Post-quantum transport layer security(PQ-TLS)is capable of effectively defending against quantum threats to current network communications,whereas its larger public key and certificate sizes as well as higher computat...Post-quantum transport layer security(PQ-TLS)is capable of effectively defending against quantum threats to current network communications,whereas its larger public key and certificate sizes as well as higher computational overhead may result in a significant performance reduction compared with conventional TLS.In this paper,we present a systematic evaluation of PQ-TLS performance across diverse deployment scenarios to address the following critical research questions.(1)What is the performance behavior of PQ-TLS across different TLS modes?(2)How does PQ-TLS perform across varying client scales?(3)Which network topology is most suitable for PQ-TLS?(4)How does PQ-TLS perform on personal computers(PCs)compared to embedded IoT devices?To the best of our knowledge,this is the first work to comprehensively address these issues,offering implementers some insights into PQ-TLS performance and guidance for optimizing it across diverse scenarios.展开更多
TheIndustrial Internet of Things(IIoT)has emerged as a cornerstone of Industry 4.0,enabling large-scale automation and data-driven decision-making across factories,supply chains,and critical infrastructures.However,th...TheIndustrial Internet of Things(IIoT)has emerged as a cornerstone of Industry 4.0,enabling large-scale automation and data-driven decision-making across factories,supply chains,and critical infrastructures.However,the massive interconnection of resource-constrained devices also amplifies the risks of eavesdropping,data tampering,and device impersonation.While digital signatures are indispensable for ensuring authenticity and non-repudiation,conventional schemes such as RSA and ECCare vulnerable to quantumalgorithms,jeopardizing long-termtrust in IIoT deployments.This study proposes a lightweight,stateless,hash-based signature scheme that achieves post-quantum security while addressing the stringent efficiency demands of IIoT.The design introduces two key optimizations:(1)Forest ofRandomSubsets(FORS)onDemand,where subset secret keys are generated dynamically via a PseudoRandom Function(PRF),thereby minimizing storage overhead and eliminating key-reuse risks;and(2)Winternitz One-Time Signature Plus(WOTS+)partial hash-chain caching,which precomputes intermediate hash values at edge gateways,reducing device-side computations,latency,and energy consumption.The architecture integrates a multi-layerMerkle authentication tree(Merkle tree)and role-based delegation across sensors,gateways,and a Signature Authority Center(SAC),supporting scalable cross-site deployment and key rotation.Froma theoretical perspective,we establish a formal(Existential Unforgeability under Chosen Message Attack)EUF-CMA security proof using a game-based reduction framework.The proof demonstrates that any successful forgerymust reduce to breaking the underlying assumptions of PRF indistinguishability,(second)preimage resistance,or collision resistance,thus quantifying adversarial advantage and ensuring unforgeability.On the implementation side,our design achieves a balanced trade-off between postquantum security and lightweight performance,offering concrete deployment guidelines for real-time industrial systems.In summary,the proposed method contributes both practical system design and formal security guarantees,providing IIoT with a deployable signature substrate that enhances resilience against quantum-era threats and supports future extensions such as device attestation,group signatures,and anomaly detection.展开更多
The advent of quantum computing poses a significant challenge to traditional cryptographic protocols,particularly those used in SecureMultiparty Computation(MPC),a fundamental cryptographic primitive for privacypreser...The advent of quantum computing poses a significant challenge to traditional cryptographic protocols,particularly those used in SecureMultiparty Computation(MPC),a fundamental cryptographic primitive for privacypreserving computation.Classical MPC relies on cryptographic techniques such as homomorphic encryption,secret sharing,and oblivious transfer,which may become vulnerable in the post-quantum era due to the computational power of quantum adversaries.This study presents a review of 140 peer-reviewed articles published between 2000 and 2025 that used different databases like MDPI,IEEE Explore,Springer,and Elsevier,examining the applications,types,and security issues with the solution of Quantum computing in different fields.This review explores the impact of quantum computing on MPC security,assesses emerging quantum-resistant MPC protocols,and examines hybrid classicalquantum approaches aimed at mitigating quantum threats.We analyze the role of Quantum Key Distribution(QKD),post-quantum cryptography(PQC),and quantum homomorphic encryption in securing multiparty computations.Additionally,we discuss the challenges of scalability,computational efficiency,and practical deployment of quantumsecure MPC frameworks in real-world applications such as privacy-preserving AI,secure blockchain transactions,and confidential data analysis.This review provides insights into the future research directions and open challenges in ensuring secure,scalable,and quantum-resistant multiparty computation.展开更多
With the rapid advancement of ICT and IoT technologies,the integration of Edge and Fog Computing has become essential to meet the increasing demands for real-time data processing and network efficiency.However,these t...With the rapid advancement of ICT and IoT technologies,the integration of Edge and Fog Computing has become essential to meet the increasing demands for real-time data processing and network efficiency.However,these technologies face critical security challenges,exacerbated by the emergence of quantum computing,which threatens traditional encryption methods.The rise in cyber-attacks targeting IoT and Edge/Fog networks underscores the need for robust,quantum-resistant security solutions.To address these challenges,researchers are focusing on Quantum Key Distribution and Post-Quantum Cryptography,which utilize quantum-resistant algorithms and the principles of quantum mechanics to ensure data confidentiality and integrity.This paper reviews the current security practices in IoT and Edge/Fog environments,explores the latest advancements in QKD and PQC technologies,and discusses their integration into distributed computing systems.Additionally,this paper proposes an enhanced QKD protocol combining the Cascade protocol and Kyber algorithm to address existing limitations.Finally,we highlight future research directions aimed at improving the scalability,efficiency,and practicality of QKD and PQC for securing IoT and Edge/Fog networks against evolving quantum threats.展开更多
Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing.To address these concerns,this paper presents the mathematica...Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing.To address these concerns,this paper presents the mathematical and computer modeling of a novel two-dimensional(2D)chaotic system for secure key generation in quantum image encryption(QIE).The proposed map employs trigonometric perturbations in conjunction with rational-saturation functions and hence,named as Trigonometric-Rational-Saturation(TRS)map.Through rigorous mathematical analysis and computational simulations,the map is extensively evaluated for bifurcation behaviour,chaotic trajectories,and Lyapunov exponents.The security evaluation validates the map’s non-linearity,unpredictability,and sensitive dependence on initial conditions.In addition,the proposed TRS map has further been tested by integrating it in a QIE scheme.The QIE scheme first quantum-encodes the classic image using the Novel Enhanced Quantum Representation(NEQR)technique,the TRS map is used for the generation of secure diffusion key,which is XOR-ed with the quantum-ready image to obtain the encrypted images.The security evaluation of the QIE scheme demonstrates superior security of the encrypted images in terms of statistical security attacks and also against Differential attacks.The encrypted images exhibit zero correlation and maximum entropy with demonstrating strong resilience due to 99.62%and 33.47%results for Number of Pixels Change Rate(NPCR)and Unified Average Changing Intensity(UACI).The results validate the effectiveness of TRS-based quantum encryption scheme in securing digital images against emerging quantum threats,making it suitable for secure image encryption in IoT and edge-based applications.展开更多
In recent decades, log system management has been widely studied fordata security management. System abnormalities or illegal operations can befound in time by analyzing the log and provide evidence for intrusions. In...In recent decades, log system management has been widely studied fordata security management. System abnormalities or illegal operations can befound in time by analyzing the log and provide evidence for intrusions. In orderto ensure the integrity of the log in the current system, many researchers havedesigned it based on blockchain. However, the emerging blockchain is facing significant security challenges with the increment of quantum computers. An attackerequipped with a quantum computer can extract the user's private key from thepublic key to generate a forged signature, destroy the structure of the blockchain,and threaten the security of the log system. Thus, blind signature on the lattice inpost-quantum blockchain brings new security features for log systems. In ourpaper, to address these, firstly, we propose a novel log system based on post-quantum blockchain that can resist quantum computing attacks. Secondly, we utilize apost-quantum blind signature on the lattice to ensure both security and blindnessof log system, which makes the privacy of log information to a large extent.Lastly, we enhance the security level of lattice-based blind signature under therandom oracle model, and the signature size grows slowly compared with others.We also implement our protocol and conduct an extensive analysis to prove theideas. The results show that our scheme signature size edges up subtly comparedwith others with the improvement of security level.展开更多
The advent of quantum computers and algorithms challenges the semantic security of symmetric and asymmetric cryptosystems. Thus, the implementation of new cryptographic primitives is essential. They must follow the br...The advent of quantum computers and algorithms challenges the semantic security of symmetric and asymmetric cryptosystems. Thus, the implementation of new cryptographic primitives is essential. They must follow the breakthroughs and properties of quantum calculators which make vulnerable existing cryptosystems. In this paper, we propose a random number generation model based on evaluation of the thermal noise power of the volume elements of an electronic system with a volume of 58.83 cm<sup>3</sup>. We prove through the sampling of the temperature of each volume element that it is difficult for an attacker to carry out an exploit. In 12 seconds, we generate for 7 volume elements, a stream of randomly generated keys of 187 digits that will be transmitted from source to destination through the properties of quantum cryptography.展开更多
The pre-and post-selection processes of the "two-state vector formalism" lead to a fair sampling loophole in Bell test, so it can be used to simulate post-quantum correlations. In this paper, we propose a ph...The pre-and post-selection processes of the "two-state vector formalism" lead to a fair sampling loophole in Bell test, so it can be used to simulate post-quantum correlations. In this paper, we propose a physical implementation of such a correlation with the help of quantum non-demolition measurement, which is realized via the cross-Kerr nonlinear interaction between the signal photon and a probe coherent beam. The indirect measurement on the polarization state of photon is realized by the direct measurement on the phase shift of the probe coherent beam, which enhances the detection efficiency greatly and leaves the signal photon unabsorbed. The maximal violation of the CHSH inequality 4 can be achieved by pre-and post-selecting maximally entangled states. The reason why we can get the post-quantum correlation is that the selection of the results after measurement opens fair-sampling loophole. The fair-sampling loophole opened here is different from the one usually used in the currently existing simulation schemes for post-quantum correlations,which are simulated by selecting the states to be measured or enlarging the Hilbert space. So, our results present an alternative way to mimic post-quantum correlations.展开更多
Blind signcryption(BSC) can guarantee the blindness and untrackability of signcrypted messages, and moreover, it provides simultaneous unforgeability and confidentiality. Most traditional BSC schemes are based on the ...Blind signcryption(BSC) can guarantee the blindness and untrackability of signcrypted messages, and moreover, it provides simultaneous unforgeability and confidentiality. Most traditional BSC schemes are based on the number theory. However, with the rapid development of quantum computing, traditional BSC systems are faced with severe security threats. As promising candidate cryptosystems with the ability to resist attacks from quantum computing, lattice-based cryptosystems have attracted increasing attention in academic fields. In this paper, a post-quantum blind signcryption scheme from lattice(PQ-LBSCS) is devised by applying BSC to lattice-based cryptosystems. PQ-LBSCS inherits the advantages of the lattice-based cryptosystem and blind signcryption technique. PQ-LBSCS is provably secure under the hard assumptions of the learning with error problem and small integer solution problem in the standard model. Simulations are carried out using the Matlab tool to analyze the computational efficiency, and the simulation results show that PQ-LBSCS is more efficient than previous schemes. PQ-LBSCS has extensive application prospects in e-commerce, mobile communication, and smart cards.展开更多
随着量子计算技术的不断发展,依赖传统公钥密码体制三大功能(密钥协商/数字签名/公钥加密)的各种应用系统将不再安全.为应对量子威胁,以美国国家标准与技术研究院(National Institute of Standards and Technology,NIST)为首的国际标准...随着量子计算技术的不断发展,依赖传统公钥密码体制三大功能(密钥协商/数字签名/公钥加密)的各种应用系统将不再安全.为应对量子威胁,以美国国家标准与技术研究院(National Institute of Standards and Technology,NIST)为首的国际标准组织积极征集与部署后量子密码(Post Quantum Cryptography,PQC)算法的标准化工作,致力于在真正实用型量子计算机问世之前,提前完成传统公钥密码算法到PQC算法的迁移过渡.Crystals-Dilithium是NIST-PQC标准中的一种基于格的数字签名算法,其安全性高,运算速度快,是实现抵抗量子攻击数字签名算法的重要路径之一.本文从主流Crystals-Dilithium数字签名算法的理论基础出发,从底层关键组件的优化方法和整体硬件构架设计方法着手,围绕硬件资源优化和性能优化等现有方法和成果对比展开分析介绍,为研究者们后续研究探明方向,希望为设计性能与硬件资源均衡的后量子数字签名密码芯片提供有力参考.展开更多
基金Special Fund for Key Technologies in Blockchain of Shanghai Scientific and Technological Committee(23511100300)。
文摘Post-quantum transport layer security(PQ-TLS)is capable of effectively defending against quantum threats to current network communications,whereas its larger public key and certificate sizes as well as higher computational overhead may result in a significant performance reduction compared with conventional TLS.In this paper,we present a systematic evaluation of PQ-TLS performance across diverse deployment scenarios to address the following critical research questions.(1)What is the performance behavior of PQ-TLS across different TLS modes?(2)How does PQ-TLS perform across varying client scales?(3)Which network topology is most suitable for PQ-TLS?(4)How does PQ-TLS perform on personal computers(PCs)compared to embedded IoT devices?To the best of our knowledge,this is the first work to comprehensively address these issues,offering implementers some insights into PQ-TLS performance and guidance for optimizing it across diverse scenarios.
文摘TheIndustrial Internet of Things(IIoT)has emerged as a cornerstone of Industry 4.0,enabling large-scale automation and data-driven decision-making across factories,supply chains,and critical infrastructures.However,the massive interconnection of resource-constrained devices also amplifies the risks of eavesdropping,data tampering,and device impersonation.While digital signatures are indispensable for ensuring authenticity and non-repudiation,conventional schemes such as RSA and ECCare vulnerable to quantumalgorithms,jeopardizing long-termtrust in IIoT deployments.This study proposes a lightweight,stateless,hash-based signature scheme that achieves post-quantum security while addressing the stringent efficiency demands of IIoT.The design introduces two key optimizations:(1)Forest ofRandomSubsets(FORS)onDemand,where subset secret keys are generated dynamically via a PseudoRandom Function(PRF),thereby minimizing storage overhead and eliminating key-reuse risks;and(2)Winternitz One-Time Signature Plus(WOTS+)partial hash-chain caching,which precomputes intermediate hash values at edge gateways,reducing device-side computations,latency,and energy consumption.The architecture integrates a multi-layerMerkle authentication tree(Merkle tree)and role-based delegation across sensors,gateways,and a Signature Authority Center(SAC),supporting scalable cross-site deployment and key rotation.Froma theoretical perspective,we establish a formal(Existential Unforgeability under Chosen Message Attack)EUF-CMA security proof using a game-based reduction framework.The proof demonstrates that any successful forgerymust reduce to breaking the underlying assumptions of PRF indistinguishability,(second)preimage resistance,or collision resistance,thus quantifying adversarial advantage and ensuring unforgeability.On the implementation side,our design achieves a balanced trade-off between postquantum security and lightweight performance,offering concrete deployment guidelines for real-time industrial systems.In summary,the proposed method contributes both practical system design and formal security guarantees,providing IIoT with a deployable signature substrate that enhances resilience against quantum-era threats and supports future extensions such as device attestation,group signatures,and anomaly detection.
文摘The advent of quantum computing poses a significant challenge to traditional cryptographic protocols,particularly those used in SecureMultiparty Computation(MPC),a fundamental cryptographic primitive for privacypreserving computation.Classical MPC relies on cryptographic techniques such as homomorphic encryption,secret sharing,and oblivious transfer,which may become vulnerable in the post-quantum era due to the computational power of quantum adversaries.This study presents a review of 140 peer-reviewed articles published between 2000 and 2025 that used different databases like MDPI,IEEE Explore,Springer,and Elsevier,examining the applications,types,and security issues with the solution of Quantum computing in different fields.This review explores the impact of quantum computing on MPC security,assesses emerging quantum-resistant MPC protocols,and examines hybrid classicalquantum approaches aimed at mitigating quantum threats.We analyze the role of Quantum Key Distribution(QKD),post-quantum cryptography(PQC),and quantum homomorphic encryption in securing multiparty computations.Additionally,we discuss the challenges of scalability,computational efficiency,and practical deployment of quantumsecure MPC frameworks in real-world applications such as privacy-preserving AI,secure blockchain transactions,and confidential data analysis.This review provides insights into the future research directions and open challenges in ensuring secure,scalable,and quantum-resistant multiparty computation.
基金supported by the National Research Foundation of Korea(NRF)funded by theMinistry of Science and ICT(2022K1A3A1A61014825)。
文摘With the rapid advancement of ICT and IoT technologies,the integration of Edge and Fog Computing has become essential to meet the increasing demands for real-time data processing and network efficiency.However,these technologies face critical security challenges,exacerbated by the emergence of quantum computing,which threatens traditional encryption methods.The rise in cyber-attacks targeting IoT and Edge/Fog networks underscores the need for robust,quantum-resistant security solutions.To address these challenges,researchers are focusing on Quantum Key Distribution and Post-Quantum Cryptography,which utilize quantum-resistant algorithms and the principles of quantum mechanics to ensure data confidentiality and integrity.This paper reviews the current security practices in IoT and Edge/Fog environments,explores the latest advancements in QKD and PQC technologies,and discusses their integration into distributed computing systems.Additionally,this paper proposes an enhanced QKD protocol combining the Cascade protocol and Kyber algorithm to address existing limitations.Finally,we highlight future research directions aimed at improving the scalability,efficiency,and practicality of QKD and PQC for securing IoT and Edge/Fog networks against evolving quantum threats.
基金funded by Deanship of Research and Graduate Studies at King Khalid University.The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Group Project under grant number(RGP.2/556/45).
文摘Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing.To address these concerns,this paper presents the mathematical and computer modeling of a novel two-dimensional(2D)chaotic system for secure key generation in quantum image encryption(QIE).The proposed map employs trigonometric perturbations in conjunction with rational-saturation functions and hence,named as Trigonometric-Rational-Saturation(TRS)map.Through rigorous mathematical analysis and computational simulations,the map is extensively evaluated for bifurcation behaviour,chaotic trajectories,and Lyapunov exponents.The security evaluation validates the map’s non-linearity,unpredictability,and sensitive dependence on initial conditions.In addition,the proposed TRS map has further been tested by integrating it in a QIE scheme.The QIE scheme first quantum-encodes the classic image using the Novel Enhanced Quantum Representation(NEQR)technique,the TRS map is used for the generation of secure diffusion key,which is XOR-ed with the quantum-ready image to obtain the encrypted images.The security evaluation of the QIE scheme demonstrates superior security of the encrypted images in terms of statistical security attacks and also against Differential attacks.The encrypted images exhibit zero correlation and maximum entropy with demonstrating strong resilience due to 99.62%and 33.47%results for Number of Pixels Change Rate(NPCR)and Unified Average Changing Intensity(UACI).The results validate the effectiveness of TRS-based quantum encryption scheme in securing digital images against emerging quantum threats,making it suitable for secure image encryption in IoT and edge-based applications.
基金supported by the NSFC(Grant Nos.92046001,61962009)JSPS KAKENHI Grant Number JP20F20080+3 种基金the Natural Science Foundation of Inner Mongolia(2021MS06006)Baotou Kundulun District Science and technology plan project(YF2020013)Inner Mongolia discipline inspection and supervision big data laboratory open project fund(IMDBD2020020)the Scientific Research Foundation of North China University of Technology.
文摘In recent decades, log system management has been widely studied fordata security management. System abnormalities or illegal operations can befound in time by analyzing the log and provide evidence for intrusions. In orderto ensure the integrity of the log in the current system, many researchers havedesigned it based on blockchain. However, the emerging blockchain is facing significant security challenges with the increment of quantum computers. An attackerequipped with a quantum computer can extract the user's private key from thepublic key to generate a forged signature, destroy the structure of the blockchain,and threaten the security of the log system. Thus, blind signature on the lattice inpost-quantum blockchain brings new security features for log systems. In ourpaper, to address these, firstly, we propose a novel log system based on post-quantum blockchain that can resist quantum computing attacks. Secondly, we utilize apost-quantum blind signature on the lattice to ensure both security and blindnessof log system, which makes the privacy of log information to a large extent.Lastly, we enhance the security level of lattice-based blind signature under therandom oracle model, and the signature size grows slowly compared with others.We also implement our protocol and conduct an extensive analysis to prove theideas. The results show that our scheme signature size edges up subtly comparedwith others with the improvement of security level.
文摘The advent of quantum computers and algorithms challenges the semantic security of symmetric and asymmetric cryptosystems. Thus, the implementation of new cryptographic primitives is essential. They must follow the breakthroughs and properties of quantum calculators which make vulnerable existing cryptosystems. In this paper, we propose a random number generation model based on evaluation of the thermal noise power of the volume elements of an electronic system with a volume of 58.83 cm<sup>3</sup>. We prove through the sampling of the temperature of each volume element that it is difficult for an attacker to carry out an exploit. In 12 seconds, we generate for 7 volume elements, a stream of randomly generated keys of 187 digits that will be transmitted from source to destination through the properties of quantum cryptography.
基金Supported by National Natural Science Foundation of China(NSFC)under Grant Nos.11274010,11374085,and 61370090Anhui Provincial Natural Science Foundation under Grant Nos.1408085MA20 and 1408085MA16the Key Program of Domestic Visiting of Anhui Province under Grant No.gxfxZD2016192
文摘The pre-and post-selection processes of the "two-state vector formalism" lead to a fair sampling loophole in Bell test, so it can be used to simulate post-quantum correlations. In this paper, we propose a physical implementation of such a correlation with the help of quantum non-demolition measurement, which is realized via the cross-Kerr nonlinear interaction between the signal photon and a probe coherent beam. The indirect measurement on the polarization state of photon is realized by the direct measurement on the phase shift of the probe coherent beam, which enhances the detection efficiency greatly and leaves the signal photon unabsorbed. The maximal violation of the CHSH inequality 4 can be achieved by pre-and post-selecting maximally entangled states. The reason why we can get the post-quantum correlation is that the selection of the results after measurement opens fair-sampling loophole. The fair-sampling loophole opened here is different from the one usually used in the currently existing simulation schemes for post-quantum correlations,which are simulated by selecting the states to be measured or enlarging the Hilbert space. So, our results present an alternative way to mimic post-quantum correlations.
基金Project supported by the Key Project of Natural Science Foundation Basic Research Program of Shaanxi Province,China (No. 2020JZ-54)the Innovation Foundation of Postgraduate of Xi’an University of Posts and Telecommunications,China (No. CXJJLY2018075)。
文摘Blind signcryption(BSC) can guarantee the blindness and untrackability of signcrypted messages, and moreover, it provides simultaneous unforgeability and confidentiality. Most traditional BSC schemes are based on the number theory. However, with the rapid development of quantum computing, traditional BSC systems are faced with severe security threats. As promising candidate cryptosystems with the ability to resist attacks from quantum computing, lattice-based cryptosystems have attracted increasing attention in academic fields. In this paper, a post-quantum blind signcryption scheme from lattice(PQ-LBSCS) is devised by applying BSC to lattice-based cryptosystems. PQ-LBSCS inherits the advantages of the lattice-based cryptosystem and blind signcryption technique. PQ-LBSCS is provably secure under the hard assumptions of the learning with error problem and small integer solution problem in the standard model. Simulations are carried out using the Matlab tool to analyze the computational efficiency, and the simulation results show that PQ-LBSCS is more efficient than previous schemes. PQ-LBSCS has extensive application prospects in e-commerce, mobile communication, and smart cards.
文摘随着量子计算技术的不断发展,依赖传统公钥密码体制三大功能(密钥协商/数字签名/公钥加密)的各种应用系统将不再安全.为应对量子威胁,以美国国家标准与技术研究院(National Institute of Standards and Technology,NIST)为首的国际标准组织积极征集与部署后量子密码(Post Quantum Cryptography,PQC)算法的标准化工作,致力于在真正实用型量子计算机问世之前,提前完成传统公钥密码算法到PQC算法的迁移过渡.Crystals-Dilithium是NIST-PQC标准中的一种基于格的数字签名算法,其安全性高,运算速度快,是实现抵抗量子攻击数字签名算法的重要路径之一.本文从主流Crystals-Dilithium数字签名算法的理论基础出发,从底层关键组件的优化方法和整体硬件构架设计方法着手,围绕硬件资源优化和性能优化等现有方法和成果对比展开分析介绍,为研究者们后续研究探明方向,希望为设计性能与硬件资源均衡的后量子数字签名密码芯片提供有力参考.
