A robust threshold elliptic curve digital signature providing a new verifiable secret sharing scheme

Robust threshold digital signature schemes are group signature schemes aiming to depart from the classical one person signer schemes. The term ´robust´ means that such schemes can tolerate errors attempted by malicious adversary and the term ´threshold´ means that given a total of n players, no coalition of players with cardinality less than or equal the threshold value can perform the signature while any coalition of players exceeding the threshold value can perform the signature correctly. The contributions in this paper are two fold. First, we propose a new verifiable secret sharing scheme (VSS) other than Feldman´s (1987) and Pedersen´s (1992) schemes suitable to protect elliptic curve secret keys. The proposed scheme utilizes a strong one way function provided by the elliptic curve cryptography based on a different type of group mathematics. Next, we employ the elliptic curve VSS to propose a robust threshold elliptic curve digital signature scheme that can withstand an n/2 eavesdropping, n/3 halting and an n/4 malicious adversary. The scheme is able to tolerate n/3 malicious adversary with the cost of higher complexity