yaole
52 lines
1.4 KiB
Markdown
52 lines
1.4 KiB
Markdown
# 两方KGC下SM9协同签名
|
|
|
|
|
|
## 协同密钥关系
|
|
- 服务端密钥 $k_s \in [1,N-1]$
|
|
- 客户端密钥 $K_c=[k_s^{-1}]ds_A$
|
|
- 用户签名密钥$ds_A = [k_s]K_c$
|
|
|
|
## 签名密钥生成
|
|
```mermaid
|
|
sequenceDiagram
|
|
participant Client
|
|
participant Server
|
|
participant KGC1
|
|
participant KGC2
|
|
Note right of Server: ks <- [1,N-1]
|
|
Note right of Server: P'1 = [ks^{-1}]P1
|
|
Server->>Client: P'1
|
|
Note left of Client: ra <- [1, N-1]
|
|
Note left of Client: R = [ra]P'1
|
|
Note right of Server: 以下同[1]中A.3流程（P1替换为P'1)
|
|
Client->>KGC1: R
|
|
KGC1->>Client: t1, T1
|
|
Client->>KGC2: T1
|
|
KGC2->>Client: T2
|
|
Note left of Client: 计算Kc(= A.3中的ds_A)和Ppub-sA
|
|
```
|
|
|
|
[1] 《SM9标识密码用户私钥分布式生成指南》
|
|
|
|
## 签名
|
|
|
|
```mermaid
|
|
sequenceDiagram
|
|
participant Client
|
|
participant Server
|
|
Note left of Client: g=e(P1, Ppub-sA)
|
|
Note left of Client: r1 <- [1,N-1]
|
|
Note left of Client: u = g^{r1}
|
|
Client->>Server:u,M(=SM3(plaintext)), ID
|
|
Note right of Server: g=e(P1, Ppub-sA)
|
|
Note right of Server: r2,r3 <- [1, N-1]
|
|
Note right of Server: w = u^{r2}·g^{r3}
|
|
Note right of Server: h = H2(M||w,N)
|
|
Note right of Server: k1 = r2·ks
|
|
Note right of Server: k2 = (r3-h)·ks
|
|
Server->>Client:h,k1,k2
|
|
Note left of Client: S=[r1·k1+k2]Kc
|
|
Note left of Client: 输出签名(h,S)
|
|
```
|
|
|