Short linkable-and-redactable ring signature and its blockchain correcting application
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摘要:
关联可编辑环签名（LRRS）可提升区块链的匿名性，防止双花攻击，修正区块链数据，但其签名大小随环成员的增多而增大。针对该问题，结合已有LRRS和简短关联环签名方案，利用动态累加器对环成员的公钥进行累加计算，依据原知识证明签名（SPK）构造出新的SPK，提出简短LRRS（SLRRS）方案，基于该签名又提出新的区块链修正协议。在随机谕言机模型下，证明所提签名具有不可伪造性、匿名性、关联性。性能评估表明：随着环成员的增多，已有签名的大小在增大，而所提签名不变；同时此类签名所消耗的时间均在增多，而所提签名的时间增速较缓且最少。
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关键词:
- 知识证明签名 /
- 动态累加器 /
- 简短关联可编辑环签名 /
- 时间更新变色龙哈希 /
- 区块链修正
Abstract:Linkable-and-redactable ring signatures (LRRS) could improve the anonymity of blockchain, prevent double-flower attacks and correct blockchain data, but its signature size increased with the increase of ring members. With the aim of addressing the issue, this paper combined the existing LRRS and short ring signature with a dynamic accumulator to gather the public keys of ring members. Subsequently, new signatures were created based on knowledge proofs (SPK) derived from the original SPK, a short LRRS (SLRRS) was suggested, and a new blockchain correcting protocol was suggested based on the signature. In the random oracle model, the proposed signature is proved to be unforgeable, anonymous and linkable. Performance analysis demonstrates that as the number of ring members rises, the size of the current signatures grows, but the size of the proposed signature stays constant. In addition, the duration of these signatures increases, but the proposed signature's time climbs the slowest.
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表 1 各签名方案性能对比
Table 1. Performance comparison of signature schemes
方案 签名生成 签名验证 编辑 更新 签名大小 LRRS[12] $\begin{gathered} (5n + 1){T_{\rm{e}}} + (4n + 2){T_{\rm{m}}}+ \\\quad\quad (n + 2){T_{\rm{H}}} + {T_{\rm{i}}} \\\end{gathered} $ $\begin{gathered}(2n + 2){T_{\rm{e}}} + (3n + 1){T_{\rm{m}}}+ \\\quad\quad(n + 1){T_{\rm{H}}}\\\end{gathered} $ $\begin{gathered} (4n + 2){T_{\rm{e}}} + (7n + 1){T_{\rm{m}}}+\\\quad\quad (n + 2){T_{\rm{H}}} \\\end{gathered} $ $\begin{gathered}2n{T_{\rm{e}}} + 4n{T_{\rm{m}}} +\\ \quad\quad(n + 1){T_{\rm{H}}} + 2{T_{\rm{i}}} \\\end{gathered} $ $\begin{gathered} (2n + 1)||G|| + \\\quad\quad n||{\bf{Z}}_q^*|| + ||{{\bf{Z}}_q}|| \\\end{gathered} $ R-LRRS[13] $\begin{gathered}(3n + 4){T_{\rm{e}}} + 3n{T_{\rm{m}}} +\\\quad\quad(n + 3){T_{\rm{H}}} + (3n + 1){T_{\rm{P}}} \\\end{gathered} $ $\begin{gathered} (3n + 1){T_{\rm{e}}} + (3n - 2){T_{\rm{m}}} +\\\quad\quad(n + 2){T_{\rm{H}}} + (3n - 2){T_{\rm{P}}}\end{gathered} $ $\begin{gathered}6{T_{\rm{e}}} + (3n + 2){T_{\rm{m}}} + 3{T_{\rm{H}}} +\\\quad\quad (3n + 1){T_{\rm{P}}} + {T_{\rm{i}}}\\\end{gathered} $ $\begin{gathered}(2n + 1)||G|| +\\\quad\quad n||{\bf{Z}}_q^*|| + ||{{\bf{Z}}_q}|| \\\end{gathered} $ SLRRS $ 10{T_{\rm{e}}} + (n + 5){T_{\rm{m}}} + 3{T_{\rm{H}}} $ $5{T_{\rm{e}}} + (n + 3){T_{\rm{m}}} + 3{T_{\rm{H}}} + 2{T_{\rm{i}}} $ $10{T_{\rm{e}}} + (n + 9){T_{\rm{m}}} + 4{T_{\rm{H}}} + 2{T_{\rm{i}}} $ $\begin{gathered}10{T_{\rm{e}}} + (n + 9){T_{\rm{m}}} + \\\quad\quad 3{T_{\rm{H}}} + 4{T_{\rm{i}}} \\\end{gathered} $ $\begin{gathered}5||G|| + 2||{U_f}|| +\\\quad\quad 2||{{\bf{Z}}_q}||\\\end{gathered} $ 
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