof
Reliability of this method comes from its grounding in polynomial interpolation. The security of shamir secret sharing is mathematically sound, meaning an attacker with unlimited computing power still cannot guess the secret without the required shares. This creates a provable boundary that protects the most sensitive data of a founding team.