Multivariable Public–Key Cryptosystems
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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. -
Authentication in Key-Exchange: Definitions, Relations and Composition
Authentication in Key-Exchange: Definitions, Relations and Composition Cyprien Delpech de Saint Guilhem1;2, Marc Fischlin3, and Bogdan Warinschi2 1 imec-COSIC, KU Leuven, Belgium 2 Dept Computer Science, University of Bristol, United Kingdom 3 Computer Science, Technische Universit¨atDarmstadt, Germany [email protected], [email protected], [email protected] Abstract. We present a systematic approach to define and study authentication notions in authenti- cated key-exchange protocols. We propose and use a flexible and expressive predicate-based definitional framework. Our definitions capture key and entity authentication, in both implicit and explicit vari- ants, as well as key and entity confirmation, for authenticated key-exchange protocols. In particular, we capture critical notions in the authentication space such as key-compromise impersonation resis- tance and security against unknown key-share attacks. We first discuss these definitions within the Bellare{Rogaway model and then extend them to Canetti{Krawczyk-style models. We then show two useful applications of our framework. First, we look at the authentication guarantees of three representative protocols to draw several useful lessons for protocol design. The core technical contribution of this paper is then to formally establish that composition of secure implicitly authenti- cated key-exchange with subsequent confirmation protocols yields explicit authentication guarantees. Without a formal separation of implicit and explicit authentication from secrecy, a proof of this folklore result could not have been established. 1 Introduction The commonly expected level of security for authenticated key-exchange (AKE) protocols comprises two aspects. Authentication provides guarantees on the identities of the parties involved in the protocol execution. -
Algebraic Cryptanalysis of Hidden Field Equations Family
MASARYK UNIVERSITY FACULTY OF INFORMATICS Algebraic cryptanalysis of Hidden Field Equations family BACHELOR'S THESIS Adam Janovsky Brno, Spring 2016 Declaration I declare that this paper is my original authorial work, which I have worked out on my own. All sources, references, and literature used or excerpted during elaboration of this work are properly cited and listed in complete reference to the due source. Adam Janovský Advisor: prof. RNDr. Jan Slovák, DrSc. i Abstract The goal of this thesis is to present a Grobner basis as a tool for algebraic cryptanalysis. Firtst, the thesis shortly introduces asymmetric cryptography. Next, a Grobner basis is presented and it is explained how a Grobner basis can be used to algorithmic equation solving. Further, fast algorithm for the Grobner basis computation, the F4, is presented. The thesis then introduces basic variant of Hidden field equations cryptosystem and discusses its vulnerability to algebraic attacks from Grobner basis perspective. Finally, the thesis gives an overview of recent results in algebraic cryptanalysis of Hidden Field Equations and suggests parameters that could make the algebraical attacks intractable. ii Keywords Grobner basis, cryptanalysis, Hidden Field Equations, F4 iii Contents 1 Introduction 1 1.1 Notation 2 2 Preliminaries 3 2.1 Asymmetric cryptography 3 2.1.1 Overview 3 2.1.2 RSA 5 2.2 Grobner basis 7 2.3 Equation solving 14 3 F4 algorithm for computing a Grobner basis 19 4 Hidden Field Equations 27 4.1 Overview of HFE 27 4.1.1 Parameters of HFE 27 4.2 Encryption and Decryption 29 4.2.1 Encryption 29 4.2.2 Decryption 31 4.3 Public key derivation 32 5 Algebraic attacks on HFE 35 5.1 Algebraic attack for q = 2 35 5.2 Algebraic attack for odd q 37 6 Conclusions 41 Appendices 42 A SAGE code 43 B Grobner basis for q=ll 47 A" 1 Introduction The thesis studies algebraic attacks against basic variant of Hidden Field Equations (HFE) cipher. -
Building Secure Public Key Encryption Scheme from Hidden Field Equations
Hindawi Security and Communication Networks Volume 2017, Article ID 9289410, 6 pages https://doi.org/10.1155/2017/9289410 Research Article Building Secure Public Key Encryption Scheme from Hidden Field Equations Yuan Ping,1,2 Baocang Wang,1,3 Yuehua Yang,1 and Shengli Tian1 1 School of Information Engineering, Xuchang University, Xuchang 461000, China 2Guizhou Provincial Key Laboratory of Public Big Data, Guiyang 550025, China 3State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China Correspondence should be addressed to Baocang Wang; [email protected] Received 4 April 2017; Accepted 5 June 2017; Published 10 July 2017 Academic Editor: Dengpan Ye Copyright © 2017 Yuan Ping et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Multivariate public key cryptography is a set of cryptographic schemes built from the NP-hardness of solving quadratic equations over finite fields, amongst which the hidden field equations (HFE) family of schemes remain the most famous. However, the original HFE scheme was insecure, and the follow-up modifications were shown to be still vulnerable to attacks. In this paper, we propose 2 a new variant of the HFE scheme by considering the special equation =defined over the finite field F3 when =0,1. We observe that the equation can be used to further destroy the special structure of the underlying central map of the HFE scheme. It is shown that the proposed public key encryption scheme is secure against known attacks including the MinRank attack, the algebraic attacks, and the linearization equations attacks. -
THE END of CRYPTOGRAPHY AS WE KNOW IT ABOUT ISARA About ISARA
THE END OF CRYPTOGRAPHY AS WE KNOW IT ABOUT ISARA About ISARA Founded in 2015, Consumers, ISARA is affiliated with governments and the rich academic and organizations should research ecosystem of benefit from the power Quantum Valley, a high- of quantum computing tech hub in Waterloo, without compromising Ontario, Canada data security. Founded Vision About ISARA We have a highly We’re building quantum experienced safe solutions, starting management team with with the launch of our backgrounds in wireless, ISARA Quantum encryption, security Resistant Toolkit. solutions, sales and standards/certification. Team Solutions 01 Threat 02 Solutions Standards 03 Quantum Computing Threat Cryptographic Challenges For A Post Quantum World Today’s security solutions rely on the complexity of the underlying mathematical problems that form the foundation for modern cryptographic systems. The massive processing capabilities found in quantum computers will challenge our current beliefs around complexity. When Does The Clock Run Out? Understanding the risks means balancing multiple factors. The answer depends on who you are, what secrets you need to keep and what the impact is if your secrets are no longer secrets. In some cases, it’s already too late. When Do You Need To Worry? Critical technologies Life of your secrets Key infrastructure Threat horizon Risk Value of your assets Assessment Ability to integrate tools Cost to defend $ Years To Quantum Y2Q: The scope of the change required is akin to Y2K. To do a risk management assessment, all protocols, clients and servers need an in-depth review. This requires coordination between vendors, OEMs and customers to catch all of the interactions. -
2.3 Diffie–Hellman Key Exchange
2.3. Di±e{Hellman key exchange 65 q q q q q q 6 q qq q q q q q q 900 q q q q q q q qq q q q q q q q q q q q q q q q q 800 q q q qq q q q q q q q q q qq q q q q q q q q q q q 700 q q q q q q q q q q q q q q q q q q q q q q q q q q qq q 600 q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q 500 q qq q q q q q qq q q q q q qqq q q q q q q q q q q q q q qq q q q 400 q q q q q q q q q q q q q q q q q q q q q q q q q 300 q q q q q q q q q q q q q q q q q q qqqq qqq q q q q q q q q q q q 200 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qq q q 100 q q q q q q q q q q q q q q q q q q q q q q q q q 0 q - 0 30 60 90 120 150 180 210 240 270 Figure 2.2: Powers 627i mod 941 for i = 1; 2; 3;::: any group and use the group law instead of multiplication. -
Elliptic Curves in Public Key Cryptography: the Diffie Hellman
Elliptic Curves in Public Key Cryptography: The Diffie Hellman Key Exchange Protocol and its relationship to the Elliptic Curve Discrete Logarithm Problem Public Key Cryptography Public key cryptography is a modern form of cryptography that allows different parties to exchange information securely over an insecure network, without having first to agree upon some secret key. The main use of public key cryptography is to provide information security in computer science, for example to transfer securely email, credit card details or other secret information between sender and recipient via the internet. There are three steps involved in transferring information securely from person A to person B over an insecure network. These are encryption of the original information, called the plaintext, transfer of the encrypted message, or ciphertext, and decryption of the ciphertext back into plaintext. Since the transfer of the ciphertext is over an insecure network, any spy has access to the ciphertext and thus potentially has access to the original information, provided he is able to decipher the message. Thus, a successful cryptosystem must be able encrypt the original message in such a way that only the intended receiver can decipher the ciphertext. The goal of public key cryptography is to make the problem of deciphering the encrypted message too difficult to do in a reasonable time (by say brute-force) unless certain key facts are known. Ideally, only the intended sender and receiver of a message should know these certain key facts. Any certain piece of information that is essential in order to decrypt a message is known as a key. -
On Multivariate Signature-Only Public Key Cryptosystems
On multivariate signature-only public key cryptosystems Nicolas T. Courtois1,2 [email protected] http://www.minrank.org 1 Syst`emes Information Signal (SIS), Universit´ede Toulon et du Var BP 132, F-83957 La Garde Cedex, France 2 INRIA Rocquencourt, Projet Codes, Domaine de Voluceau BP 105, 78153 Le Chesnay, France Abstract. In a paper published at Asiacrypt 2000 a signature scheme that (apparently) cannot be abused for encryption is published. The problem is highly non-trivial and every solution should be looked upon with caution. What is especially hard to achieve is to avoid that the pub- lic key should leak some information, to be used as a possible ”shadow” secondary public key. In the present paper we argument that the problem has many natural solutions within the framework of the multivariate cryptography. First of all it seems that virtually any non-injective multivariate public key is inherently unusable for encryption. Unfortunately having a lot of leakage is inherent to multivariate cryp- tosystems. Though it may appear hopeless at the first sight, we use this very property to remove leakage. In our new scenario the Certification Authority (CA) makes extensive modifications of the public key such that the user can still use the internal trapdoor, but has no control on any publicly verifiable property of the actual public key equations published by CA. Thus we propose a very large class of multivariate non-encryption PKI schemes with many parameters q, d, h, v, r, u, f, D. The paper is also of independent interest, as it contains all variants of the HFE trapdoor public key cryptosystem. -
Study on the Use of Cryptographic Techniques in Europe
Study on the use of cryptographic techniques in Europe [Deliverable – 2011-12-19] Updated on 2012-04-20 II Study on the use of cryptographic techniques in Europe Contributors to this report Authors: Edward Hamilton and Mischa Kriens of Analysys Mason Ltd Rodica Tirtea of ENISA Supervisor of the project: Rodica Tirtea of ENISA ENISA staff involved in the project: Demosthenes Ikonomou, Stefan Schiffner Agreements or Acknowledgements ENISA would like to thank the contributors and reviewers of this study. Study on the use of cryptographic techniques in Europe III About ENISA The European Network and Information Security Agency (ENISA) is a centre of network and information security expertise for the EU, its member states, the private sector and Europe’s citizens. ENISA works with these groups to develop advice and recommendations on good practice in information security. It assists EU member states in implementing relevant EU leg- islation and works to improve the resilience of Europe’s critical information infrastructure and networks. ENISA seeks to enhance existing expertise in EU member states by supporting the development of cross-border communities committed to improving network and information security throughout the EU. More information about ENISA and its work can be found at www.enisa.europa.eu. Contact details For contacting ENISA or for general enquiries on cryptography, please use the following de- tails: E-mail: [email protected] Internet: http://www.enisa.europa.eu Legal notice Notice must be taken that this publication represents the views and interpretations of the au- thors and editors, unless stated otherwise. This publication should not be construed to be a legal action of ENISA or the ENISA bodies unless adopted pursuant to the ENISA Regulation (EC) No 460/2004 as lastly amended by Regulation (EU) No 580/2011. -
Public Key Infrastructure (PKI)
Public Key Infrastructure Public Key Infrastructure (PKI) Neil F. Johnson [email protected] http://ise.gmu.edu/~csis Assumptions • Understanding of – Fundamentals of Public Key Cryptosystems – Hash codes for message digests and integrity check – Digital Signatures Copyright 1999, Neil F. Johnson 1 Public Key Infrastructure Overview • Public Key Cryptosystems – Quick review – Cryptography – Digital Signatures – Key Management Issues • Certificates – Certificates Information – Certificate Authority – Track Issuing a Certificate • Putting it all together – PKI applications – Pretty Good Privacy (PGP) – Privacy Enhanced Mail (PEM) Public Key Cryptosystems – Quick Review • Key distribution problem of secret key systems – You must share the secret key with another party before you can initiate communication – If you want to communicate with n parties, you require n different keys • Public Key cryptosystems solve the key distribution problem in secret key systems (provided a reliable channel for communication of public keys can be implemented) • Security is based on the unfeasibility of computing B’s private key given the knowledge of – B’s public key, – chosen plaintext, and – maybe chosen ciphertext Copyright 1999, Neil F. Johnson 2 Public Key Infrastructure Key Distribution (n)(n-1) 2 Bob Bob Alice 1 Alice 2 Chris Chris 7 5 8 9 Ellie 3 Ellie 6 David 4 David Secret Key Distribution Directory of Public Keys (certificates) Public Key Cryptosystem INSECURE CHANNEL Plaintext Ciphertext Plaintext Encryption Decryption Algorithm Algorithm Bob’s PUBLIC -
On the Differential Security of the Hfev- Signature Primitive
On the Differential Security of the − HF Ev Signature Primitive Ryann Cartor1, Ryan Gipson1, Daniel Smith-Tone1,2, and Jeremy Vates1 1Department of Mathematics, University of Louisville, Louisville, Kentucky, USA 2National Institute of Standards and Technology, Gaithersburg, Maryland, USA [email protected], [email protected], [email protected], [email protected] Abstract. Multivariate Public Key Cryptography (MPKC) is one of the most attractive post-quantum options for digital signatures in a wide array of applications. The history of multivariate signature schemes is tumultuous, however, and solid security arguments are required to in- spire faith in the schemes and to verify their security against yet undis- covered attacks. The effectiveness of “differential attacks" on various field-based systems has prompted the investigation of the resistance of schemes against differential adversaries. Due to its prominence in the area and the recent optimization of its parameters, we prove the secu- rity of HF Ev− against differential adversaries. We investigate the newly suggested parameters and conclude that the proposed scheme is secure against all known attacks and against any differential adversary. Key words: Multivariate Cryptography, HFEv-, Discrete Differential, MinRank, Q-rank 1 Introduction and Outline In the mid 1990s, Peter Shor discovered a way to efficiently implement quantum period finding algorithms on structures of exponential size and showed how the modern world as we know it will change forever once the behemoth engineering challenge of constructing a large scale quantum computing device is overcome. His polynomial time quantum Fourier transforms for smooth integers can be employed to factor integers, to compute discrete logarithms and is powerful enough to efficiently solve hidden subgroup problems for well behaved (usually Abelian) groups. -
Analysing and Patching SPEKE in ISO/IEC
1 Analysing and Patching SPEKE in ISO/IEC Feng Hao, Roberto Metere, Siamak F. Shahandashti and Changyu Dong Abstract—Simple Password Exponential Key Exchange reported. Over the years, SPEKE has been used in several (SPEKE) is a well-known Password Authenticated Key Ex- commercial applications: for example, the secure messaging change (PAKE) protocol that has been used in Blackberry on Blackberry phones [11] and Entrust’s TruePass end-to- phones for secure messaging and Entrust’s TruePass end-to- end web products. It has also been included into international end web products [16]. SPEKE has also been included into standards such as ISO/IEC 11770-4 and IEEE P1363.2. In the international standards such as IEEE P1363.2 [22] and this paper, we analyse the SPEKE protocol as specified in the ISO/IEC 11770-4 [24]. ISO/IEC and IEEE standards. We identify that the protocol is Given the wide usage of SPEKE in practical applications vulnerable to two new attacks: an impersonation attack that and its inclusion in standards, we believe a thorough allows an attacker to impersonate a user without knowing the password by launching two parallel sessions with the victim, analysis of SPEKE is both necessary and important. In and a key-malleability attack that allows a man-in-the-middle this paper, we revisit SPEKE and its variants specified in (MITM) to manipulate the session key without being detected the original paper [25], the IEEE 1363.2 [22] and ISO/IEC by the end users. Both attacks have been acknowledged by 11770-4 [23] standards.