🚀 go-pugleaf

In article <1993Jan24.213350.17257@news.cs.indiana.edu>, Marc VanHeyningen <mvanheyn@whale.cs.indiana.edu> writes:
> An interesting generalization of the above is how to cryptographically
> create a situation whereby any m people in a group of n (of course,
> the problem is only hard when n > m > 1) must cooperate to read a
> message.  I seem to recall having heard that it's possible, but I
> don't remember the details.

I suspect you're thinking of

@article{sharesecret,
   author = {Adi Shamir},
   journal = {Communications of the ACM},
   number = {11},
   pages = {612-613},
   title = {How to Share a Secret},
   volume = {22},
   year = {1979}
}

This relies on polynomial interpolation.  If you're missing even one
piece of the shared key, all possible values become equally likely.

A totally different way to solve the same problem is given in

@article{sealing,
   author = {David K. Gifford},
   journal = {Communications of the ACM},
   number = {4},
   pages = {274--286},
   title = {Cryptographic Sealing for Information Secrecy and Authentication},
   volume = {25},
   year = {1982}
}

Gifford shows how to use a combination of symmetric and asymmetric
cryptography to implement things like Key-And, Key-Or, the problem
described above, etc.