Weaknesses in some threshold cryptosystems

Abstract

Threshold cryptosystems allow n members of a group to share a private key such that any k of them can use the key without revealing its value. These systems can be divided into two categories, systems which use a trusted center to generate the shares and systems which create the shares in a distributed manner. This paper describes a number of security weaknesses which arise in systems which do not use a trusted center. We show that the n-out-of-n threshold undeniable signature scheme [8] has an actual security of only 2-out-of-n. The discrete log based threshold signature schemes [7, 11, 12] have a weakness in the key generation protocol. Finally, the generalized threshold cryptosystem [9] is not secure for some access structures.