As a fundamental cryptographic tool, (t,n)-threshold secret sharing ((t,n)-SS) divides a secret among n shareholders and requires at least t, (t<=n), of them to reconstruct the secret. Ideal (t,n)-SSs are most desirable in security and efficiency among basic (t,n)-SSs. However, an adversary, even without any valid share, may mount Illegal Participant (IP) attack or t/2-Private Channel Cracking (t/2-PCC) attack to obtain the secret in most (t,n)-SSs.To secure ideal (t,n)-SSs against the 2 attacks, 1) the paper introduces the notion of Ideal Tightly cOupled (t,m,n) Secret Sharing (or (t,m,n)-ITOSS ) to thwart IP attack without Verifiable SS; (t,m,n)-ITOSS binds all m, (m>=t), participants into a tightly coupled group and requires all participants to be legal shareholders before recovering the secret. 2) As an example, the paper presents a polynomial-based (t,m,n)-ITOSS scheme, in which the proposed k-round Random Number Selection (RNS) guarantees that adversaries have to crack at least symmetrical private channels among participants before obtaining the secret. Therefore, k-round RNS enhances the robustness of (t,m,n)-ITOSS against t/2-PCC attack to the utmost. 3) The paper finally presents a generalized method of converting an ideal (t,n)-SS into a (t,m,n)-ITOSS, which helps an ideal (t,n)-SS substantially improve the robustness against the above 2 attacks.
翻译:作为基本的加密工具, (t,n) 秘密分享(t,n) 秘密分享(t,n) 在股东之间划分一个秘密, 并且至少要求股东重建秘密。 理想( t,n) SS 在基本( t,n) SS之间最需要安全和效率。 但是, 对手, 即使没有任何有效份额, 也可能发动非法参与者( IP) 攻击或 //2 私人通道裂缝( t/2- PC) 攻击, 以获得大多数( t,n) SS 的秘密。 要确保理想( t,n) 安全( t,n) 安全( t,n) 秘密分享( t,n) 最理想( IT) 概念, 秘密分享( 或 (t,m,n) IT(t,n) 防止IP袭击, (t,m) 秘密( NS, (m) SS) 参与者组成一个紧密的小组, 要求所有参与者在恢复秘密之前成为法律股东( t) 秘密(t) 秘密(r) 方法, 最后展示(i) 纸- 数字(i) (i) 显示, 数字。