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针对门限多重代理多重签名方案中存在的内部成员合谋攻击、伪造攻击、签名方权限不同等安全问题,文章利用hash函数的单向性,基于离散对数问题的难解性,结合Shamir(t,n)门限方案,提出一种存在特权集的多重代理多重签名方案。方案中,任意t_1个或t_1个以上的原始签名者且特权集中至少有t′1个特权用户可以代表原始签名群UO将签名权委托给代理签名群UP,任意t_2个或t_2个以上的代理签名者且特权集至少有t′_2个特权用户可以代表代理签名群UP对消息M进行签名。安全性分析表明,方案具有门限代理签名应具有的安全性。
Aiming at the security problems of internal member collusion attack, counterfeit attack, different authority of signer and so on, which exist in the threshold multi-proxy multi-signature scheme, this paper makes use of the unidirectionality of hash function and the disjointness of discrete logarithm problem. Combined with Shamir (t, n) threshold scheme, a multi-proxy multi-signature scheme with privilege set is proposed. In the scheme, any t_1 or t_1 original signers and at least t’1 privileged users in the privilege set may entrust the signature right to the proxy signature group UP, any proxy of t_2 or more than t_2 on behalf of the original signature group UO Signed and Privilege Sets At least t’_2 privileged users can sign the message M on behalf of the proxy signed group UP. Security analysis shows that the scheme should have the security of threshold proxy signature.