Possible Uses for Mathematical Secret Sharing

Secret Sharing is difficult mathematically, but has been accomplished “recently,” as such developments go. It is analogous to developing a Cartesian equation of an order of the number of participants, plus one, and then choosing such points on the line, as to compute the Y-intercept, from the known data, without the formula. The Shamir Secret Sharing Scheme, accomplishes this with matrix algebra.

As with other mathematical novelties, applications might be hard to imagine. DNSSec has used SSSS, (demo) to secure the root certificate authority.

Two other applications include, a family system administration authority, and a drug dealer border violation gambit.

In the family admin example, the shares would number four, and the quorum would be three, such that both parents and any single minor child, would need to agree, to break privilege. This would require one share to be destroyed at generation, or stored with a will and testament. A similar effort, wherein there are three keys, but the third key can be is distributed to all junior participants equally, would require a different scheme, to implement it. If the shares were three, and the quorum two, then the adults would not need consent, whereas either of these could ask a minor to conspire against the other.

In the example of a drug dealer, the intruder would encrypt and transmit across the theorized border, with five shares and a quorum of three. Then, he would send couriers across the border, one at a time, establishing safe arrival of each. At any time that two were detained, the system would be abandoned, the data re-encrypted with new keys, and the “game” restarted.

While that is largely theoretical, we hope to moot an interesting discussion, and prime the pump for other legitimate applications of secret sharing.


About James Johnson

I am an amateur mathematician & political theorist who enjoys (occasionally cerebral) humor.
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