The Inevitability of Side-Channel Leakage in Encrypted Traffic

LIU Guangjie; CHENG Guang; LIU Weiwei

doi:10.12263/DZXB.20251034

您当前的位置：

首页 >

文章列表页 >

The Inevitability of Side-Channel Leakage in Encrypted Traffic

PAPERS | 更新时间：2026-05-28

- The Inevitability of Side-Channel Leakage in Encrypted Traffic
- ACTA ELECTRONICA SINICA Vol. 54, Issue 2, Pages: 837-850(2026)
- 作者机构：
  
  1.南京信息工程大学电子与信息工程学院，江苏南京 210044
  2.东南大学网络空间安全学院，江苏南京 211189
  3.南京理工大学自动化学院，江苏南京 210094
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(U24366001;U22B2025)
- DOI：10.12263/DZXB.20251034
  CLC： TP391;
- Received：30 December 2025，
  
  Accepted：24 February 2026，
  
  Published：25 February 2026
- 稿件说明：
移动端阅览
刘光杰, 程光, 刘伟伟. 加密流量侧信道泄漏的不可避免性[J]. 电子学报, 2026, 54(02): 837-850.

LIU Guangjie, CHENG Guang, LIU Weiwei. The Inevitability of Side-Channel Leakage in Encrypted Traffic[J]. Acta Electronica Sinica, 2026, 54(02): 837-850.
刘光杰, 程光, 刘伟伟. 加密流量侧信道泄漏的不可避免性[J]. 电子学报, 2026, 54(02): 837-850. DOI：10.12263/DZXB.20251034

LIU Guangjie, CHENG Guang, LIU Weiwei. The Inevitability of Side-Channel Leakage in Encrypted Traffic[J]. Acta Electronica Sinica, 2026, 54(02): 837-850. DOI：10.12263/DZXB.20251034

摘要

TLS 1.3与QUIC的普及使载荷内容不可见，流量分析转而依赖侧信道特征，但侧信道泄漏在加密通信中为何不可避免，长期缺乏严谨论证。本文从信息论与系统设计出发，构建形式化模型

</mo><mi>Ω</mi><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259852&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259839&type=

11.93799973

2.87866688

，其中加密通信模型

</mo><mi>Π</mi><mo>

</mo><mi>Φ</mi><mo>

</mo><mi>N</mi><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259841&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259840&type=

19.04999924

2.87866688

描述“应用生成、协议封装、加密变换、网络传输”的因果链，观察模型

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259817&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259832&type=

2.37066650

2.28600001

刻画外部观测能力。该框架将完整通信过程抽象为因果可测的马尔可夫链

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259856&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259843&type=

38.43866730

3.21733332

，使语义变量到可观测特征之间的互信息严格可定义。基于复合信道结构、数据处理不等式与有界Lipschitz统计量的稳定传递性，提出并证明“侧信道存在性定理”：对于可辨识的语义对，在系统满足映射非退化性（度量期望有界

</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></mfenced><mo>∣</mo><mi>X</mi></mrow></mfenced><mo>≤</mo><mi>C</mi></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259846&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259865&type=

25.90800095

4.48733330

）、协议层统计可辨识性（期望差

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259867&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259858&type=

4.14866638

2.70933342

）、统计量Lipschitz连续性、观测非退化性（保留比例

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259894&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259882&type=

6.18066692

2.87866688

）以及可辨识性传递条件（

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259869&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259861&type=

12.27666664

3.64066648

）的前提下，观测特征与语义变量的互信息

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259909&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259908&type=

9.99066734

2.96333337

必然严格为正且存在显式下界。推论表明，在效率优先的多元语义系统中，只要存在至少一对应用在统计上可区分，侧信道泄漏就不可避免。3个关键因素共同决定泄漏边界：映射非退化常数

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259887&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259910&type=

2.28600001

受效率约束限制，反映带宽、时延等实用性要求；语义可辨识性

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259912&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259899&type=

1.94733346

2.70933342

源于应用多样性，体现不同应用在统计特征上的固有差异；观测非退化性

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259901&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259874&type=

1.77800000

2.87866688

由分析者能力决定。本文进一步通过全变差与Chernoff信息的下界链条，建立了从信息论下界到分类准确率的量化联系，揭示了多次观测使识别错误率指数衰减的必然性。理论分析表明，降低泄漏面临三种困境：增大度量偏差需牺牲效率，减小语义可辨识性将破坏应用功能，而观测非退

化性由分析者控制。因此，侧信道并非协议实现的偶发瑕疵，而是满足实用性约束的网络通信系统的内在属性，正确的工程目标是在给定效率约束下最小化泄漏的约束优化问题。本文首次为加密流量侧信道建立严格的信息论基础，为攻击可达性提供可检验的预测，为防御机制提供可量化的性能基准，并为效率-隐私权衡的工程决策提供数学依据。

Abstract

The widespread adoption of TLS 1.3 and QUIC renders payload content invisible

shifting traffic analysis toward side-channel features. However

rigorous justification for “why side-channel leakage is inevitable in encrypted communications” has long been lacking. This paper establishes a strict foundation from information theory and system design by constructing a formal model

</mo><mi>Ω</mi><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259876&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259914&type=

11.93799973

2.87866688

where the encrypted communication system

</mo><mi>Π</mi><mo>

</mo><mi>Φ</mi><mo>

</mo><mi>N</mi><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259904&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259892&type=

19.04999924

2.87866688

describes the causal chai

n of “application generation-protocol encapsulation-encryption transformation-network transmission”

and the observation model

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259939&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259924&type=

2.37066650

2.28600001

characterizes external observation capabilities. This framework abstracts the complete communication process as a causally measurable Markov chain

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259920&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259926&type=

38.43866730

3.21733332

enabling the mutual information between semantic variables and observable features to be rigorously defined. Based on the composite channel structure

data processing inequality

and stable propagation of bounded Lipschitz statistics

we propose and pro

ve the “Side-Channel Existence Theorem”: for distinguishable semantic pairs

under the conditions that the system satisfies mapping non-degeneracy (bounded metric expectation

</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></mfenced><mo>∣</mo><mi>X</mi></mrow></mfenced><mo>≤</mo><mi>C</mi><mtext> </mtext><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259929&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259953&type=

27.34733391

4.48733330

protocol-layer statistical distinguishability (expectation difference

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259968&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259954&type=

4.14866638

2.70933342

)

Lipschitz continuity of statistics

observation non-degeneracy (preservation ratio

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259932&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259955&type=

6.18066692

2.87866688

)

and the distinguishability propagation condition (

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259947&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259970&type=

12.27666664

3.64066648

)

the mutual information

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259972&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259971&type=

9.31333351

2.87866688

between observed features and semantic variables is necessarily strictly positive with an explicit lower bound. The corollary demon

strates that in efficiency-prioritized multi-semantic systems

side-channel leakage is inevitable as long as at least one pair of applications is statistically distinguishable. Three key factors jointly determine the leakage boundary: the mapping non-degeneracy constant

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259937&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259949&type=

2.28600001

is constrained by efficiency requirements

reflecting practical demands such as bandwidth and latency; semantic distinguishability

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259983&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259975&type=

1.94733346

2.70933342

stems from application diversity

embodying inherent differences in statistical characteristics across applications; and observation non-degeneracy

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259952&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=109259977&type=

1.77800000

2.87866688

is determined by analyst capabilities. This paper further establishes a quantitative connection from information-theoretic lower bounds to classification accuracy through the chain of total variation and Chernoff information bounds

revealing the inevitability that multiple observations cause recognition error rates to decay exponentially. Theoretical analysis shows that reducing leakage faces a trilemma: increasing metric deviation requires sacrificing efficiency

reducing semantic distinguishability disrupts application functionality

while observation non-degeneracy is controlled by analysts. Therefore

side channels are not incidental flaws in protocol implementations but inherent properties of network communication systems subject to practicality constraints

and the correct engineering objective is a constrained optimization problem that minimizes leakage under given efficiency constraints. This paper establishes

for the first time

a rigorous information-theoretic foundation for encrypted traffic side channels

providing verifiable predictions for attack feasibility

quantifiable performance benchmarks for defense mechanisms

and mathematical basis for engineering decisions on efficiency-privacy tradeoffs.

关键词

Keywords

references

Wang T , Cai X , Nithyanand R , et al . Effective attacks and provable defenses for website fingerprinting [C ] // Proceedings of the 23rd USENIX conference on Security Symposium . New York : ACM , 2014 : 143 - 157 .

Shen M , Zhang J P , Zhu L H , et al . Accurate decentralized application identification via encrypted traffic analysis using graph neural networks [J ] . IEEE Transactions on Information Forensics and Security , 2021 , 16 : 2367 - 2380 . DOI: 10.1109/tifs.2021.3050608 http://dx.doi.org/10.1109/tifs.2021.3050608

Mei H T , Cheng G , Yuan Y L . High precision and efficient anonymous traffic classification in the real-world [J ] . IEEE Transactions on Networking , 2025 , 33 ( 3 ): 966 - 981 . DOI: 10.1109/ton.2024.3518976 http://dx.doi.org/10.1109/ton.2024.3518976

Kocher P C . Timing attacks on implementations of diffie-Hellman, RSA, DSS, and other systems [C ] // Advances in Cryptology - CRYPTO’96 . Berlin, Heidelberg : Springer , 1996 : 104 - 113 . DOI: 10.1007/3-540-68697-5_9 http://dx.doi.org/10.1007/3-540-68697-5_9

Kocher P , Jaffe J , Jun B . Differential power analysis [C ] // Advances in Cryptology - CRYPTO’99 . Berlin, Heidelberg : Springer , 1999 : 388 - 397 . DOI: 10.1007/3-540-48405-1_25 http://dx.doi.org/10.1007/3-540-48405-1_25

Hintz A . Fingerprinting websites using traffic analysis [M ] // Privacy enhancing technologies . Berlin, Heidelberg : Springer , 2003 : 171 - 178 . DOI: 10.1007/3-540-36467-6_13 http://dx.doi.org/10.1007/3-540-36467-6_13

Lin X J , Xiong G , Gou G P , et al . ET-BERT: A contextualized datagram representation with pre-training transformers for encrypted traffic classification [C ] // Proceedings of the ACM Web Conference 2022 . New York : ACM , 2022 : 633 - 642 . DOI: 10.1145/3485447.3512217 http://dx.doi.org/10.1145/3485447.3512217

Shen M , Ye K , Liu X T , et al . Machine learning-powered encrypted network traffic analysis: A comprehensive survey [J ] . IEEE Communications Surveys & Tutorials , 2023 , 25 ( 1 ): 791 - 824 . DOI: 10.1109/comst.2022.3208196 http://dx.doi.org/10.1109/comst.2022.3208196

Li S , Guo H , Hopper N . Measuring information leakage in website fingerprinting attacks and defenses [C ] // Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security . New York : ACM , 2018 : 1977 - 1992 . DOI: 10.1145/3243734.3243832 http://dx.doi.org/10.1145/3243734.3243832

Cai X , Nithyanand R , Wang T , et al . A systematic approach to developing and evaluating website fingerprinting defenses [C ] // Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security . New York : ACM , 2014 : 227 - 238 . DOI: 10.1145/2660267.2660362 http://dx.doi.org/10.1145/2660267.2660362

Dwork C , Kenthapadi K , McSherry F , et al . Our data, ourselves: Privacy via distributed noise generation [C ] // Advances in Cryptology - EUROCRYPT 2006 . Berlin, Heidelberg : Springer , 2006 : 486 - 503 . DOI: 10.1007/11761679_29 http://dx.doi.org/10.1007/11761679_29

Sabzi A , Vora R , Goswami S , et al . NetShaper: A differentially private network side-channel mitigation system [C ] // Proceedings of the 33rd USENIX Security Symposium . Berkeley : USENIX Association , 2024 : 3385 - 3402 .

Chaum D L . Untraceable electronic mail, return addresses, and digital pseudonyms [J ] . Communications of the ACM , 1981 , 24 ( 2 ): 84 - 90 . DOI: 10.1145/358549.358563 http://dx.doi.org/10.1145/358549.358563

Díaz C , Seys S , Claessens J , et al . Towards measuring anonymity [M ] // Privacy enhancing technologies . Berlin, Heidelberg : Springer , 2003 : 54 - 68 . DOI: 10.1007/3-540-36467-6_5 http://dx.doi.org/10.1007/3-540-36467-6_5

Deng Y X , Pang J , Wu P . Measuring anonymity with relative entropy [C ] // Formal Aspects in Security and Trust . Berlin, Heidelberg : Springer , 2007 : 65 - 79 .

Serjantov A , Danezis G . Towards an information theoretic metric for anonymity [C ] // Privacy Enhancing Technologies . Berlin, Heidelberg : Springer , 2003 : 41 - 53 . DOI: 10.1007/3-540-36467-6_4 http://dx.doi.org/10.1007/3-540-36467-6_4

Chatzikokolakis K , Palamidessi C , Panangaden P . Anonymity protocols as noisy channels [J ] . Information and Computation , 2008 , 206 ( 2/3/4 ): 378 - 401 . DOI: 10.1016/j.ic.2007.07.003 http://dx.doi.org/10.1016/j.ic.2007.07.003

Kedogan D , Agrawal D , Penz S . Limits of anonymity in open environments [M ] // Information Hiding . Berlin, Heidelberg : Springer , 2002 : 53 - 69 . DOI: 10.1007/3-540-36415-3_4 http://dx.doi.org/10.1007/3-540-36415-3_4

Danezis G . Statistical disclosure attacks [M ] // Security and privacy in the age of uncertainty . Boston, MA : Springer US , 2003 : 421 - 426 . DOI: 10.1007/978-0-387-35691-4_40 http://dx.doi.org/10.1007/978-0-387-35691-4_40

Jelle V D H , Lazar D , Zaharia M , et al . Vuvuzela: Scalable private messaging resistant to traffic analysis [C ] // Proceedings of the 25th Symposium on Operating Systems Principles . New York : ACM , 2015 : 137 - 152 . DOI: 10.1145/2815400.2815417 http://dx.doi.org/10.1145/2815400.2815417

Tyagi N , Gilad Y , Leung D , et al . Stadium: A distributed metadata-private messaging system [C ] // Proceedings of the 26th Symposium on Operating Systems Principles . New York : ACM , 2017 : 423 - 440 . DOI: 10.1145/3132747.3132783 http://dx.doi.org/10.1145/3132747.3132783

Panchenko A , Niessen L , Zinnen A , et al . Website fingerprinting in onion routing based anonymization networks [C ] // Proceedings of the 10th Annual ACM Workshop on Privacy in the Electronic Society . New York : ACM , 2011 : 103 - 114 . DOI: 10.1145/2046556.2046570 http://dx.doi.org/10.1145/2046556.2046570

Dyer K P , Coull S E , Ristenpart T , et al . Peek-a-boo, I still see you: Why efficient traffic analysis countermeasures fail [C ] // 2012 IEEE Symposium on Security and Privacy . Piscataway : IEEE , 2012 : 332 - 346 . DOI: 10.1109/sp.2012.28 http://dx.doi.org/10.1109/sp.2012.28

Wang T , Goldberg I . Walkie-talkie: An efficient defense against passive website fingerprinting attacks [C ] // Proceedings of the 26th USENIX Security Symposium . Berkeley : USENIX Association , 2017 : 1375 - 1390 .

Huang J N , Liu W W , Liu G J , et al . STAP: Leveraging state-transition adversarial perturbations for asymmetric website fingerprinting defenses [J ] . IEEE Transactions on Network and Service Management , 2025 , 22 ( 6 ): 6200 - 6214 . DOI: 10.1109/tnsm.2025.3597075 http://dx.doi.org/10.1109/tnsm.2025.3597075

Wright C V , Coull S E , Monrose F . Traffic morphing: An efficient defense against statistical traffic analysis [C ] // Proceedings of the 16th Network and Distributed Security Symposium . Reston : The Internet Society , 2009 : 237 - 250 .

Cherubin G . Bayes, not Naïve: Security bounds on website fingerprinting defenses [J ] . Proceedings on Privacy Enhancing Technologies , 2017 , 2017( 4 ): 215 - 231 . DOI: 10.1515/popets-2017-0046 http://dx.doi.org/10.1515/popets-2017-0046

Fu C P , Li Q , Shen M , et al . Realtime robust malicious traffic detection via frequency domain analysis [C ] // Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security . New York : ACM , 2021 : 3431 - 3446 . DOI: 10.1145/3460120.3484585 http://dx.doi.org/10.1145/3460120.3484585

Fu C P , Li Q , Shen M , et al . Detecting tunneled flooding traffic via deep semantic analysis of packet length patterns [C ] // Proceedings of the 2024 on ACM SIGSAC Conference on Computer and Communications Security . New York : ACM , 2024 : 3659 - 3673 . DOI: 10.1145/3658644.3670353 http://dx.doi.org/10.1145/3658644.3670353

Fu C P , Li Q , Xu K . Detecting unknown encrypted malicious traffic in real time via flow interaction graph analysis [PP/OL ] . V1. arXiv ( 2023-01-31 )[ 2025-12-29 ] . https://arXiv.org/abs/2301.13686 https://arXiv.org/abs/2301.13686 . DOI: 10.14722/ndss.2023.23080 http://dx.doi.org/10.14722/ndss.2023.23080

Camenisch J , Lysyanskaya A . A formal treatment of onion routing [C ] // Advances in Cryptology - CRYPTO 2005 . Berlin, Heidelberg : Springer , 2005 : 169 - 187 . DOI: 10.1007/11535218_11 http://dx.doi.org/10.1007/11535218_11

Feigenbaum J , Johnson A , Syverson P . A model of onion routing with provable anonymity [C ] // Financial Cryptography and Data Security . Berlin, Heidelberg : Springer , 2007 : 57 - 71 . DOI: 10.1007/978-3-540-77366-5_9 http://dx.doi.org/10.1007/978-3-540-77366-5_9

Danezis G , Goldberg I . Sphinx: A compact and provably secure mix format [C ] // 2009 30th IEEE Symposium on Security and Privacy . Piscataway : IEEE , 2009 : 269 - 282 . DOI: 10.1109/sp.2009.15 http://dx.doi.org/10.1109/sp.2009.15

Gray R M . Probability, random processes, and ergodic properties [M ] . New York : Springer , 1988 . DOI: 10.1007/978-1-4757-2024-2_6 http://dx.doi.org/10.1007/978-1-4757-2024-2_6

Cover T M , Thomas J A . Elements of information theory [M ] . 2nd ed . Hoboken : J. Wiley , 2006 .

Shen M , Ji K X , Wu J H , et al . Real-time website fingerprinting defense via traffic cluster anonymization [C ] // 2024 IEEE Symposium on Security and Privacy . Piscataway : IEEE , 2024 : 3238 - 3256 . DOI: 10.1109/sp54263.2024.00247 http://dx.doi.org/10.1109/sp54263.2024.00247

Cai X , Nithyanand R , Johnson R . CS-BuFLO: A congestion sensitive website fingerprinting defense [C ] // Proceedings of the 13th Workshop on Privacy in the Electronic Society . New York : ACM , 2014 : 121 - 130 . DOI: 10.1145/2665943.2665949 http://dx.doi.org/10.1145/2665943.2665949

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Unknown Encrypted Malicious Traffic Detection via Burst Feature Token Self-Learning

SMT Port Side Channel Attack Defending Method Based on Dynamic Branch Filter

A Review of Encryption Traffic Analysis Methods Based on Large Language Models

Automatic Modulation Recognition Method via Conceal-Truth-While-Showing-Fake Strategy in Non-Cooperative Adversarial Scenarios

Radar Target Unsupervised Anomaly Detection with Multi-Domain Representation Alignment and Fusion

Related Author

SHEN Meng

JIA Ji-zhe

ZHAO Bu-fan

CHANG Li-yuan

YANG Ming

ZHU Lie-huang

SONG Yue

REN Chen-chen

Related Institution

National Supercomputing Center in Jinan

Department of Basic Ability, China Telecom Cybersecurity Technology Co., Ltd.

School of Cyberspace Science and Technology, Beiijing Institute of Technology

University of Chinese Academy of Sciences

National Engineering Research Center for Fundamental Software, Institute of Software, Chinese Academy of Sciences

⁰