# American Institute of Mathematical Sciences

May  2020, 14(2): 207-232. doi: 10.3934/amc.2020016

## Efficient traceable ring signature scheme without pairings

 School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China

* Corresponding author: Ke Gu

Received  February 2018 Revised  March 2019 Published  May 2020 Early access  September 2019

Fund Project: This work is supported by the National Natural Science Foundations of China (No.61402055), the Hunan Provincial Natural Science Foundation of China (No.2018JJ2445) and the Open Research Fund of Key Laboratory of Network Crime Investigation of Hunan Provincial Colleges (No.2017WLFZZC003)

Although currently several traceable (or linkable) ring signature schemes have been proposed, most of them are constructed on pairings. In this paper, we present an efficient traceable ring signature (TRS) scheme without pairings, which is based on the modified EDL signature (first proposed by D.Chaum et al. in Crypto 92). Compared with other ring signature schemes, the proposed scheme does not employ pairing computation and has some computational advantages, whose security can be reduced to the computational Diffie-Hellman (CDH) and decisional Diffie-Hellman (DDH) assumptions in the random oracle model. Also, the proposed scheme is similar to certificateless signature scheme, where user and key generating center make interaction to generate ring key. We give a formal security model for ring signature and prove that the proposed scheme has the properties of traceability and anonymity.

Citation: Ke Gu, Xinying Dong, Linyu Wang. Efficient traceable ring signature scheme without pairings. Advances in Mathematics of Communications, 2020, 14 (2) : 207-232. doi: 10.3934/amc.2020016
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##### References:
Performance comparisons of the Six Schemes
 Signature Size Signing Cost Verification Cost Scheme [40] $O(n)$ $(4\cdot n+3)\cdot e_1+2\cdot n\cdot m_1$ $4\cdot n\cdot e_1+n\cdot m_1$ Scheme [55] $O(n)$ $(28\cdot n+9)\cdot m_3+(22\cdot n+14)\cdot a$ $28\cdot n\cdot m_3+19\cdot n\cdot a$ Scheme [25] $O(\sqrt{n})$ $(n+9)\cdot e_1+(n+2)\cdot m_1$ $(2\cdot n+3)\cdot e_1+2\cdot n\cdot m_1+9\cdot p$ Scheme [26] $O(n)$ $(5\cdot n-1)e_1+(3\cdot n-2)\cdot m_1$ $5\cdot n\cdot e_1+3\cdot n\cdot m_1$ Scheme [4] $O(1)$ $7\cdot e_1+7\cdot m_1$ $9\cdot e_1+5\cdot m_1+7\cdot e_2+8\cdot m_2+12\cdot p$ Our Scheme $O(1)$ $5\cdot e_1+(n+1)\cdot m_1$ $4\cdot e_1+(n+3)\cdot m_1$
 Signature Size Signing Cost Verification Cost Scheme [40] $O(n)$ $(4\cdot n+3)\cdot e_1+2\cdot n\cdot m_1$ $4\cdot n\cdot e_1+n\cdot m_1$ Scheme [55] $O(n)$ $(28\cdot n+9)\cdot m_3+(22\cdot n+14)\cdot a$ $28\cdot n\cdot m_3+19\cdot n\cdot a$ Scheme [25] $O(\sqrt{n})$ $(n+9)\cdot e_1+(n+2)\cdot m_1$ $(2\cdot n+3)\cdot e_1+2\cdot n\cdot m_1+9\cdot p$ Scheme [26] $O(n)$ $(5\cdot n-1)e_1+(3\cdot n-2)\cdot m_1$ $5\cdot n\cdot e_1+3\cdot n\cdot m_1$ Scheme [4] $O(1)$ $7\cdot e_1+7\cdot m_1$ $9\cdot e_1+5\cdot m_1+7\cdot e_2+8\cdot m_2+12\cdot p$ Our Scheme $O(1)$ $5\cdot e_1+(n+1)\cdot m_1$ $4\cdot e_1+(n+3)\cdot m_1$
Other comparisons of the Six Schemes
 Cryptography Traceability Model Scheme [40] Public Key No random oracle Scheme [55] Public Key No random oracle Scheme [25] Public Key Yes without random oracle Scheme [26] Public Key Yes random oracle Scheme [4] Identity-Based Yes random oracle Our Scheme Public Key Yes random oracle
 Cryptography Traceability Model Scheme [40] Public Key No random oracle Scheme [55] Public Key No random oracle Scheme [25] Public Key Yes without random oracle Scheme [26] Public Key Yes random oracle Scheme [4] Identity-Based Yes random oracle Our Scheme Public Key Yes random oracle

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