Circuit-Extension Handshakes for Tor Achieving Forward Secrecy in a Quantum World
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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. -
Bilinear Map Cryptography from Progressively Weaker Assumptions
Full version of an extended abstract published in Proceedings of CT-RSA 2013, Springer-Verlag, Feb. 2013. Available from the IACR Cryptology ePrint Archive as Report 2012/687. The k-BDH Assumption Family: Bilinear Map Cryptography from Progressively Weaker Assumptions Karyn Benson, Hovav Shacham ∗ Brent Watersy University of California, San Diego University of Texas at Austin fkbenson, [email protected] [email protected] February 4, 2013 Abstract Over the past decade bilinear maps have been used to build a large variety of cryptosystems. In addition to new functionality, we have concurrently seen the emergence of many strong assump- tions. In this work, we explore how to build bilinear map cryptosystems under progressively weaker assumptions. We propose k-BDH, a new family of progressively weaker assumptions that generalizes the de- cisional bilinear Diffie-Hellman (DBDH) assumption. We give evidence in the generic group model that each assumption in our family is strictly weaker than the assumptions before it. DBDH has been used for proving many schemes secure, notably identity-based and functional encryption schemes; we expect that our k-BDH will lead to generalizations of many such schemes. To illustrate the usefulness of our k-BDH family, we construct a family of selectively secure Identity-Based Encryption (IBE) systems based on it. Our system can be viewed as a generalization of the Boneh-Boyen IBE, however, the construction and proof require new ideas to fit the family. We then extend our methods to produces hierarchical IBEs and CCA security; and give a fully secure variant. In addition, we discuss the opportunities and challenges of building new systems under our weaker assumption family. -
Implementation and Performance Evaluation of XTR Over Wireless Network
Implementation and Performance Evaluation of XTR over Wireless Network By Basem Shihada [email protected] Dept. of Computer Science 200 University Avenue West Waterloo, Ontario, Canada (519) 888-4567 ext. 6238 CS 887 Final Project 19th of April 2002 Implementation and Performance Evaluation of XTR over Wireless Network 1. Abstract Wireless systems require reliable data transmission, large bandwidth and maximum data security. Most current implementations of wireless security algorithms perform lots of operations on the wireless device. This result in a large number of computation overhead, thus reducing the device performance. Furthermore, many current implementations do not provide a fast level of security measures such as client authentication, authorization, data validation and data encryption. XTR is an abbreviation of Efficient and Compact Subgroup Trace Representation (ECSTR). Developed by Arjen Lenstra & Eric Verheul and considered a new public key cryptographic security system that merges high level of security GF(p6) with less number of computation GF(p2). The claim here is that XTR has less communication requirements, and significant computation advantages, which indicate that XTR is suitable for the small computing devices such as, wireless devices, wireless internet, and general wireless applications. The hoping result is a more flexible and powerful secure wireless network that can be easily used for application deployment. This project presents an implementation and performance evaluation to XTR public key cryptographic system over wireless network. The goal of this project is to develop an efficient and portable secure wireless network, which perform a variety of wireless applications in a secure manner. The project literately surveys XTR mathematical and theoretical background as well as system implementation and deployment over wireless network. -
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. -
DRAFT Special Publication 800-56A, Recommendation for Pair-Wise Key
The attached DRAFT document (provided here for historical purposes) has been superseded by the following publication: Publication Number: NIST Special Publication (SP) 800-56A Revision 2 Title: Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography Publication Date: 05/13/2013 • Final Publication: https://doi.org/10.6028/NIST.SP.800-56Ar2 (which links to http://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Ar2.pdf). • Information on other NIST Computer Security Division publications and programs can be found at: http://csrc.nist.gov/ The following information was posted with the attached DRAFT document: Aug 20, 2012 SP 800-56 A Rev.1 DRAFT Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography (Draft Revision) NIST announces the release of draft revision of Special Publication 800-56A, Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography. SP 800-56A specifies key-establishment schemes based on the discrete logarithm problem over finite fields and elliptic curves, including several variations of Diffie-Hellman and MQV key establishment schemes. The revision is made on the March 2007 version. The main changes are listed in Appendix D. Please submit comments to 56A2012rev-comments @ nist.gov with "Comments on SP 800-56A (Revision)" in the subject line. The comment period closes on October 31, 2012. NIST Special Publication 800-56A Recommendation for Pair-Wise August 2012 Key-Establishment Schemes Using Discrete Logarithm Cryptography (Draft Revision) Elaine Barker, Lily Chen, Miles Smid and Allen Roginsky C O M P U T E R S E C U R I T Y Abstract This Recommendation specifies key-establishment schemes based on the discrete logarithm problem over finite fields and elliptic curves, including several variations of Diffie-Hellman and MQV key establishment schemes. -
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. -
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............... -
How to Strengthen Ntruencrypt to Chosen-Ciphertext Security in the Standard Model
NTRUCCA: How to Strengthen NTRUEncrypt to Chosen-Ciphertext Security in the Standard Model Ron Steinfeld1?, San Ling2, Josef Pieprzyk3, Christophe Tartary4, and Huaxiong Wang2 1 Clayton School of Information Technology Monash University, Clayton VIC 3800, Australia [email protected] 2 Div. of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371 lingsan,[email protected] 3 Centre for Advanced Computing - Algorithms and Cryptography, Dept. of Computing, Macquarie University, Sydney, NSW 2109, Australia [email protected] 4 Institute for Theoretical Computer Science, Tsinghua University, People's Republic of China [email protected] Abstract. NTRUEncrypt is a fast and practical lattice-based public-key encryption scheme, which has been standardized by IEEE, but until re- cently, its security analysis relied only on heuristic arguments. Recently, Stehlé and Steinfeld showed that a slight variant (that we call pNE) could be proven to be secure under chosen-plaintext attack (IND-CPA), assum- ing the hardness of worst-case problems in ideal lattices. We present a variant of pNE called NTRUCCA, that is IND-CCA2 secure in the standard model assuming the hardness of worst-case problems in ideal lattices, and only incurs a constant factor overhead in ciphertext and key length over the pNE scheme. To our knowledge, our result gives the rst IND- CCA2 secure variant of NTRUEncrypt in the standard model, based on standard cryptographic assumptions. As an intermediate step, we present a construction for an All-But-One (ABO) lossy trapdoor function from pNE, which may be of independent interest. Our scheme uses the lossy trapdoor function framework of Peik- ert and Waters, which we generalize to the case of (k −1)-of-k-correlated input distributions. -
Timing Attacks and the NTRU Public-Key Cryptosystem
Eindhoven University of Technology BACHELOR Timing attacks and the NTRU public-key cryptosystem Gunter, S.P. Award date: 2019 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 Timing Attacks and the NTRU Public-Key Cryptosystem by Stijn Gunter supervised by prof.dr. Tanja Lange ir. Leon Groot Bruinderink A thesis submitted in partial fulfilment of the requirements for the degree of Bachelor of Science July 2019 Abstract As we inch ever closer to a future in which quantum computers exist and are capable of break- ing many of the cryptographic algorithms that are in use today, more and more research is being done in the field of post-quantum cryptography. -
Introduction to Post-Quantum Cryptography
8/28/19 Introduction to Post-Quantum Cryptography CERG: Cryptographic Engineering Research Group 3 faculty members, 9 Ph.D. students, 6 affiliated scholars 2 1 8/28/19 Previous Cryptographic Contests IX.1997 X.2000 AES 15 block ciphers ® 1 winner NESSIE I.2000 XII.2002 CRYPTREC XI.2004 IV.2008 34 stream 4 HW winners eSTREAM ciphers ® + 4 SW winners X.2007 X.2012 51 hash functions ® 1 winner SHA-3 I.2013 II. 2019 57 authenticated ciphers ® multiple winners CAESAR 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 time Cryptographic Contests 2007-Present Completed 51 hash functions ® 1 winner X.2007 X.2012 In progress SHA-3 I.2013 II.2019 57 authenticated ciphers CAESAR ® multiple winners XII.2016 TBD 69 Public-Key Post-Quantum Post-Quantum Cryptography Schemes VIII.2018 TBD 56 Lightweight authenticated ciphers & hash functions Lightweight 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 Year 2 8/28/19 Why Cryptographic Contests? Avoid back-door theories Speed-up the acceptance of a new standard Stimulate non-classified research on methods of designing a specific cryptographic transformation Focus the effort of a relatively small cryptographic community 5 Evaluation Criteria Security Software Efficiency Hardware Efficiency µProcessors µControllers FPGAs ASICs Flexibility Simplicity Licensing 6 3 8/28/19 AES Contest, 1997-2000: Block Ciphers GMU FPGA Results Straw Poll @ NIST AES 3 conference Rijndael second best in FPGAs, selected as a winner due to much better performance in software & ASICs 7 SHA-3 Round 2: 14 candidates Throughput Best: Fast & Small Worst: Slow & Big Area Throughput vs. -
21. the Diffie-Hellman Problem
Chapter 21 The Diffie-Hellman Problem This is a chapter from version 2.0 of the book “Mathematics of Public Key Cryptography” by Steven Galbraith, available from http://www.math.auckland.ac.nz/˜sgal018/crypto- book/crypto-book.html The copyright for this chapter is held by Steven Galbraith. This book was published by Cambridge University Press in early 2012. This is the extended and corrected version. Some of the Theorem/Lemma/Exercise numbers may be different in the published version. Please send an email to [email protected] if youfind any mistakes. This chapter gives a thorough discussion of the computational Diffie-Hellman problem (CDH) and related computational problems. We give a number of reductions between computational problems, most significantly reductions from DLP to CDH. We explain self-correction of CDH oracles, study the static Diffie-Hellman problem, and study hard bits of the DLP and CDH. We always use multiplicative notation for groups in this chapter (except for in the Maurer reduction where some operations are specific to elliptic curves). 21.1 Variants of the Diffie-Hellman Problem We present some computational problems related to CDH, and prove reductions among them. The main result is to prove that CDH and Fixed-CDH are equivalent. Most of the results in this section apply to both algebraic groups (AG) and algebraic group quotients (AGQ) of prime orderr (some exceptions are Lemma 21.1.9, Lemma 21.1.16 and, later, Lemma 21.3.1). For the algebraic group quotientsG considered in this book then one can obtain all the results by lifting from the quotient to the covering groupG ′ and applying the results there. -
Public-Key Cryptography
Public-key Cryptogra; Theory and Practice ABHIJIT DAS Department of Computer Science and Engineering Indian Institute of Technology Kharagpur C. E. VENIMADHAVAN Department of Computer Science and Automation Indian Institute ofScience, Bangalore PEARSON Chennai • Delhi • Chandigarh Upper Saddle River • Boston • London Sydney • Singapore • Hong Kong • Toronto • Tokyo Contents Preface xiii Notations xv 1 Overview 1 1.1 Introduction 2 1.2 Common Cryptographic Primitives 2 1.2.1 The Classical Problem: Secure Transmission of Messages 2 Symmetric-key or secret-key cryptography 4 Asymmetric-key or public-key cryptography 4 1.2.2 Key Exchange 5 1.2.3 Digital Signatures 5 1.2.4 Entity Authentication 6 1.2.5 Secret Sharing 8 1.2.6 Hashing 8 1.2.7 Certification 9 1.3 Public-key Cryptography 9 1.3.1 The Mathematical Problems 9 1.3.2 Realization of Key Pairs 10 1.3.3 Public-key Cryptanalysis 11 1.4 Some Cryptographic Terms 11 1.4.1 Models of Attacks 12 1.4.2 Models of Passive Attacks 12 1.4.3 Public Versus Private Algorithms 13 2 Mathematical Concepts 15 2.1 Introduction 16 2.2 Sets, Relations and Functions 16 2.2.1 Set Operations 17 2.2.2 Relations 17 2.2.3 Functions 18 2.2.4 The Axioms of Mathematics 19 Exercise Set 2.2 20 2.3 Groups 21 2.3.1 Definition and Basic Properties . 21 2.3.2 Subgroups, Cosets and Quotient Groups 23 2.3.3 Homomorphisms 25 2.3.4 Generators and Orders 26 2.3.5 Sylow's Theorem 27 Exercise Set 2.3 29 2.4 Rings 31 2.4.1 Definition and Basic Properties 31 2.4.2 Subrings, Ideals and Quotient Rings 34 2.4.3 Homomorphisms 37 2.4.4