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    • 63. 发明申请
    • SIGNING METHODS FOR DELIVERING PARTIAL SIGNATURES, AND/OR THRESHOLD SIGNATURES, CORRESPONDING VERIFICATION METHODS, AND CORRESPONDING ELECTRONIC DEVICES
    • 用于传递部分信号和/或阈值信号的签名方法,相应的验证方法和相应的电子设备
    • WO2015118160A1
    • 2015-08-13
    • PCT/EP2015/052681
    • 2015-02-10
    • THOMSON LICENSING
    • JOYE, MarcLIBERT, Benoit
    • H04L9/32
    • H04L9/3255
    • In one embodiment, it is proposed a signing method delivering a partial signature associated with a message, said partial signature being used in a threshold signing method, the signing method being executed on an electronic device. The signing method is remarkable in that it comprises: - obtaining a partial secret key SK i being obtained from an output of a secret sharing scheme, said partial secret key SK i being equal to {u1 ( i ), u K+1 ( i )}, where elements u j ( i ) ∈ Z p for all j ∈ {1,..., K + 1}, with p being a prime number, and K being an integer greater or equal to one; - determining from said partial key, K elements tj = g -uj(i) , with j ∈ {1,..., K + 1} and g being a generator of a group G, said group G being part of a bilinear group (G, Ĝ, G T ) with Ĝ being a group and G T being a target group; - determining from said message a vector so as to define a Groth-Sahai common reference string; - determining Groth-Sahai commitments on said K + 1 elements t j with j ∈ {1,..., Κ + 1} from said Groth-Sahai common reference string, said Groth-Sahai commitments belonging to said group G; and - determining a non-interactive witness indistinguishable proof comprising K ( K + 1) elements, all the K ( K + 1) elements belonging to said group Ĝ, said proof guarantying that said K + 1 elements tj verify K pairing equations; - delivering said partial signature associated with said message, said partial signature comprising said Groth-Sahai commitments, and said non-interactive witness indistinguishable proof.
    • 在一个实施例中,提出了传递与消息相关联的部分签名的签名方法,所述部分签名在阈值签名方法中使用,所述签名方法在电子设备上执行。 签名方法是显着的,其包括: - 获得从秘密共享方案的输出获得的部分秘密密钥SK i,所述部分秘密密钥SK i等于{u1(i),uK + 1(i) },其中对于所有j∈{1,...,K + 1},元素uj(i)∈Zp,其中p是素数,K是大于或等于1的整数; - 从所述部分密钥确定K个元素tj = g -uj(i),其中j∈{1,...,K + 1},g是组G的生成器,所述组G是双线性 组(G,Ĝ,GT),Ĝ为组,GT为目标组; - 从所述消息确定向量以定义Groth-Sahai公共参考串; 表示所罗门群岛G所表示的Groth-Sahai承诺,对所述第K + 1个元素t j确定了Groth-Sahai承诺,其中j∈{1,...,Κ+ 1} 以及 - 确定包含K(K + 1)个元素,属于所述组,的所有K(K + 1)个元素的非交互式证据不可区分的证明,所述证明保证所述K + 1个元素tj验证K个配对方程; - 提供与所述消息相关联的所述部分签名,所述部分签名包括所述Groth-Sahai承诺,以及所述非交互式证人不可区分的证明。