基于神经网络的随机数生成器评估综述

doi:10.3969/j.issn.1671-1122.2026.02.001

摘要/Abstract

摘要：

随机数在密码学应用和密码系统中扮演着关键角色，其质量直接关系到系统的安全性。文章综述了基于神经网络的随机数生成器评估方法的最新研究进展。首先，介绍随机数生成器及其现有随机性测试套件；其次，重点分析基于神经网络的评估方法，包括预测模型与分类模型；再次，通过与传统评估方法对比，详细阐述神经网络在随机数生成器评估中的优势与潜力；最后，指出当前研究中存在的关键问题及未来改进方向。

关键词: 随机数生成器, 神经网络, 熵估计, 密码学

Abstract:

Random numbers play a crucial role in cryptographic applications and cryptosystems, and their quality directly affects the security of these systems. This article reviewed recent advances in evaluation methods for random number generators based on neural networks. First, it introduced random number generators and existing randomness test suites. Second, it focused on neural network-based evaluation methods, including prediction models and classification models. Third, by comparing with traditional evaluation methods, it elaborated on the advantages and potential of neural networks in assessing random number generators. Finally, it identified key challenges in current research and outlined future directions for improvement.

Key words: random number generator, neural networks, entropy estimation, cryptographic

中图分类号:

TP309

韩益亮, 冯浩康, 吴旭光, 孙钰腾, 王圆圆. 基于神经网络的随机数生成器评估综述[J]. 信息网络安全, 2026, 26(2): 171-188.

HAN Yiliang, FENG Haokang, WU Xuguang, SUN Yuteng, WANG Yuanyuan. A Survey of Neural Network-Based Evaluation of Random Number Generators[J]. Netinfo Security, 2026, 26(2): 171-188.

图/表 14

图1

表1

图2

图3

图4

表2

图5

表3

表4

图6

图7

图8

图9

表5

参考文献 60

[1]	CHEN Dongyu, CHEN Hua, FAN Limin, et al. Research on Test Strategy for Randomness Based on Deep Learning[J]. Journal on Communications, 2023, 44(6): 23-33. doi: 10.11959/j.issn.1000-436x.2023111
	陈东昱, 陈华, 范丽敏, 等. 基于深度学习的随机性检验策略研究[J]. 通信学报, 2023, 44(6): 23-33. doi: 10.11959/j.issn.1000-436x.2023111
[2]	YOSHIYA K, TERASHIMA Y, KANNO K, et al. Entropy Evaluation of White Chaos Generated by Optical Heterodyne for Certifying Physical Random Number Generators[J]. Optics Express, 2020, 28(3): 3686-3698. doi: 10.1364/OE.382234 pmid: 32122032
[3]	WANG Anbang, WANG Yuncai, WANG Bingjie, et al. Physical White Chaos Generation[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2015, 21(6): 531-540. doi: 10.1109/JSTQE.2015.2427253 URL
[4]	MARSAGLIA G. Random Number CDROM Including the Diehard Battery of Tests of Randomness[EB/OL]. (1995-12-09).[2025-02-03]. https://cir.nii.ac.jp/crid/1571698600607540352.
[5]	L’ECUYER P, SIMARD R. TestU01: A C Library for Empirical Testing of Random Number Generators[J]. ACM Transactions on Mathematical Software, 2007, 33(4): 1-40.
[6]	TURAN M S, BARKER E, KELSEY J, et al. Recommendation for the Entropy Sources Used for Random Bit Generation: NIST SP 800-90b[EB/OL]. (2025-01-27)[2025-03-27]. https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-90B.pdf.
[7]	GISIN N, RIBORDY G, TITTEL W, et al. Quantum Cryptography[J]. Reviews of Modern Physics, 2002, 74(1): 145-195. doi: 10.1103/RevModPhys.74.145 URL
[8]	FENG Yulong, HAO Lingyi. Testing Randomness Using Artificial Neural Network[J]. IEEE Access, 2020, 8: 163685-163693.
[9]	VOLOVICH I V. Randomness in Classical Mechanics and Quantum Mechanics[J]. Foundations of Physics, 2011, 41(3): 516-528.
[10]	OZKAYNAK F. Cryptographically Secure Random Number Generator with Chaotic Additional Input[J]. Nonlinear Dynamics, 2014, 78(3): 2015-2020. doi: 10.1007/s11071-014-1591-y URL
[11]	PRENEEL B, DODUNEKOV S, RIJMEN V. Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes[M]. Amsterdam: IOS Press, 2000.
[12]	HAAHR M. Introduction to Randomness and Random Numbers[J]. Statistics, 1999(8): 1-4.
[13]	LEE J S, CLEAVER G B. The Cosmic Microwave Background Radiation Power Spectrum as a Random Bit Generator for Symmetric and Asymmetric-Key Cryptography[J]. Heliyon, 2017, 3(10): 1-11.
[14]	ZHUN Huang, CHENHongyi. A Truly Random Number Generator Based on Thermal Noise[C]// IEEE. The 4th International Conference on ASIC. New York: IEEE, 2001: 62-86.
[15]	HAMBURG M, KOCHER P, MARSON M E. Analysis of Intel’s Ivy Bridge Digital Random Number Generator[R]. San Francisco, CA: Cryptography Research, Inc., Intel_TRNG_Report_20120312, 2012.
[16]	STOJANOVSKI T, PIHL J, KOCAREV L. Chaos-Based Random Number Generators[J]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2001, 48(3): 382-385. doi: 10.1109/81.915396 URL
[17]	ANANTHASWAMY A. How to Ttrn a Quantum Computer into the Ultimate Randomness Generator[EB/OL]. (2019-06-19)[2025-03-27]. https://www.quantamagazine.org/how-to-turn-a-quantum-computer-into-the-ultimate-randomness-generator-20190619/.
[18]	ELMAN J L. Finding Structure in Time[J]. Cognitive Science, 1990, 14(2): 179-211. doi: 10.1207/s15516709cog1402_1 URL
[19]	LECUN Y, BOTTOU L, BENGIO Y, et al. Gradient-Based Learning Applied to Document Recognition[J]. Proceedings of the IEEE, 1998, 86(11): 2278-2324. doi: 10.1109/5.726791 URL
[20]	VASWANI A, SHAZEER N, PARMAR N, et al. Attention Is All You Need[EB/OL]. (2017-11-07)[2025-03-27]. https://arxiv.org/abs/1706.03762..
[21]	HOCHREITER S, SCHMIDHUBER J. Long Short-Term Memory[J]. Neural Computation, 1997, 9(8): 1735-1780. doi: 10.1162/neco.1997.9.8.1735 pmid: 9377276
[22]	CHO K, MERRIENBOER B, GULCEHRE C, et al. Learning Phrase Representations Using RNN Encoder-Decoder for Statistical Machine Translation[EB/OL]. (2014-09-03)[2025-03-29]. http://arxiv.org/abs/1406.1078.
[23]	RUKHIN A, SOTO J, NECHVATAL J, et al. A Statistical Test Suite for Random and Pseudo Random Number Generators for Cryptographic Applications[M]. Gaithersburg: NIST, 2001.
[24]	GM/T 0005-2021 Randomness Testing Specification[S]. Beijing: State Cryptography Administration, 2021.
	GM/T 0005-2021 随机性检测规范[S]. 北京: 国家密码管理局, 2021.
[25]	HURLEY-SMITH D, HERNANDEZ-CASTRO J. Certifiably Biased: An In-Depth Analysis of a Common Criteria EAL4+ Certified TRNG[J]. IEEE Transactions on Information Forensics and Security, 2018, 13(4): 1031-1041. doi: 10.1109/TIFS.2017.2777342 URL
[26]	MANTIN I, SHAMIR A. A Practical Attack on Broadcast RC4[C]// Springer. Fast Software Encryption Conference. Heidelberg: Springer, 2002: 152-164.
[27]	CRYPTREC. Investigation Reports on Cryptographic Techniques[EB/OL]. (2023-02-12)[2025-03-29]. https://www.cryptrec.go.jp/en/tech_reports.html.
[28]	SHANNON C E. Prediction and Entropy of Printed English[J]. Bell System Technical Journal, 1951, 30(1): 50-64. doi: 10.1002/bltj.1951.30.issue-1 URL
[29]	HAGERTY P, DRAPER T. Entropy Bounds and Statistical Tests[C]// NIST. The NIST Random Bit Generation Workshop. Gaithersburg: NIST, 2012: 5-6.
[30]	GOLIC J D. New Methods for Digital Generation and Postprocessing of Random Data[J]. IEEE Transactions on Computers, 2006, 55(10): 1217-1229.
[31]	WIECZOREK P Z, GOŁOFIT K. Dual-Metastability Time-Competitive True Random Number Generator[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2014, 61(1): 134-145.
[32]	TURAN M S, BARKER E, KELSEY J, et al. Recommendation for the Entropy Sources Used for Random Bit Generation[R]. Gaithersburg: National Institute of Standards and Technology, NIST SP 800-90b, 2018.
[33]	KELSEY J, MCKAY K, TURAN M. Predictive Models for Min-Entropy Estimation[C]// Springer. Cryptographic Hardware and Embedded Systems Conference. Heidelberg: Springer, 2015: 373-392.
[34]	ZHU Shuangyi, MA Yuan, CHEN Tianyu, et al. Analysis and Improvement of Entropy Estimators in NIST SP 800-90B for Non-IID Entropy Sources[J]. IACR Transactions on Symmetric Cryptology, 2017(6): 151-168.
[35]	MENEZES A J, OORSCHOT P C, VANSTONE S A. Handbook of Applied Cryptography[M]. Boca Raton: CRC Press, 2018.
[36]	SAVIR J, MCANNEY W H. A Multiple Seed Linear Feedback Shift Register[C]// IEEE. International Test Conference. New York: IEEE, 1990: 657-659.
[37]	LI Youru, ZHU Zhenfeng, KONG Deqiang, et al. EA-LSTM: Evolutionary Attention-Based LSTM for Time Series Prediction[J]. Knowledge-Based Systems, 2019, 181: 85-96.
[38]	NIU Zhenwen, YU Zeyuan, TANG Wenhu, et al. Wind Power Forecasting Using Attention-Based Gated Recurrent Unit Network[J]. Energy, 2020, 196: 70-81.
[39]	YUAN Ye, JIA Kebin, MA Fenglong, et al. A Hybrid Self-Attention Deep Learning Framework for Multivariate Sleep Stage Classification[J]. BMC Bioinformatics, 2019, 20(16): 586-595. doi: 10.1186/s12859-019-3075-z
[40]	FAN Fenglei, WANG Ge. Learning from Pseudo-Randomness with an Artificial Neural Network-Does God Play Pseudo-Dice?[J]. IEEE Access, 2018, 6: 22987-22992.
[41]	FISCHER T. Testing Cryptographically Secure Pseudo Random Number Generators with Artificial Neural Networks[C]// IEEE. The 17th IEEE International Conference on Trust, Security and Privacy in Computing and Communications. New York: IEEE, 2018: 1214-1223.
[42]	YANG Jing, ZHU Shuangyi, CHEN Tianyu, et al. Neural Network Based Min-Entropy Estimation for Random Number Generators[C]// Springer. Security and Privacy in Communication Networks. Heidelberg: Springer, 2018: 231-250.
[43]	TRUONG N D, HAW J Y, ASSAD S M, et al. Machine Learning Cryptanalysis of a Quantum Random Number Generator[J]. IEEE Transactions on Information Forensics and Security, 2019, 14(2): 403-414.
[44]	LI Cai, ZHANG Jianguo, SANG Luxiao, et al. Deep Learning-Based Security Verification for a Random Number Generator Using White Chaos[J]. Entropy, 2020, 22(10): 11-34.
[45]	LYU Na, CHEN Tianyu, ZHU Shuangyi, et al. High-Efficiency Min-Entropy Estimation Based on Neural Network for Random Number Generators[J]. Security and Communication Networks, 2020, 20: 1-18.
[46]	LI Haohao, ZHANG Jianguo, LI Zhihua, et al. Improvement of Min-Entropy Evaluation Based on Pruning and Quantized Deep Neural Network[J]. IEEE Transactions on Information Forensics and Security, 2023, 18: 1410-1420.
[47]	BLANCO-ROMERO J, LORENZO V, ALMENARES M F, et al. Machine Learning Predictors for Min-Entropy Estimation[J]. Entropy, 2025, 27(2): 156-165.
[48]	CAO Jian, ZHANG Minghui, LIU Weiqi, et al. Deep Learning-Based Security Analysis of Quantum Random Numbers Generated by Imperfect Devices[J]. IEEE Transactions on Information Forensics and Security, 2024, 19: 7841-7852.
[49]	HUANG Yilong, FAN Fan, HUANG Chaofeng, et al. MA-DG: Learning Features of Sequences in Different Dimensions for Min-Entropy Evaluation via 2D-CNN and Multi-Head Self-Attention[J]. IEEE Transactions on Information Forensics and Security, 2024, 19: 7879-7894.
[50]	ZHU Shuangyi, MA Yuan, LI Xusheng, et al. On the Analysis and Improvement of Min-Entropy Estimation on Time-Varying Data[J]. IEEE Transactions on Information Forensics and Security, 2020, 15: 1696-1708.
[51]	KIMURA H, ISOBE T, OHIGASHI T. Neural-Network-Based Pseudo-Random Number Generator Evaluation Tool for Stream Ciphers[C]// IEEE. 2019 Seventh International Symposium on Computing and Networking Workshops. New York: IEEE, 2019: 333-338.
[52]	CRESPO J, GONZALEZ-VILLA J, GUTIERREZ J, et al. Assessing the Quality of Random Number Generators through Neural Networks[J]. Machine Learning: Science and Technology, 2024, 5(2): 72-83.
[53]	SINHA S, ISLAM S H, OBAIDAT M S. A Comparative Study and Analysis of Some Pseudorandom Number Generator Algorithms[J]. Security and Privacy, 2018, 1(6): 46-52.
[54]	PIRANDOLA S, ANDERSEN U L, BANCHI L, et al. Advances in Quantum Cryptography[J]. Advances in Optics and Photonics, 2020, 12(4): 1012-1236.
[55]	KIM K, CHOI S, KWON H, et al. FACE-LIGHT: Fast AES-CTR Mode Encryption for Low-End Microcontrollers[C]// Springer. Information Security and Cryptology- ICISC 2019. Heidelberg: Springer, 2020: 102-114.
[56]	ZHOU Haoyi, ZHANG Shanghang, PENG Jiepeng, et al. Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting[C]// AAAI. The AAAI Conference on Artificial Intelligence. Cambridge: AAAI, 2021: 11106-11115.
[57]	YU Han, GUO Peikun, SANO A. AdaWaveNet: Adaptive Wavelet Network for Time Series Analysis[EB/OL]. (2024-05-17)[2025-03-11]. http://arxiv.org/abs/2405.11124.
[58]	LI Yanan, WANG Zhimin, XING Ruipeng, et al. Quantum Gated Recurrent Neural Networks[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2025, 47(4): 2493-2504.
[59]	LIU Junhua, LIM K H, WOOD K L, et al. Hybrid Quantum-Classical Convolutional Neural Networks[J]. Science China Physics, Mechanics & Astronomy, 2021, 64(9): 290-311.
[60]	SCARANI V, BECHMANN-PASQUINUCCI H, CERF N J, et al. The Security of Practical Quantum Key Distribution[J]. Reviews of Modern Physics, 2009, 81(3): 1301-1350.

测试	块长度/bit
Block Frequency Test	20000
NonOverlapping Template Test	9
Overlapping Template Test	9
Approximate Entropy Test	500
Serial Test	10
Linear Complexity Test	10

由平稳源生成的模拟数据集	由非平稳源生成的模拟数据集
离散均匀分布	时变正态分布取整
离散近似均匀分布
整数舍入的正态分布
马尔可夫模型
三角分布取整

数据集	${{P}_{m}}$	${{H}_{\min }}$
离散均匀分布序列	$1/{{2}^{8}}$	8
离散近似均匀分布序列	0.00586	7.41439
正态分布序列	0.01614	5.95339
三角分布取整序列	$1/{{2}^{7}}$	7
M序列	1	0

方案	模型	随机数生成器	评估标准	对比对象
FAN^[40]等人方案	FNN	PRNG	成功预测概率	无
FISCHER^[41]方案	LSTM、GRU、BLSTM、BGRU	PRNG、CSPRNG	统计学标准	Diehard测试
YANG^[42] 等人方案	FNN和RNN	PRNG	最小熵	NIST 800-90B
TRUONG^[43]等人方案	RCNN（LSTM+CNN）	TRNG、CSRNG	最小熵	NIST STS
LI^[44]等人方案	TPA-LSTM	TRNG、PRNG	最小熵	NIST SP 800-22
LYU^[45]等人方案	FNN和RNN	PRNG	最小熵	NIST 800-90B
LI^[46]等人方案	TPA-LSTM	PRNG	最小熵	NIST 800-90B、FNN、RNN
BLANCO-ROMERO^[47]等人方案	RCNN、Transformer	PRNG	平均最小熵	NIST 800-90B
CAO^[48]等人方案	CNN-BiLSTM	TRNG	最小熵	NIST SP 800-22、RCNN
HUANG^[49]等人方案	GAF-DFA+二维CNN+ 多头自注意力机制	PRNG	最小熵	NIST 800-90B、FNN、RNN、RCNN、TPA-LSTM

分类方案	模型	RNG	评估标准	对比对象
KIMURA^[51] 等人方案	LSTM	PRNG	平均比特值	NIST SP 800-22
CRESPO^[52] 等人方案	LSTM、CNN	PRNG、TRNG	平均比特值	NIST SP 800-22