Quantum Safe Authenticated Key Exchange Protocol for Automotive

Total Page:16

File Type:pdf, Size:1020Kb

Quantum Safe Authenticated Key Exchange Protocol for Automotive Quantum Safe Authenticated Key Exchange 4 connection to the OEM Backend for ECUs, that already in the field. The symmetric algorithms used are supposed to be secure against quantum attacks and these keys can Quantum Safe Authenticated Key Exchange be used as anchors of trust, something that of course requires a centralized key man- Protocol for Automotive Application agement in place and the usage of hardware security anchors, such as HSMs or TPMs. Some ideas worth discussing are the following: Julius Hermelink1, Thomas P¨oppelmann2, Marc St¨ottinger3, Yi Wang4, and Taking advantage of a centralized architecture allows OEMs to focus on the con- Yong Wan4 nected and less resource-constraint Gateway ECUs as a first step. Future domain- based automotive architectures should be already well-suited for this purpose. 1 Research Institute CODE Handling the security use cases for older ECUs in the field in a specialized way: Universit¨atder Bundeswehr M¨unchen different certificates in parallel, only new ECUs handle the PQ Signatures. Older 2 Infineon Technologies, Germany ECUs could only get updates in controlled repair-shop environment, in case the clas- 3 Continental AG, Germany sical certificates are already broken. 4 Continental Automotive, Singapore “Smooth transition”: using classic certificates to perform secure online flashing. In the extreme case that asymmetric cryptography is broken, before a transition has been made: the trust anchor can be a (e.g. hardware aided) symmetric key. This al- Abstract. In this work, we propose an instantiation of a quantum-safe ready poses some requirements for automotive development, to incorporate hard- security protocol for authenticated key establishment (AKE) with for- ware security into the most critical ECUs, and focus on algorithm “agility” when ward secrecy. As core primitives, we use Newhope and XMSS and avoid designing those. signatures in the key exchange to achieve better performance. Exem- plary, the implemented protocol could be used to establish a secured and authentic communication channel between the electrical control unit (ECU) and a testing device for on-board diagnosis (OBD). To verify the 3 Conclusion feasibility, we implement an XMSS-based public key infrastructure (PKI) and the AKE protocol on the AURIX automotive embedded microcon- In conclusion, the technological transformation originating from the eve of quantum troller platform. We provide a breakdown of cycle cost and communica- tion overhead and demonstrate that a modern post-quantum AKE can computers poses a variety of challenges and risks for the automotive industry. In our be executed efficiently on our target platform. presentation, we want to address those and discuss some ideas regarding the steps needed towards overcoming them. 1 Introduction The automotive sector has seen a huge increase of connectivity and automation References over the last decade, resulting in the necessity for strong cryptography to preserve privacy, confidentiality, and authenticity of safety-critical data. In addition, most [1] Lov K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings applications and services implemented in each automotive electrical control unit of the Twenty-eighth Annual ACM Symposium on Theory of Computing, pages 212–219. 1996. (ECU) need to be secured over the entire life cycle. Diagnostic services of an ECU [2] Michele Mosca. Cybersecurity in an era with quantum computers: will we be ready? 2015. are one of the most important feature of every automotive ECU. Thus, these [3] National Institute of Standards and Technology. Post quantum cryptography, 2018. diagnostic service must be protected against unauthorized usage throughout the [4] Peter W. Shor. Algorithms for quantum computation. In Proceedings 35th Annual Sympo- entire life cycle of the ECU. During a remote diagnostic service for a software over sium on Foundations of Computer Science, pages 124–134. IEEE Computer Society Press, the air update, a session key is required to be exchanged between the ECU and 1994. the back end to authenticate and optionally encrypt the transferred data. Hence, [5] Peter W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms cryptographic schemes are implemented to prevent an abuse of the functions of on a quantum computer. 26:1484–1509, 1997. the diagnosis service to carry out attacks against the ECU. A quantum computer breaking common cryptographic schemes in the future could compromise products deployed much earlier with severe implications for the safety of automotive products still in use. This issue is currently addressed by the cryptographic community and standardization bodies. The main driv- ing force is the NIST post-quantum cryptography standardization process [32], 69 J. Hermelink et al. 2 Hermelink et al. which is currently in round 3 with 15 schemes remaining [33]. In parallel, NIST is working on an official standard [16] for the stateful hash-based signature schemes XMSS [20] and LMS [31]. The schemes are promising due to their well under- stood security level and high level of trust. While the schemes instigated by NIST are most likely a major foundation for future secured systems, it is not sufficient to only look at isolated schemes. Most use cases in the automotive domain, e.g., secured channel establishment for remote diagnosis services, require more advanced protocols (see [11]). In this context, it is not sufficient to simply establish a shared secret to communicate using symmetric encryption, especially when a remote connection is used for diagnostic services. Both parties may need forward secrecy and mutual authen- tication, which usually implies the need for long term certificates. It is thus important to investigate the integration of NIST PQC primitives into protocols and real-world systems and to provide feedback on the suitability of possible future algorithms. In general, classic authenticated key exchange (AKE) protocols use a Diffie- Hellman key exchange that is authenticated with a signature and symmetric mes- sage authentication code (MAC). Popular examples are SIGMA [30] or Trans- port Layer Security (TLS) [36]. However, with the need for a migration to post- quantum AKE several issues arise. First, the size of certain elements (e.g., public keys and signatures) is considerably larger than for RSA or ECC. This may lead to increased latency and memory requirements. Moreover, it currently seems that post-quantum digital signatures are more complicated to construct and to secure than public key encryption (PKE) or key encapsulation mechanisms (KEM). In addition, they are typically slower than PKE schemes of a comparable security level (see Section 3) and may even exhibit no deterministic runtime. Such non deterministic runtime may make it impossible to guarantee a response within a defined timeframe. On the other hand, stateful hash-based signatures look very promising due to the high confidence level. However, the usage of stateful hash- based signatures requires more careful management of the state of the private key compared to stateless signature schemes. As a consequence, the practical deployment of PQC in the automotive do- main appears challenging due to often limited computational power and re- quirements for defined response times. First works already implemented and optimized schemes like Newhope for automotive microcontrollers [18]. However, it is necessary to increase the understanding of the cost and performance of a full AKE. In addition, it is necessary to determine where specific low-level optimizations (e.g., assembly code, compiler directives) are most effective. A promising proposal for efficient AKE is a protocol proposed by Guilhem, Smart, and Warinschi [37] that explicitly avoids signing operations in the protocol. The protocol achieves authenticated key exchange between devices by using an IND- CPA secured key exchange protocol, an IND-CCA secured private key encryption protocol, a symmetric cipher, and a hash function for message authentication. Contribution. In this work, we investigate challenges and the performance of AKE protocols designed for instantiation with quantum-safe algorithms [37] 70 Quantum Safe Authenticated Key Exchange Quantum Safe Authenticated Key Exchange 3 on the automotive microcontroller platform AURIXTM[22]. We provide an in- stantiation of the protocol with a selection of ciphers that aim for high security and simple implementation. We thus employ Newhope1024-CPA-KEM [2] for ephemeral key exchange, NewHope1024-CCA-KEM for encrypted-based authen- tication, AES256-GCM for data encryption and SHA3 as MAC. To protect the PKI we use XMSS-SHA2 10 256 [20] signatures. We chose a lattice-based KEM scheme for the session key exchange for having a relatively small key size, good performance, and fast key generation for ephemeral key exchange. We selected a stateful hash-based signature scheme for the verification of the long term certifi- cate because of the small public key and very good long term security properties. To get a better understanding of the lower boundary of the overhead and prac- ticability of AKE protocol, we implemented the entire scheme using open-source reference implementations of the cryptographic algorithms. As an initial step, we used reference implementations to identify possible bottlenecks and to get the big picture on the overall performance of the AKE protocol and the certificate validation. We provide information on message sizes and discuss standalone per- formance of the cryptographic
Recommended publications
  • Name of the Proposed Cryptosystem: Newhope Principal Submitter: C/O
    Name of the proposed cryptosystem: NewHope Principal submitter: c/o Thomas Pöppelmann Infineon Technologies AG Am Campeon 1–12 85579 Neubiberg, Germany email: thomas.poeppelmann@infineon.com phone: +49 (89) 234-64019 Auxiliary submitters: Erdem Alkim Roberto Avanzi Joppe Bos Léo Ducas Antonio de la Piedra Peter Schwabe Douglas Stebila Additional Round Two Contributors: Martin R. Albrecht Emmanuela Orsini Valery Osheter Kenneth G. Paterson Guy Peer Nigel P. Smart Inventors of the cryptosystem Erdem Alkim, Léo Ducas, Thomas Pöppel- mann, and Peter Schwabe, based on a large collection of previous work, most importantly by Vadim Lyubashevsky, Chris Peikert, Oded Regev, Eiichiro Fujisaki, and Tatsuaki Okamoto. Owner of the cryptosystem None (dedicated to the public domain) Thomas Pöppelmann 1 Alternative points of contact: Peter Schwabe Radboud University Toernooiveld 212 6525 EC Nijmegen The Netherlands email: [email protected] phone: +31243653456 2 NewHope Algorithm Specifications and Supporting Documentation Original Submitters: Erdem Alkim, Roberto Avanzi, Joppe Bos, Léo Ducas, Antonio de la Piedra, Thomas Pöppelmann, Peter Schwabe, Douglas Stebila Additional Round Two Contributors: Martin R. Albrecht, Emmanuela Orsini, Valery Osheter, Kenneth G. Paterson, Guy Peer, Nigel P. Smart Version 1.03 - (Updated July 10, 2019) 1 Contents 1 Written specification 4 1.1 Mathematical background......................................4 1.1.1 Basic definitions.......................................4 1.1.2 Computational problems on lattices............................4 1.1.3 Ring-LWE problem......................................5 1.2 Algorithm description........................................6 1.2.1 IND-CPA-secure public key encryption scheme......................6 1.2.2 Interconversion to IND-CPA KEM............................. 12 1.2.3 Transform from IND-CPA PKE to IND-CCA KEM..................
    [Show full text]
  • Post-Quantum Cryptography
    Post-quantum cryptography Daniel J. Bernstein & Tanja Lange University of Illinois at Chicago; Ruhr University Bochum & Technische Universiteit Eindhoven 12 September 2020 I Motivation #1: Communication channels are spying on our data. I Motivation #2: Communication channels are modifying our data. I Literal meaning of cryptography: \secret writing". I Achieves various security goals by secretly transforming messages. I Confidentiality: Eve cannot infer information about the content I Integrity: Eve cannot modify the message without this being noticed I Authenticity: Bob is convinced that the message originated from Alice Cryptography with symmetric keys AES-128. AES-192. AES-256. AES-GCM. ChaCha20. HMAC-SHA-256. Poly1305. SHA-2. SHA-3. Salsa20. Cryptography with public keys BN-254. Curve25519. DH. DSA. ECDH. ECDSA. EdDSA. NIST P-256. NIST P-384. NIST P-521. RSA encrypt. RSA sign. secp256k1. Cryptography / Sender Receiver \Alice" \Bob" Tsai Ing-Wen picture credit: By =q府, Attribution, Wikimedia. Donald Trump picture credit: By Shealah Craighead - White House, Public Domain, Wikimedia. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography2 Cryptography with symmetric keys AES-128. AES-192. AES-256. AES-GCM. ChaCha20. HMAC-SHA-256. Poly1305. SHA-2. SHA-3. Salsa20. I Literal meaning of cryptography: \secret writing". Cryptography with public keys Achieves various security goals by secretly transforming messages. BN-254I . Curve25519. DH. DSA. ECDH. ECDSA. EdDSA. NIST P-256. NIST P-384. Confidentiality: Eve cannot infer information about the content NISTI P-521. RSA encrypt. RSA sign. secp256k1. I Integrity: Eve cannot modify the message without this being noticed I Authenticity: Bob is convinced that the message originated from Alice Cryptography / Sender Untrustworthy network Receiver \Alice" \Eve" \Bob" I Motivation #1: Communication channels are spying on our data.
    [Show full text]
  • DESIGN and CRYPTANALYSIS of POST QUANTUM CRYPTOSYSTEMS Olive Chakraborty
    DESIGN AND CRYPTANALYSIS OF POST QUANTUM CRYPTOSYSTEMS Olive Chakraborty To cite this version: Olive Chakraborty. DESIGN AND CRYPTANALYSIS OF POST QUANTUM CRYPTOSYSTEMS. Cryptography and Security [cs.CR]. Sorbonne Université, 2020. English. tel-03135217 HAL Id: tel-03135217 https://tel.archives-ouvertes.fr/tel-03135217 Submitted on 12 Feb 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE DE DOCTORANT DE SORBONNE UNIVERSITÉ Spécialité Informatique École Doctorale Informatique, Télécommunications et Électronique (Paris) Présentée par OLIVE CHAKRABORTY Pur obtenir le grade de DOCTEUR DE SORBONNE UNIVERSITÈ DESIGN AND CRYPTANALYSIS OF POST QUANTUM CRYPTOSYSTEMS Thèse dirigée par JEAN-CHARLES FAUGÈRE et LUDOVIC PERRET après avis des rapporteurs: Mme. Delaram KAHROBAEI Professeur, University of York, U.K M. Jacques PATARIN Professeur, Université de Versailles devant le jury composé de : M. Jean-Charles FAUGÈRE Directeur de recherche, INRIA Paris M. Stef GRAILLAT Professeur, Sorbonne Université, LIP6 Mme. Delaram KAHROBAEI Professeur, University of York, U.K M. Jacques PATARIN Professeur, Université de Versailles M. Ludovic PERRET Maître de Conférences, Sorbonne Université, LIP6 M. Mohab SAFEY EL DIN Professeur, Sorbonne Université, LIP6 Date de soutenance : 16-12-2020 Résumé La résolution de systèmes polynomiaux est l’un des problèmes les plus anciens et des plus importants en Calcul Formel et a de nombreuses applications.
    [Show full text]
  • Comparison Analysis of Ding's Rlwe-Based Key Exchange
    Advances in Mathematics of Communications doi:10.3934/amc.2019015 Volume 13, No. 2, 2019, 221{233 COMPARISON ANALYSIS OF DING'S RLWE-BASED KEY EXCHANGE PROTOCOL AND NEWHOPE VARIANTS Xinwei Gao∗ Beijing Key Laboratory of Security and Privacy in Intelligent Transportation Beijing Jiaotong University No.3 ShangYuanCun, Haidian District, Beijing 100044, China (Communicated by Jintai Ding) Abstract. In this paper, we present a comparison study on three RLWE key exchange protocols: one from Ding et al. in 2012 (DING12) and two from Alkim et al. in 2016 (NewHope and NewHope-Simple). We compare and an- alyze protocol construction, notion of designing and realizing key exchange, signal computation, error reconciliation and cost of these three protocols. We show that NewHope and NewHope-Simple share very similar notion as DING12 in the sense that NewHope series also send small additional bits with small size (i.e. signal) to assist error reconciliation, where this idea was first practically proposed in DING12. We believe that DING12 is the first work that pre- sented complete LWE & RLWE-based key exchange constructions. The idea of sending additional information in order to realize error reconciliation and key exchange in NewHope and NewHope-Simple remain the same as DING12, despite concrete approaches to compute signal and reconcile error are not the same. 1. Introduction Diffie and Hellman (DH) proposed the first public key cryptography algorithm in 1976 by introducing a key exchange protocol [9]. DH key exchange allows two parties to agree on same key without any prior knowledge over public (insecure) channel. In DH key exchange, both parties send their own public key to the other side.
    [Show full text]
  • CRYSTALS-Dilithium: a Lattice-Based Digital Signature Scheme
    CRYSTALS-Dilithium: A Lattice-Based Digital Signature Scheme Léo Ducas1, Eike Kiltz2, Tancrède Lepoint3, Vadim Lyubashevsky4, Peter Schwabe5, Gregor Seiler6 and Damien Stehlé7 1 CWI, Netherlands 2 Ruhr Universität Bochum, Germany 3 SRI International, USA 4 IBM Research – Zurich, Switzerland 5 Radboud University, Netherlands 6 IBM Research – Zurich and ETH Zurich, Switzerland 7 ENS de Lyon, France Abstract. In this paper, we present the lattice-based signature scheme Dilithium, which is a component of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) suite that was submitted to NIST’s call for post-quantum cryptographic standards. The design of the scheme avoids all uses of discrete Gaussian sampling and is easily implementable in constant-time. For the same security levels, our scheme has a public key that is 2.5X smaller than the previously most efficient lattice-based schemes that did not use Gaussians, while having essentially the same signature size. In addition to the new design, we significantly improve the running time of the main component of many lattice-based constructions – the number theoretic transform. Our AVX2-based implementation results in a speed-up of roughly a factor of 2 over the previously best algorithms that appear in the literature. The techniques for obtaining this speed-up also have applications to other lattice-based schemes. Keywords: Lattice Cryptography · Digital Signatures · Constant-Time Implementa- tion · AVX2 1 Introduction Cryptography based on the hardness of lattice problems is seen as a very promising replacement of traditional cryptography after the eventual coming of quantum computers. In this paper, we present a new digital signature scheme Dilithium, whose security is based on the hardness of finding short vectors in lattices.
    [Show full text]
  • A Systematic Study of Lattice-Based NIST PQC Algorithms: from Reference Implementations to Hardware Accelerators
    A Systematic Study of Lattice-based NIST PQC Algorithms: from Reference Implementations to Hardware Accelerators Malik Imran, Zain Ul Abideen and Samuel Pagliarini Centre for Hardware Security (CHS), Tallinn University of Technology (TalTech), Estonia, {malik.imran,zain.abideen,samuel.pagliarini}@taltech.ee Abstract. Security of currently deployed public key cryptography algorithms is foreseen to be vulnerable against quantum computer attacks. Hence, a community effort exists to develop post-quantum cryptography (PQC) algorithms, i.e., algorithms that are resistant to quantum attacks. In this work, we have investigated how lattice- based candidate algorithms from the NIST PQC standardization competition fare when conceived as hardware accelerators. To achieve this, we have assessed the reference implementations of selected algorithms with the goal of identifying what are their basic building blocks. We assume the hardware accelerators will be implemented in application specific integrated circuit (ASIC) and the targeted technology in our experiments is a commercial 65nm node. In order to estimate the characteristics of each algorithm, we have assessed their memory requirements, use of multipliers, and how each algorithm employs hashing functions. Furthermore, for these building blocks, we have collected area and power figures for 12 candidate algorithms. For memories, we make use of a commercial memory compiler. For logic, we make use of a standard cell library. In order to compare the candidate algorithms fairly, we select a reference frequency of operation of 500MHz. Our results reveal that our area and power numbers are comparable to the state of the art, despite targeting a higher frequency of operation and a higher security level in our experiments.
    [Show full text]
  • Qdsa: Small and Secure Digital Signatures with Curve-Based Diffie
    qDSA: Small and Secure Digital Signatures with Curve-based Diffie–Hellman Key Pairs Joost Renes1? and Benjamin Smith2 1 Digital Security Group, Radboud University, The Netherlands [email protected] 2 INRIA and Laboratoire d’Informatique de l’École polytechnique (LIX), Université Paris–Saclay, France [email protected] Abstract. qDSA is a high-speed, high-security signature scheme that facilitates implementa- tions with a very small memory footprint, a crucial requirement for embedded systems and IoT devices, and that uses the same public keys as modern Diffie–Hellman schemes based on Montgomery curves (such as Curve25519) or Kummer surfaces. qDSA resembles an adaptation of EdDSA to the world of Kummer varieties, which are quotients of algebraic groups by ±1. Interestingly, qDSA does not require any full group operations or point recovery: all computa- tions, including signature verification, occur on the quotient where there is no group law. We include details on four implementations of qDSA, using Montgomery and fast Kummer surface arithmetic on the 8-bit AVR ATmega and 32-bit ARM Cortex M0 platforms. We find that qDSA significantly outperforms state-of-the-art signature implementations in terms of stack usage and code size. We also include an efficient compression algorithm for points on fast Kummer surfaces, reducing them to the same size as compressed elliptic curve points for the same security level. Keywords. Signatures, Kummer, Curve25519, Diffie–Hellman, elliptic curve, hyperelliptic curve. 1 Introduction Modern asymmetric cryptography based on elliptic and hyperelliptic curves [31, 33] achieves two important goals. The first is efficient key exchange using the Diffie–Hellman protocol [18], using the fact that the (Jacobian of the) curve carries the structure of an abelian group.
    [Show full text]
  • Efficient Parallel Implementations of LWE-Based Post-Quantum
    mathematics Article Efficient Parallel Implementations of LWE-Based Post-Quantum Cryptosystems on Graphics Processing Units SangWoo An 1 and Seog Chung Seo 2,* 1 Department of Financial Information Security, Kookmin University, Seoul 02707, Korea; [email protected] 2 Department of Information Security, Cryptology, and Mathematics, Kookmin University, Seoul 02707, Korea * Correspondence: [email protected]; Tel.: +82-02-910-4742 Received: 13 September 2020; Accepted: 8 October 2020; Published: 14 October 2020 Abstract: With the development of the Internet of Things (IoT) and cloud computing technology, various cryptographic systems have been proposed to protect increasing personal information. Recently, Post-Quantum Cryptography (PQC) algorithms have been proposed to counter quantum algorithms that threaten public key cryptography. To efficiently use PQC in a server environment dealing with large amounts of data, optimization studies are required. In this paper, we present optimization methods for FrodoKEM and NewHope, which are the NIST PQC standardization round 2 competition algorithms in the Graphics Processing Unit (GPU) platform. For each algorithm, we present a part that can perform parallel processing of major operations with a large computational load using the characteristics of the GPU. In the case of FrodoKEM, we introduce parallel optimization techniques for matrix generation operations and matrix arithmetic operations such as addition and multiplication. In the case of NewHope, we present a parallel processing technique for polynomial-based operations. In the encryption process of FrodoKEM, the performance improvements have been confirmed up to 5.2, 5.75, and 6.47 times faster than the CPU implementation in FrodoKEM-640, FrodoKEM-976, and FrodoKEM-1344, respectively.
    [Show full text]
  • Newhope: a Mobile Implementation of a Post-Quantum Cryptographic Key Encapsulation Mechanism
    Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-26-2020 NewHope: A Mobile Implementation of a Post-Quantum Cryptographic Key Encapsulation Mechanism Jessica A. Switzler Follow this and additional works at: https://scholar.afit.edu/etd Part of the Computer Sciences Commons Recommended Citation Switzler, Jessica A., "NewHope: A Mobile Implementation of a Post-Quantum Cryptographic Key Encapsulation Mechanism" (2020). Theses and Dissertations. 3190. https://scholar.afit.edu/etd/3190 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. NewHope: A Mobile Implementation of a Post-Quantum Crytographic Key Encapsulation Mechanism THESIS Jessica A. Switzler AFIT-ENG-MS-20-M-063 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this document are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Department of Defense or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENG-MS-20-M-063 NewHope: A Mobile Implementation of a Post-Quantum Crytographic Key Encapsulation Mechanism THESIS Presented to the Faculty Department of Electrical and Computer Engineering Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Fulfillment of the Requirements for the Degree of Master of Science in Cyber Operations Jessica A.
    [Show full text]
  • High-Speed Key Encapsulation from NTRU
    High-speed key encapsulation from NTRU Andreas Hülsing1, Joost Rijneveld2, John Schanck3;4, and Peter Schwabe2 ? 1 Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, The Netherlands [email protected] 2 Digital Security Group, Radboud University, The Netherlands [email protected], [email protected] 3 Institute for Quantum Computing, University of Waterloo, Canada, and 4 Security Innovation, Wilmington, MA, USA [email protected] Abstract. This paper presents software demonstrating that the 20- year-old NTRU cryptosystem is competitive with more recent lattice- based cryptosystems in terms of speed, key size, and ciphertext size. We present a slightly simplified version of textbook NTRU, select param- eters for this encryption scheme that target the 128-bit post-quantum security level, construct a KEM that is CCA2-secure in the quantum random oracle model, and present highly optimized software targeting Intel CPUs with the AVX2 vector instruction set. This software takes only 307 914 cycles for the generation of a keypair, 48 646 for encapsu- lation, and 67 338 for decapsulation. It is, to the best of our knowledge, the first NTRU software with full protection against timing attacks. Keywords. Post-quantum crypto, lattice-based crypto, NTRU, CCA2- secure KEM, QROM, AVX2. 1 Introduction In December 2016, NIST issued a call for proposals for “post-quantum cryptogra- phy” [34] to select schemes for standardization. More specifically, NIST requests algorithms in three categories: public-key encryption, key exchange or key en- capsulation mechanisms (KEMs), and digital signatures. Obviously, the central requirement is that proposed schemes are indeed “post-quantum”, i.e., that they resist attacks by a large quantum computer.
    [Show full text]
  • The 2Nd Round of the NIST PQC Standardization Process
    An Update on NIST’s Post-Quantum Crypto Standardization DUSTIN MOODY NIST Crypto Standards Areas: ◦ Block ciphers ◦ Key-establishment ◦ Hash functions ◦ Post-quantum crypto (signatures ◦ Message authentication codes + key establishment) (MACs) ◦ Random bit generation ◦ Digital signatures ◦ etc… FIPS, SP’s, and NISTIRs NISTIR 7977 – NIST’s process for developing crypto standards Cooperation with other SDO’s Principles: Transparency, openness, balance, integrity, technical merit, global acceptability, usability, continuous improvement, innovation and intellectual property Stakeholders: Primarily the US federal government, broader industry and public/private organizations Quantum Computers Exploit quantum mechanics to process information Use quantum bits = “qubits” instead of 0’s and 1’s Intel’s 49-qubit chip Superposition – ability of quantum system to be in “Tangle-Lake” multiple states at the same time Potential to vastly increase computational power IBM’s 50-qubit beyond classical computing limit quantum computer Limitations: ◦ When a measurement is made on quantum system, Google’s 72-qubit chip superposition collapses “Bristlecone” ◦ Only good at certain problems ◦ Quantum states are very fragile and must be extremely well isolated Quantum Computing Progress A lot of progress, but still a long way to go [Image credit: M. Devoret and R. Schoelkopf] Quantum Algorithms 1994, Peter Shor created a quantum algorithm that would give an exponential speed-up over classical computers ◦ Factoring large integers ◦ Finding discrete logarithms Grover’s
    [Show full text]
  • NIST Status Update on Elliptic Curves and Post-Quantum Crypto
    NIST status update on Elliptic Curves and Post-Quantum Crypto Dustin Moody Elliptic Curve Crypto in NIST Standards ▪ FIPS 186-4, Digital Signature Standard ▪ Elliptic Curve Digital Signature Algorithm (ECDSA) ▪ 15 recommended curves ▪ Also has DSA, RSA signatures ▪ SP 800-56A, Recommendation for Pair-Wise Key Establishment Schemes using Discrete Logarithm Cryptography ▪ Elliptic Curve Diffie Hellman (ECDH) ▪ Elliptic Curve authenticated key agreement (ECMQV) Changes in FIPS 186-5 ▪ New requirement to publish seeds for DSA signatures ▪ X9.31 RSA signatures removed ▪ Larger key sizes (2048 bits or more) for RSA signatures allowed ▪ More elliptic curve details added ▪ New SP 800-186 has most of them ▪ New elliptic curves specified (Edwards25519 and Edwards448) ▪ The EdDSA signature algorithm is included ▪ Deterministic version of ECDSA included ▪ Various minor improvements/corrections to algorithms in appendices DSA signatures ▪ Two of the domain parameters for DSA are prime numbers p and q, where 1 = · ▪ These primes are supposed to be generated deterministically, from a random seed − ℎ ▪ Recent research showed that DSA primes could be generated in such a way that there is a trapdoor ▪ With knowledge of the trapdoor, one can compute discrete logs efficiently, which breaks the security of DSA ▪ It seems hard to detect if such a trapdoor is present ▪ Recommended remedy: publish the seed ▪ The trapdoor primes have to be specially constructed; publishing the seed shows this wasn’t done ▪ FIPS 186-5 makes publishing the seeds mandatory RSA
    [Show full text]