Towards Post-Quantum Blockchain: A Review on Blockchain Cryptography Resistant to Quantum Computing Attacks

Blockchain and other Distributed Ledger Technologies (DLTs) have evolved significantly in the last years and their use has been suggested for numerous applications due to their ability to provide transparency, redundancy and accountability. In the case of blockchain, such characteristics are provided through public-key cryptography and hash functions. However, the fast progress of quantum computing has opened the possibility of performing attacks based on Grover’s and Shor’s algorithms in the near future. Such algorithms threaten both public-key cryptography and hash functions, forcing to redesign blockchains to make use of cryptosystems that withstand quantum attacks, thus creating which are known as post-quantum, quantum-proof, quantum-safe or quantum-resistant cryptosystems. For such a purpose, this article first studies current state of the art on post-quantum cryptosystems and how they can be applied to blockchains and DLTs. Moreover, the most relevant post-quantum blockchain systems are studied, as well as their main challenges. Furthermore, extensive comparisons are provided on the characteristics and performance of the most promising post-quantum public-key encryption and digital signature schemes for blockchains. Thus, this article seeks to provide a broad view and useful guidelines on post-quantum blockchain security to future blockchain researchers and developers.

[1]  William E. Burr,et al.  Recommendation for Key Management, Part 1: General (Revision 3) , 2006 .

[2]  Dixys L. Hernández-Rojas,et al.  Design and Practical Evaluation of a Family of Lightweight Protocols for Heterogeneous Sensing through BLE Beacons in IoT Telemetry Applications , 2017, Sensors.

[3]  Ralph C. Merkle,et al.  A Certified Digital Signature , 1989, CRYPTO.

[4]  Chris Peikert,et al.  A Toolkit for Ring-LWE Cryptography , 2013, IACR Cryptol. ePrint Arch..

[5]  Johannes Blömer,et al.  Sampling Methods for Shortest Vectors, Closest Vectors and Successive Minima , 2007, ICALP.

[6]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[7]  Quanlong Wang,et al.  Towards Quantum-Secured Permissioned Blockchain: Signature, Consensus, and Logic , 2019, Entropy.

[8]  Ron Steinfeld,et al.  Making NTRU as Secure as Worst-Case Problems over Ideal Lattices , 2011, EUROCRYPT.

[9]  Frederik Vercauteren,et al.  Saber: Module-LWR based key exchange, CPA-secure encryption and CCA-secure KEM , 2018, IACR Cryptol. ePrint Arch..

[10]  Eli Ben-Sasson,et al.  Scalable, transparent, and post-quantum secure computational integrity , 2018, IACR Cryptol. ePrint Arch..

[11]  Christian Decker,et al.  Information propagation in the Bitcoin network , 2013, IEEE P2P 2013 Proceedings.

[12]  Tibor Juhas The use of elliptic curves in cryptography , 2007 .

[13]  Jonathan Jogenfors,et al.  Quantum Bitcoin: An Anonymous, Distributed, and Secure Currency Secured by the No-Cloning Theorem of Quantum Mechanics , 2016, 2019 IEEE International Conference on Blockchain and Cryptocurrency (ICBC).

[14]  Jintai Ding,et al.  Rainbow, a New Multivariable Polynomial Signature Scheme , 2005, ACNS.

[15]  Moni Naor,et al.  Universal one-way hash functions and their cryptographic applications , 1989, STOC '89.

[16]  Chen-Mou Cheng,et al.  New Differential-Algebraic Attacks and Reparametrization of Rainbow , 2008, ACNS.

[17]  Matt Visser,et al.  Quantum Blockchain using entanglement in time , 2018, Quantum Reports.

[18]  Sergey Krendelev,et al.  Parametric Hash Function Resistant to Attack by Quantum Computer , 2018, 2018 Federated Conference on Computer Science and Information Systems (FedCSIS).

[19]  Tiago M. Fernandez-Carames,et al.  From Pre-Quantum to Post-Quantum IoT Security: A Survey on Quantum-Resistant Cryptosystems for the Internet of Things , 2020, IEEE Internet of Things Journal.

[20]  Jintai Ding,et al.  A New Variant of the Matsumoto-Imai Cryptosystem through Perturbation , 2004, Public Key Cryptography.

[21]  Oded Goldreich,et al.  Definitions and properties of zero-knowledge proof systems , 1994, Journal of Cryptology.

[22]  Jon Cartwright NSA keys into quantum computing , 2014 .

[23]  Craig Costello,et al.  Frodo: Take off the Ring! Practical, Quantum-Secure Key Exchange from LWE , 2016, IACR Cryptol. ePrint Arch..

[24]  Bo-Yin Yang,et al.  Design Principles for HFEv- Based Multivariate Signature Schemes , 2015, ASIACRYPT.

[25]  Zhenfeng Zhang,et al.  Tighter security proofs for generic key encapsulation mechanism in the quantum random oracle model , 2019, IACR Cryptol. ePrint Arch..

[26]  Luis Castedo,et al.  A Methodology for Evaluating Security in Commercial RFID Systems , 2017 .

[27]  Léo Ducas,et al.  Lattice Signatures and Bimodal Gaussians , 2013, IACR Cryptol. ePrint Arch..

[28]  Sooyong Park,et al.  Where Is Current Research on Blockchain Technology?—A Systematic Review , 2016, PloS one.

[29]  Satoshi Nakamoto Bitcoin : A Peer-to-Peer Electronic Cash System , 2009 .

[30]  Christof Zalka,et al.  Shor's discrete logarithm quantum algorithm for elliptic curves , 2003, Quantum Inf. Comput..

[31]  Máire O'Neill,et al.  Practical homomorphic encryption: A survey , 2014, 2014 IEEE International Symposium on Circuits and Systems (ISCAS).

[32]  John M. Easton,et al.  Towards Encrypting Industrial Data on Public Distributed Networks , 2018, 2018 IEEE International Conference on Big Data (Big Data).

[33]  Pierre-Louis Cayrel,et al.  Efficient Implementation of a CCA2-Secure Variant of McEliece Using Generalized Srivastava Codes , 2012, Public Key Cryptography.

[34]  Jian Li,et al.  A New Lattice-Based Signature Scheme in Post-Quantum Blockchain Network , 2019, IEEE Access.

[35]  Jong-Seon No,et al.  Punctured Reed-Muller code-based McEliece cryptosystems , 2017, IET Commun..

[36]  Alexander Rostovtsev,et al.  Public-Key Cryptosystem Based on Isogenies , 2006, IACR Cryptol. ePrint Arch..

[37]  Jian Li,et al.  A New Anti-Quantum Proxy Blind Signature for Blockchain-Enabled Internet of Things , 2019 .

[38]  Jacques Patarin,et al.  Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms , 1996, EUROCRYPT.

[39]  Joseph H. Silverman,et al.  NTRU: A Ring-Based Public Key Cryptosystem , 1998, ANTS.

[40]  Anne Canteaut,et al.  Cryptanalysis of the Original McEliece Cryptosystem , 1998, ASIACRYPT.

[41]  David Chaum,et al.  Blind Signatures for Untraceable Payments , 1982, CRYPTO.

[42]  David Jao,et al.  Constructing elliptic curve isogenies in quantum subexponential time , 2010, J. Math. Cryptol..

[43]  Mostafa Belkasmi,et al.  Bitcoin Security with Post Quantum Cryptography , 2019, NETYS.

[44]  James Brown,et al.  Blockchained Post-Quantum Signatures , 2018, 2018 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData).

[45]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[46]  Paulo S. L. M. Barreto,et al.  Sharper Ring-LWE Signatures , 2016, IACR Cryptol. ePrint Arch..

[47]  Wouter van der Linde Post-quantum blockchain using one-time signature chains , 2018 .

[48]  Samuel Neves,et al.  BLAKE2: Simpler, Smaller, Fast as MD5 , 2013, ACNS.

[49]  William Whyte,et al.  Choosing Parameters for NTRUEncrypt , 2017, CT-RSA.

[50]  Chanathip Namprempre,et al.  From Identification to Signatures via the Fiat-Shamir Transform: Minimizing Assumptions for Security and Forward-Security , 2002, EUROCRYPT.

[51]  Romain Alléaume,et al.  Implementation Security of Quantum Cryptography: Introduction, challenges, solutions , 2018 .

[52]  Tiago M. Fernández-Caramés,et al.  A Review on IoT Deep Learning UAV Systems for Autonomous Obstacle Detection and Collision Avoidance , 2019, Remote. Sens..

[53]  Han Jiang,et al.  A New Post-Quantum Blind Signature From Lattice Assumptions , 2018, IEEE Access.

[54]  Anastas Mishev,et al.  Blockchain solutions for big data challenges: A literature review , 2017, IEEE EUROCON 2017 -17th International Conference on Smart Technologies.

[55]  Melanie Swan,et al.  Blockchain: Blueprint for a New Economy , 2015 .

[56]  Tiago M. Fernández-Caramés,et al.  A Review on the Application of Blockchain to the Next Generation of Cybersecure Industry 4.0 Smart Factories , 2019, IEEE Access.

[57]  Erdem Alkim,et al.  Post-quantum Key Exchange - A New Hope , 2016, USENIX Security Symposium.

[58]  Jing Li,et al.  Cryptographic primitives in blockchains , 2019, J. Netw. Comput. Appl..

[59]  Guomin Yang,et al.  A Lattice-Based Linkable Ring Signature Supporting Stealth Addresses , 2019, ESORICS.

[60]  Yael Tauman Kalai,et al.  How to Leak a Secret: Theory and Applications of Ring Signatures , 2001, Essays in Memory of Shimon Even.

[61]  David Jao,et al.  Efficient Compression of SIDH Public Keys , 2017, EUROCRYPT.

[62]  Vlastimil Clupek,et al.  Secure digital archiving in post-quantum era , 2015, 2015 38th International Conference on Telecommunications and Signal Processing (TSP).

[63]  Tanja Lange,et al.  Attacking and defending the McEliece cryptosystem , 2008, IACR Cryptol. ePrint Arch..

[64]  Tiago M. Fernández-Caramés,et al.  Towards The Internet-of-Smart-Clothing: A Review on IoT Wearables and Garments for Creating Intelligent Connected E-Textiles , 2018, Electronics.

[65]  Alex Pentland,et al.  Enigma: Decentralized Computation Platform with Guaranteed Privacy , 2015, ArXiv.

[66]  Yumin Wang,et al.  Toward Quantum-Resistant Strong Designated Verifier Signature from Isogenies , 2012, 2012 Fourth International Conference on Intelligent Networking and Collaborative Systems.

[67]  Marco Baldi,et al.  Post-quantum cryptography based on codes: State of the art and open challenges , 2017, 2017 AEIT International Annual Conference.

[68]  Lov K. Grover A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[69]  Tanja Lange,et al.  NTRU Prime: Reducing Attack Surface at Low Cost , 2017, SAC.

[70]  Damien Stehlé,et al.  Worst-case to average-case reductions for module lattices , 2014, Designs, Codes and Cryptography.

[71]  Chris Peikert,et al.  Better Key Sizes (and Attacks) for LWE-Based Encryption , 2011, CT-RSA.

[72]  Alex Pentland,et al.  Decentralizing Privacy: Using Blockchain to Protect Personal Data , 2015, 2015 IEEE Security and Privacy Workshops.

[73]  David Jao,et al.  A Quantum Algorithm for Computing Isogenies between Supersingular Elliptic Curves , 2014, INDOCRYPT.

[74]  Sidi Mohamed El Yousfi Alaoui,et al.  Code-Based Identification and Signature Schemes in Software , 2013, CD-ARES Workshops.

[75]  N. Koblitz Elliptic curve cryptosystems , 1987 .

[76]  Dominique Unruh,et al.  Non-Interactive Zero-Knowledge Proofs in the Quantum Random Oracle Model , 2015, EUROCRYPT.

[77]  Reza Azarderakhsh,et al.  A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies , 2017, Financial Cryptography.

[78]  Lav R. Varshney,et al.  Distributed Storage Meets Secret Sharing on the Blockchain , 2018, 2018 Information Theory and Applications Workshop (ITA).

[79]  Leslie Lamport,et al.  Constructing Digital Signatures from a One Way Function , 2016 .

[80]  Gilles Zémor,et al.  Ouroboros: A Simple, Secure and Efficient Key Exchange Protocol Based on Coding Theory , 2017, PQCrypto.

[81]  Stanislav Bulygin,et al.  Selecting Parameters for the Rainbow Signature Scheme , 2010, PQCrypto.

[82]  Jintai Ding,et al.  Cryptanalysis of HFEv and Internal Perturbation of HFE , 2005, Public Key Cryptography.

[83]  Rajiv Ranjan,et al.  SAFE: SDN-Assisted Framework for Edge–Cloud Interplay in Secure Healthcare Ecosystem , 2019, IEEE Transactions on Industrial Informatics.

[84]  B. F. França,et al.  Homomorphic Mini-blockchain Scheme , 2015 .

[85]  Siavash Bayat-Sarmadi,et al.  Post-Quantum Cryptoprocessors Optimized for Edge and Resource-Constrained Devices in IoT , 2019, IEEE Internet of Things Journal.

[86]  Ron Steinfeld,et al.  Post-Quantum One-Time Linkable Ring Signature and Application to Ring Confidential Transactions in Blockchain (Lattice RingCT v1.0) , 2018, IACR Cryptol. ePrint Arch..

[87]  Johannes A. Buchmann,et al.  XMSS - A Practical Forward Secure Signature Scheme based on Minimal Security Assumptions , 2011, IACR Cryptol. ePrint Arch..

[88]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[89]  Paulo S. L. M. Barreto,et al.  MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes , 2013, 2013 IEEE International Symposium on Information Theory.

[90]  Andrea Coladangelo,et al.  Smart contracts meet quantum cryptography , 2019, ArXiv.

[91]  Craig Costello,et al.  Efficient Algorithms for Supersingular Isogeny Diffie-Hellman , 2016, CRYPTO.

[92]  William J. Knottenbelt,et al.  Committing to quantum resistance: a slow defence for Bitcoin against a fast quantum computing attack , 2018, Royal Society Open Science.

[93]  Michele Mosca,et al.  Cybersecurity in an Era with Quantum Computers: Will We Be Ready? , 2017, IEEE Security & Privacy.

[94]  Zibin Zheng,et al.  An Overview of Blockchain Technology: Architecture, Consensus, and Future Trends , 2017, 2017 IEEE International Congress on Big Data (BigData Congress).

[95]  Nicolas Courtois On multivariate signature-only public key cryptosystems , 2001, IACR Cryptol. ePrint Arch..

[96]  Daniele Micciancio,et al.  Improving Lattice Based Cryptosystems Using the Hermite Normal Form , 2001, CaLC.

[97]  Francisco Falcone,et al.  Design and Experimental Validation of a LoRaWAN Fog Computing Based Architecture for IoT Enabled Smart Campus Applications † , 2019, Sensors.

[98]  David Cash,et al.  Bonsai Trees, or How to Delegate a Lattice Basis , 2010, Journal of Cryptology.

[99]  Robert J. McEliece,et al.  A public key cryptosystem based on algebraic coding theory , 1978 .

[100]  Peter Manohar,et al.  Succinct Arguments in the Quantum Random Oracle Model , 2019, IACR Cryptol. ePrint Arch..

[101]  Qiaoyan Wen,et al.  An Anti-Quantum Transaction Authentication Approach in Blockchain , 2018, IEEE Access.

[102]  Danilo Gligoroski,et al.  SoK of Used Cryptography in Blockchain , 2019, IEEE Access.

[103]  Alysson Bessani,et al.  Using Blockchains to Implement Distributed Measuring Systems , 2019, IEEE Transactions on Instrumentation and Measurement.

[104]  T. Malkin,et al.  To BLISS-B or not to be : attacking strong Swan ' s implementation of post-quantum signatures , 2018 .

[105]  Mohamed Hamdi,et al.  Secure data aggregation with homomorphic primitives in wireless sensor networks: A critical survey and open research issues , 2016, 2016 IEEE 13th International Conference on Networking, Sensing, and Control (ICNSC).

[106]  Tanja Lange,et al.  Flush, Gauss, and reload : a cache attack on the BLISS lattice-based signature scheme , 2016 .

[107]  Robert Campbell,et al.  Evaluation of Post-Quantum Distributed Ledger Cryptography , 2019, The Journal of the British Blockchain Association.

[108]  Steven D. Galbraith,et al.  Identification Protocols and Signature Schemes Based on Supersingular Isogeny Problems , 2017, ASIACRYPT.

[109]  Eli Ben-Sasson,et al.  Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture , 2014, USENIX Security Symposium.

[110]  Bo-Yin Yang,et al.  Tame Transformation Signatures With Topsy-Turvy Hashes , .

[111]  Yonggang Wen,et al.  A Survey on Consensus Mechanisms and Mining Strategy Management in Blockchain Networks , 2018, IEEE Access.

[112]  Adi Shamir,et al.  Identity-Based Cryptosystems and Signature Schemes , 1984, CRYPTO.

[113]  Tiago M. Fernández-Caramés,et al.  Enabling the Internet of Mobile Crowdsourcing Health Things: A Mobile Fog Computing, Blockchain and IoT Based Continuous Glucose Monitoring System for Diabetes Mellitus Research and Care , 2019, Sensors.

[114]  Alexander Vasiliev,et al.  Quantum-Assisted Blockchain , 2018, Lobachevskii Journal of Mathematics.

[115]  David Jao,et al.  Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies , 2011, J. Math. Cryptol..

[116]  Tiago M. Fernández-Caramés,et al.  Reverse Engineering and Security Evaluation of Commercial Tags for RFID-Based IoT Applications , 2016, Sensors.

[117]  Tiago M. Fernández-Caramés,et al.  A Review on Blockchain Technologies for an Advanced and Cyber-Resilient Automotive Industry , 2019, IEEE Access.

[118]  Mikael Sjöberg Post-quantum algorithms for digital signing in Public Key Infrastructures , 2017 .

[119]  Zhe Liu,et al.  Securing Edge Devices in the Post-Quantum Internet of Things Using Lattice-Based Cryptography , 2018, IEEE Communications Magazine.

[120]  Feng Xiong,et al.  A Key Protection Scheme Based on Secret Sharing for Blockchain-Based Construction Supply Chain System , 2019, IEEE Access.

[121]  Feipei Lai,et al.  Tractable Rational Map Signature , 2005, Public Key Cryptography.

[122]  Kazuki Ikeda,et al.  qBitcoin: A Peer-to-Peer Quantum Cash System , 2017, Advances in Intelligent Systems and Computing.

[123]  Tim Güneysu,et al.  Towards lightweight Identity-Based Encryption for the post-quantum-secure Internet of Things , 2017, 2017 18th International Symposium on Quality Electronic Design (ISQED).

[124]  Dominique Unruh,et al.  Post-quantum Security of Fiat-Shamir , 2017, ASIACRYPT.

[125]  Yunlei Zhao,et al.  Aggregation of Gamma-Signatures and Applications to Bitcoin , 2018, IACR Cryptol. ePrint Arch..

[126]  Tiago M. Fernández-Caramés,et al.  A Review on the Use of Blockchain for the Internet of Things , 2018, IEEE Access.

[127]  Miklós Ajtai,et al.  Generating Hard Instances of Lattice Problems , 1996, Electron. Colloquium Comput. Complex..

[128]  Erdem Alkim,et al.  NewHope without reconciliation , 2016, IACR Cryptol. ePrint Arch..

[129]  Tiago M. Fernández-Caramés,et al.  Towards an Autonomous Industry 4.0 Warehouse: A UAV and Blockchain-Based System for Inventory and Traceability Applications in Big Data-Driven Supply Chain Management , 2019, Sensors.

[130]  Tiago M. Fernández-Caramés,et al.  Clock Frequency Impact on the Performance of High-Security Cryptographic Cipher Suites for Energy-Efficient Resource-Constrained IoT Devices † , 2018, Sensors.

[131]  Tiago M. Fernández-Caramés,et al.  A Practical Evaluation on RSA and ECC-Based Cipher Suites for IoT High-Security Energy-Efficient Fog and Mist Computing Devices , 2018, Sensors.

[132]  Morris J. Dworkin,et al.  SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions , 2015 .

[133]  Alfred Menezes,et al.  A Riddle Wrapped in an Enigma , 2016, IEEE Security & Privacy.

[134]  Gilles Brassard,et al.  Quantum cryptanalysis of hash and claw-free functions , 1997, SIGA.

[135]  Reza Azarderakhsh,et al.  Key Compression for Isogeny-Based Cryptosystems , 2016, AsiaPKC '16.

[136]  Michael Devetsikiotis,et al.  Blockchains and Smart Contracts for the Internet of Things , 2016, IEEE Access.

[137]  Peter Schwabe,et al.  SPHINCS: Practical Stateless Hash-Based Signatures , 2015, EUROCRYPT.

[138]  Ying Sun,et al.  A Secure Cryptocurrency Scheme Based on Post-Quantum Blockchain , 2018, IEEE Access.

[139]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[140]  Rui Guo,et al.  An Anti-Quantum E-Voting Protocol in Blockchain With Audit Function , 2019, IEEE Access.

[141]  Zhen Liu,et al.  Secure Scheme Against Compromised Hash in Proof-of-Work Blockchain , 2018, NSS.

[142]  Man Ho Au,et al.  Anonymous Post-Quantum Cryptocash , 2018, IACR Cryptol. ePrint Arch..

[143]  Pin Lv,et al.  BeeKeeper: A Blockchain-Based IoT System With Secure Storage and Homomorphic Computation , 2018, IEEE Access.

[144]  Damien Stehlé,et al.  CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM , 2017, 2018 IEEE European Symposium on Security and Privacy (EuroS&P).

[145]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[146]  Denis Lukianov,et al.  Compact Confidential Transactions for Bitcoin , 2015 .

[147]  Gilles Brassard,et al.  Strengths and Weaknesses of Quantum Computing , 1997, SIAM J. Comput..

[148]  P. Giungato,et al.  Current Trends in Sustainability of Bitcoins and Related Blockchain Technology , 2017 .

[149]  Ben A. Amaba,et al.  Blockchain technology innovations , 2017, 2017 IEEE Technology & Engineering Management Conference (TEMSCON).

[150]  Olivier Blazy,et al.  Efficient Encryption From Random Quasi-Cyclic Codes , 2016, IEEE Transactions on Information Theory.

[151]  Miguel Castro,et al.  Practical byzantine fault tolerance and proactive recovery , 2002, TOCS.

[152]  Yuval Yarom,et al.  To BLISS-B or not to be: Attacking strongSwan's Implementation of Post-Quantum Signatures , 2017, IACR Cryptol. ePrint Arch..

[153]  Shin'ichiro Matsuo,et al.  Long-Term Public Blockchain: Resilience against Compromise of Underlying Cryptography , 2017, 2017 26th International Conference on Computer Communication and Networks (ICCCN).

[154]  Mario E. Magaña,et al.  Post-quantum hybrid security mechanism for MIMO systems , 2017, 2017 International Conference on Computing, Networking and Communications (ICNC).

[155]  Tiago M. Fernández-Caramés,et al.  A Practical Evaluation of a High-Security Energy-Efficient Gateway for IoT Fog Computing Applications , 2017, Sensors.

[156]  Deepak Puthal,et al.  Everything You Wanted to Know About the Blockchain: Its Promise, Components, Processes, and Problems , 2018, IEEE Consumer Electronics Magazine.

[157]  Jintai Ding,et al.  The Cubic Simple Matrix Encryption Scheme , 2014, PQCrypto.

[158]  Tim Güneysu,et al.  Practical Lattice-Based Cryptography: A Signature Scheme for Embedded Systems , 2012, CHES.

[159]  Kwangjo Kim,et al.  QChain: Quantum-resistant and decentralized PKI using Blockchain , 2018 .

[160]  Paulo S. L. M. Barreto,et al.  CAKE: Code-Based Algorithm for Key Encapsulation , 2017, IMACC.

[161]  Tiago M. Fernández-Caramés,et al.  A Cost-Effective IoT System for Monitoring Indoor Radon Gas Concentration , 2018, Sensors.

[162]  Tiago M. Fernández-Caramés,et al.  Reverse engineering the communications protocol of an RFID public transportation card , 2017, 2017 IEEE International Conference on RFID (RFID).

[163]  Elwyn R. Berlekamp,et al.  On the inherent intractability of certain coding problems (Corresp.) , 1978, IEEE Trans. Inf. Theory.