# 基于身份的数字签名算法

2019/03/31

## 预备知识

1. Bilinear Pairing

$(G_{1},*),(G_{2},*),(G_{T},*)$ are three cyclic groups of the same prime order $p$. Let $g_{1}$ be a generator of $G_{1}$ and $g_{2}$ be a generator of $G_{2}$. e: $G_{1} × G_{2} → G_{T}$ is a bilinear map, which satisfies:

1. Bilinear: $e(u^{a},v^{b}) = e(u,v)^{ab}$ for all $u ∈ G_{1}, v ∈ G_{2}$ and $a, b ∈ Z_{p}$;

2. Non-degeneracy: $e(g_{1}, g_{2})\neq1_{G_{T}}$;

3. Admissible: the map $e$ is efficiently computable.

2. Elliptic Curve Discrete Logarithm Problem

Given a point $P$ of order $q$ on an elliptic curve, and a point $Q$ on the same curve, the ECDLP problem is to determine the integer $l,0\leq l\leq q−1$,such that $Q=lP$.

3. Computational Diffie-Hellman problem

Given two unknowns $a, b ∈ Z_{q}$, the CDH problem is given $P,aP,bP ∈G$,compute $abP ∈G$.

## 方案二

### 初始化

$s$为私钥，其余可以公开的参数为：

## 参考文献

CPAS：An Efficient Conditional Privacy-Preserving Authentication Scheme for Vehicular Sensor Networks

## 补充

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