Coding Theorems for a (2,2)-Threshold Scheme With Detectability of Impersonation Attacks
Coding theorems on a (2, 2) -threshold scheme with an opponent are discussed in an asymptotic setup, where the opponent tries to impersonate one of the two participants. A situation is considered where n secrets S-n from a memoryless source is blockwisely encoded to two shares and the two shares are decoded to S-n with permitting negligible decoding error. We introduce correlation level of the two shares and characterize the minimum attainable rates of the shares and a uniform random number for realizing a -threshold scheme that is secure against the impersonation attack by the opponent. It is shown that if the correlation level between the two shares equals to l >= 0, the minimum attainable rates coincide with H(S) + l, where H(S) denotes the entropy of the source, and the maximum attainable exponent of the success probability of the impersonation attack equals to l. It is also shown that a simple scheme using an ordinary (2, 2)-threshold scheme attains all the bounds as well.
impersonation attack correlated sources hypothesis testing secret sharing scheme threshold scheme