Threshold Kleptographic Attacks on Discrete Logarithm Based Signatures

In an ` out of n threshold scheme, ` out of n members must cooperate to recover a secret. A kleptographic attack is a backdoor which can be implemented in an algorithm and further used to retrieve a user’s secret key. We combine the notions of threshold scheme and kleptographic attack to construct the first ` out of n threshold kleptographic attack on discrete logarithm based digital signatures and prove its security in the standard and random oracle models.