The Whole Is Less Than the Sum of Its Parts: Constructing More Efficient Lattice-Based Akes?
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Etsi Gr Qsc 001 V1.1.1 (2016-07)
ETSI GR QSC 001 V1.1.1 (2016-07) GROUP REPORT Quantum-Safe Cryptography (QSC); Quantum-safe algorithmic framework 2 ETSI GR QSC 001 V1.1.1 (2016-07) Reference DGR/QSC-001 Keywords algorithm, authentication, confidentiality, security ETSI 650 Route des Lucioles F-06921 Sophia Antipolis Cedex - FRANCE Tel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16 Siret N° 348 623 562 00017 - NAF 742 C Association à but non lucratif enregistrée à la Sous-Préfecture de Grasse (06) N° 7803/88 Important notice The present document can be downloaded from: http://www.etsi.org/standards-search The present document may be made available in electronic versions and/or in print. The content of any electronic and/or print versions of the present document shall not be modified without the prior written authorization of ETSI. In case of any existing or perceived difference in contents between such versions and/or in print, the only prevailing document is the print of the Portable Document Format (PDF) version kept on a specific network drive within ETSI Secretariat. Users of the present document should be aware that the document may be subject to revision or change of status. Information on the current status of this and other ETSI documents is available at https://portal.etsi.org/TB/ETSIDeliverableStatus.aspx If you find errors in the present document, please send your comment to one of the following services: https://portal.etsi.org/People/CommiteeSupportStaff.aspx Copyright Notification No part may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm except as authorized by written permission of ETSI. -
Circuit-Extension Handshakes for Tor Achieving Forward Secrecy in a Quantum World
Proceedings on Privacy Enhancing Technologies ; 2016 (4):219–236 John M. Schanck*, William Whyte, and Zhenfei Zhang Circuit-extension handshakes for Tor achieving forward secrecy in a quantum world Abstract: We propose a circuit extension handshake for 2. Anonymity: Some one-way authenticated key ex- Tor that is forward secure against adversaries who gain change protocols, such as ntor [13], guarantee that quantum computing capabilities after session negotia- the unauthenticated peer does not reveal their iden- tion. In doing so, we refine the notion of an authen- tity just by participating in the protocol. Such pro- ticated and confidential channel establishment (ACCE) tocols are deemed one-way anonymous. protocol and define pre-quantum, transitional, and post- 3. Forward Secrecy: A protocol provides forward quantum ACCE security. These new definitions reflect secrecy if the compromise of a party’s long-term the types of adversaries that a protocol might be de- key material does not affect the secrecy of session signed to resist. We prove that, with some small mod- keys negotiated prior to the compromise. Forward ifications, the currently deployed Tor circuit extension secrecy is typically achieved by mixing long-term handshake, ntor, provides pre-quantum ACCE security. key material with ephemeral keys that are discarded We then prove that our new protocol, when instantiated as soon as the session has been established. with a post-quantum key encapsulation mechanism, Forward secret protocols are a particularly effective tool achieves the stronger notion of transitional ACCE se- for resisting mass surveillance as they resist a broad curity. Finally, we instantiate our protocol with NTRU- class of harvest-then-decrypt attacks. -
NSS: an NTRU Lattice –Based Signature Scheme
ISSN(Online) : 2319 - 8753 ISSN (Print) : 2347 - 6710 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 4, Issue 4, April 2015 NSS: An NTRU Lattice –Based Signature Scheme S.Esther Sukila Department of Mathematics, Bharath University, Chennai, Tamil Nadu, India ABSTRACT: Whenever a PKC is designed, it is also analyzed whether it could be used as a signature scheme. In this paper, how the NTRU concept can be used to form a digital signature scheme [1] is described. I. INTRODUCTION Digital Signature Schemes The notion of a digital signature may prove to be one of the most fundamental and useful inventions of modern cryptography. A digital signature or digital signature scheme is a mathematical scheme for demonstrating the authenticity of a digital message or document. The creator of a message can attach a code, the signature, which guarantees the source and integrity of the message. A valid digital signature gives a recipient reason to believe that the message was created by a known sender and that it was not altered in transit. Digital signatures are commonly used for software distribution, financial transactions etc. Digital signatures are equivalent to traditional handwritten signatures. Properly implemented digital signatures are more difficult to forge than the handwritten type. 1.1A digital signature scheme typically consists of three algorithms A key generationalgorithm, that selects a private key uniformly at random from a set of possible private keys. The algorithm outputs the private key and a corresponding public key. A signing algorithm, that given a message and a private key produces a signature. -
Lattice-Based Cryptography - a Comparative Description and Analysis of Proposed Schemes
Lattice-based cryptography - A comparative description and analysis of proposed schemes Einar Løvhøiden Antonsen Thesis submitted for the degree of Master in Informatics: programming and networks 60 credits Department of Informatics Faculty of mathematics and natural sciences UNIVERSITY OF OSLO Autumn 2017 Lattice-based cryptography - A comparative description and analysis of proposed schemes Einar Løvhøiden Antonsen c 2017 Einar Løvhøiden Antonsen Lattice-based cryptography - A comparative description and analysis of proposed schemes http://www.duo.uio.no/ Printed: Reprosentralen, University of Oslo Acknowledgement I would like to thank my supervisor, Leif Nilsen, for all the help and guidance during my work with this thesis. I would also like to thank all my friends and family for the support. And a shoutout to Bliss and the guys there (you know who you are) for providing a place to relax during stressful times. 1 Abstract The standard public-key cryptosystems used today relies mathematical problems that require a lot of computing force to solve, so much that, with the right parameters, they are computationally unsolvable. But there are quantum algorithms that are able to solve these problems in much shorter time. These quantum algorithms have been known for many years, but have only been a problem in theory because of the lack of quantum computers. But with recent development in the building of quantum computers, the cryptographic world is looking for quantum-resistant replacements for today’s standard public-key cryptosystems. Public-key cryptosystems based on lattices are possible replacements. This thesis presents several possible candidates for new standard public-key cryptosystems, mainly NTRU and ring-LWE-based systems. -
Overview of Post-Quantum Public-Key Cryptosystems for Key Exchange
Overview of post-quantum public-key cryptosystems for key exchange Annabell Kuldmaa Supervised by Ahto Truu December 15, 2015 Abstract In this report we review four post-quantum cryptosystems: the ring learning with errors key exchange, the supersingular isogeny key exchange, the NTRU and the McEliece cryptosystem. For each protocol, we introduce the underlying math- ematical assumption, give overview of the protocol and present some implementa- tion results. We compare the implementation results on 128-bit security level with elliptic curve Diffie-Hellman and RSA. 1 Introduction The aim of post-quantum cryptography is to introduce cryptosystems which are not known to be broken using quantum computers. Most of today’s public-key cryptosys- tems, including the Diffie-Hellman key exchange protocol, rely on mathematical prob- lems that are hard for classical computers, but can be solved on quantum computers us- ing Shor’s algorithm. In this report we consider replacements for the Diffie-Hellmann key exchange and introduce several quantum-resistant public-key cryptosystems. In Section 2 the ring learning with errors key exchange is presented which was introduced by Peikert in 2014 [1]. We continue in Section 3 with the supersingular isogeny Diffie–Hellman key exchange presented by De Feo, Jao, and Plut in 2011 [2]. In Section 5 we consider the NTRU encryption scheme first described by Hoffstein, Piphe and Silvermain in 1996 [3]. We conclude in Section 6 with the McEliece cryp- tosystem introduced by McEliece in 1978 [4]. As NTRU and the McEliece cryptosys- tem are not originally designed for key exchange, we also briefly explain in Section 4 how we can construct key exchange from any asymmetric encryption scheme. -
Qchain: Quantum-Resistant and Decentralized PKI Using Blockchain
SCIS 2018 2018 Symposium on Cryptography and Information Security Niigata, Japan, Jan. 23 - 26, 2018 The Institute of Electronics, Copyright c 2018 The Institute of Electronics, Information and Communication Engineers Information and Communication Engineers QChain: Quantum-resistant and Decentralized PKI using Blockchain Hyeongcheol An ∗ Kwangjo Kim ∗ Abstract: Blockchain was developed under public domain and distributed database using the P2P connection. Therefore, blockchain does not have any central administrator or Certificate Au- thority(CA). However, Public Key Infrastructure(PKI) must have CA which issues and signs the digital certificates. PKI CA must be fully trusted by all parties in a domain. Also, current public key cryptosystem can be broken using quantum computing attacks. The post-quantum cryptography (PQC) must be secure against the quantum adversary. We combine blockchain technique with one of post-quantum cryptography lattice-based cryptosystems. In this paper, we suggest QChain which is quantum-resistant decentralized PKI system using blockchain. We propose modified lattice-based GLP signature scheme. QChain uses modified GLP signature which uses Number Theoretic Transformation (NTT). We compare currently used X.509 v3 PKI and QChain certificate. Keywords: blockchain, post-quantum cryptography, lattice, decentralized PKI 1 Introduction ficulty of Discrete Logarithm Problem (DLP) and In- teger Factorization Problem (IFP). However, DLP and 1.1 Motivation IFP can be solved within the polynomial time by Shor's Public-key cryptosystem needs Public Key Infras- algorithm[3] using the quantum computer. Therefore, tructure (PKI) which is to guarantee the integrity of we need secure public key cryptosystem against the for all user's public key. Currently used PKI system quantum adversary. -
On the Security of Lattice-Based Cryptography Against Lattice Reduction and Hybrid Attacks
On the Security of Lattice-Based Cryptography Against Lattice Reduction and Hybrid Attacks Vom Fachbereich Informatik der Technischen Universit¨atDarmstadt genehmigte Dissertation zur Erlangung des Grades Doktor rerum naturalium (Dr. rer. nat.) von Dipl.-Ing. Thomas Wunderer geboren in Augsburg. Referenten: Prof. Dr. Johannes Buchmann Dr. Martin Albrecht Tag der Einreichung: 08. 08. 2018 Tag der m¨undlichen Pr¨ufung: 20. 09. 2018 Hochschulkennziffer: D 17 Wunderer, Thomas: On the Security of Lattice-Based Cryptography Against Lattice Reduction and Hybrid Attacks Darmstadt, Technische Universit¨atDarmstadt Jahr der Ver¨offentlichung der Dissertation auf TUprints: 2018 Tag der m¨undlichen Pr¨ufung:20.09.2018 Ver¨offentlicht unter CC BY-SA 4.0 International https://creativecommons.org/licenses/ Abstract Over the past decade, lattice-based cryptography has emerged as one of the most promising candidates for post-quantum public-key cryptography. For most current lattice-based schemes, one can recover the secret key by solving a corresponding instance of the unique Shortest Vector Problem (uSVP), the problem of finding a shortest non-zero vector in a lattice which is unusually short. This work is concerned with the concrete hardness of the uSVP. In particular, we study the uSVP in general as well as instances of the problem with particularly small or sparse short vectors, which are used in cryptographic constructions to increase their efficiency. We study solving the uSVP in general via lattice reduction, more precisely, the Block-wise Korkine-Zolotarev (BKZ) algorithm. In order to solve an instance of the uSVP via BKZ, the applied block size, which specifies the BKZ algorithm, needs to be sufficiently large. -
Eindhoven University of Technology MASTER Towards Post-Quantum
Eindhoven University of Technology MASTER Towards post-quantum bitcoin side-channel analysis of bimodal lattice signatures Groot Bruinderink, L. Award date: 2016 Link to publication Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain Towards Post-Quantum Bitcoin Side-Channel Analysis of Bimodal Lattice Signatures Leon Groot Bruinderink Email: [email protected] Student-ID: 0682427 A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Industrial and Applied Mathematics Supervisors: prof.dr. Tanja Lange (TU/e) dr. Andreas H¨ulsing(TU/e) dr. Lodewijk Bonebakker (ING) January 2016 Acknowledgements This thesis is the result of many months of work, both at my internship company ING and university TU/e. -
A Quantum-Safe Circuit-Extension Handshake for Tor
A quantum-safe circuit-extension handshake for Tor John Schanck, William Whyte, and Zhenfei Zhang Security Innovation, Wilmington, MA 01887 fjschanck,wwhyte,[email protected] Abstract. We propose a method for integrating NTRUEncrypt into the ntor key exchange protocol as a means of achieving a quantum-safe variant of forward secrecy. The proposal is a minimal change to ntor, essentially consisting of an NTRUEncrypt-based key exchange performed in parallel with the ntor handshake. Performance figures are provided demonstrating that the client bears most of the additional overhead, and that the added load on the router side is acceptable. We make this proposal for two reasons. First, we believe it to be an interesting case study into the practicality of quantum-safe cryptography and into the difficulties one might encounter when transi tioning to quantum-safe primitives within real-world protocols and code-bases. Second, we believe that Tor is a strong candidate for an early transition to quantum-safe primitives; users of Tor may be jus tifiably concerned about adversaries who record traffic in the present and store it for decryption when technology or cryptanalytic techniques improve in the future. 1 Introduction such as [12,23], as well as some Diffie-Hellman proto cols like ntor [8]. A key exchange protocol allows two parties who share no common secrets to agree on a common key over Forward secrecy. A protocol achieves forward secrecy a public channel. In addition to achieving this ba if the compromise of any party’s long-term key ma sic goal, key exchange protocols may satisfy various terial does not affect the secrecy of session keys de secondary properties that are deemed important to rived prior to the compromise. -
A Study on the Security of Ntrusign Digital Signature Scheme
A Thesis for the Degree of Master of Science A Study on the Security of NTRUSign digital signature scheme SungJun Min School of Engineering Information and Communications University 2004 A Study on the Security of NTRUSign digital signature scheme A Study on the Security of NTRUSign digital signature scheme Advisor : Professor Kwangjo Kim by SungJun Min School of Engineering Information and Communications University A thesis submitted to the faculty of Information and Commu- nications University in partial fulfillment of the requirements for the degree of Master of Science in the School of Engineering Daejeon, Korea Jan. 03. 2004 Approved by (signed) Professor Kwangjo Kim Major Advisor A Study on the Security of NTRUSign digital signature scheme SungJun Min We certify that this work has passed the scholastic standards required by Information and Communications University as a thesis for the degree of Master of Science Jan. 03. 2004 Approved: Chairman of the Committee Kwangjo Kim, Professor School of Engineering Committee Member Jae Choon Cha, Assistant Professor School of Engineering Committee Member Dae Sung Kwon, Ph.D NSRI M.S. SungJun Min 20022052 A Study on the Security of NTRUSign digital signature scheme School of Engineering, 2004, 43p. Major Advisor : Prof. Kwangjo Kim. Text in English Abstract The lattices have been studied by cryptographers for last decades, both in the field of cryptanalysis and as a source of hard problems on which to build encryption schemes. Interestingly, though, research about building secure and efficient -
Masking the GLP Lattice-Based Signature Scheme at Any Order
Masking the GLP Lattice-Based Signature Scheme at Any Order Gilles Barthe1, Sonia Bela¨ıd2, omas Espitau3, Pierre-Alain Fouque4, Benjamin Gregoire´ 5, Melissa´ Rossi6;7, and Mehdi Tibouchi8 1 IMDEA Soware Institute [email protected] 2 CryptoExperts [email protected] 3 Sorbonne Universite,´ Laboratoire d’informatique de Paris VI [email protected] 4 Universite´ de Rennes [email protected] 5 Inria Sophia Antipolis [email protected] 6 ales 7 Ecole´ Normale Superieure´ de Paris, Departement´ d’informatique, CNRS, PSL Research University, INRIA [email protected] 8 NTT Secure Platform Laboratories [email protected] Abstract. Recently, numerous physical aacks have been demonstrated against laice- based schemes, oen exploiting their unique properties such as the reliance on Gaussian distributions, rejection sampling and FFT-based polynomial multiplication. As the call for concrete implementations and deployment of postquantum cryptography becomes more pressing, protecting against those aacks is an important problem. However, few counter- measures have been proposed so far. In particular, masking has been applied to the decryp- tion procedure of some laice-based encryption schemes, but the much more dicult case of signatures (which are highly non-linear and typically involve randomness) has not been considered until now. In this paper, we describe the rst masked implementation of a laice-based signature scheme. Since masking Gaussian sampling and other procedures involving contrived prob- ability distribution would be prohibitively inecient, we focus on the GLP scheme of Guneysu,¨ Lyubashevsky and Poppelmann¨ (CHES 2012). We show how to provably mask it in the Ishai–Sahai–Wagner model (CRYPTO 2003) at any order in a relatively ecient man- ner, using extensions of the techniques of Coron et al. -
Optimizing NTRU Using AVX2
Master Thesis Computing Science Cyber Security Specialisation Radboud University Optimizing NTRU using AVX2 Author: First supervisor/assessor: Oussama Danba dr. Peter Schwabe Second assessor: dr. Lejla Batina July, 2019 Abstract The existence of Shor's algorithm, Grover's algorithm, and others that rely on the computational possibilities of quantum computers raise problems for some computational problems modern cryptography relies on. These algo- rithms do not yet have practical implications but it is believed that they will in the near future. In response to this, NIST is attempting to standardize post-quantum cryptography algorithms. In this thesis we will look at the NTRU submission in detail and optimize it for performance using AVX2. This implementation takes about 29 microseconds to generate a keypair, about 7.4 microseconds for key encapsulation, and about 6.8 microseconds for key decapsulation. These results are achieved on a reasonably recent notebook processor showing that NTRU is fast and feasible in practice. Contents 1 Introduction3 2 Cryptographic background and related work5 2.1 Symmetric-key cryptography..................5 2.2 Public-key cryptography.....................6 2.2.1 Digital signatures.....................7 2.2.2 Key encapsulation mechanisms.............8 2.3 One-way functions........................9 2.3.1 Cryptographic hash functions..............9 2.4 Proving security......................... 10 2.5 Post-quantum cryptography................... 12 2.6 Lattice-based cryptography................... 15 2.7 Side-channel resistance...................... 16 2.8 Related work........................... 17 3 Overview of NTRU 19 3.1 Important NTRU operations................... 20 3.1.1 Sampling......................... 20 3.1.2 Polynomial addition................... 22 3.1.3 Polynomial reduction.................. 22 3.1.4 Polynomial multiplication...............