Key Reconstruction

The key reconstruction problem is an application of (n,t)-threshold schemes. Such schemes permit an arbitrary piece of information to be ‘broken’ into n different ‘fragments,’ any t of which may be used to completely reconstruct the original information. No smaller number of fragments provides any information concerning the original, aside from its size in bits. These n fragments may then be distributed to different individuals, any t of whom can later cooperate in the reconstruction of the original information. For our purposes, the original information might be a private key in a public key cryptosystem.