Two Improved Proxy Multi-signature Schemes Based on the Elliptic Curve Cryptosystem

In, a proxy signature scheme, one original signer delegates a proxy signer to sign messages on behalf of the original signer. In a proxy multi-signature scheme, n original signers cooperate to delegate their signing power to one proxy signer. In 2003, Chen, Chung and Huang proposed one proxy-protected proxy multi-signature scheme (CCH1 scheme) based on the elliptic curve cryptosystem. Park et al. pointed out that CCH1 scheme is insecure, however, they didn't provide a modified scheme or new schemes. To resist the forgery attack from the original signer proposed by Park et al., based on CCH1 scheme, one improved scheme is proposed. In 2004, Chen, Chung and Huang proposed another proxy multi-signature scheme (CCH2 scheme) also based on the elliptic curve cryptosystem. By observation, Park et al. showed that CCH2 scheme can't resist the conspiracy attack from all original signers. As to CCH2 scheme, Park et al. neither provided an improved version or new version. Based on CCH2 scheme, a modified scheme is brought forward.