User Manual V.1.3 (“NTRU Release”) 1 What Is Goldbug?
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Can We Trust Cryptographic Software? Cryptographic Flaws in GNU Privacy Guard V1.2.3
Can We Trust Cryptographic Software? Cryptographic Flaws in GNU Privacy Guard v1.2.3 Phong Q. Nguyen CNRS/Ecole´ normale sup´erieure D´epartement d’informatique 45 rue d’Ulm, 75230 Paris Cedex 05, France. [email protected] http://www.di.ens.fr/˜pnguyen Abstract. More and more software use cryptography. But how can one know if what is implemented is good cryptography? For proprietary soft- ware, one cannot say much unless one proceeds to reverse-engineering, and history tends to show that bad cryptography is much more frequent than good cryptography there. Open source software thus sounds like a good solution, but the fact that a source code can be read does not imply that it is actually read, especially by cryptography experts. In this paper, we illustrate this point by examining the case of a basic In- ternet application of cryptography: secure email. We analyze parts of thesourcecodeofthelatestversionofGNUPrivacyGuard(GnuPGor GPG), a free open source alternative to the famous PGP software, com- pliant with the OpenPGP standard, and included in most GNU/Linux distributions such as Debian, MandrakeSoft, Red Hat and SuSE. We ob- serve several cryptographic flaws in GPG v1.2.3. The most serious flaw has been present in GPG for almost four years: we show that as soon as one (GPG-generated) ElGamal signature of an arbitrary message is released, one can recover the signer’s private key in less than a second on a PC. As a consequence, ElGamal signatures and the so-called ElGamal sign+encrypt keys have recently been removed from GPG. -
Jeffrey Hoffstein Jill Pipher Joseph H. Silverman
Undergraduate Texts in Mathematics Je rey Ho stein Jill Pipher Joseph H. Silverman An Introduction to Mathematical Cryptography Second Edition Undergraduate Texts in Mathematics Undergraduate Texts in Mathematics Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA Advisory Board: Colin Adams, Williams College, Williamstown, MA, USA Alejandro Adem, University of British Columbia, Vancouver, BC, Canada Ruth Charney, Brandeis University, Waltham, MA, USA Irene M. Gamba, The University of Texas at Austin, Austin, TX, USA Roger E. Howe, Yale University, New Haven, CT, USA David Jerison, Massachusetts Institute of Technology, Cambridge, MA, USA Jeffrey C. Lagarias, University of Michigan, Ann Arbor, MI, USA Jill Pipher, Brown University, Providence, RI, USA Fadil Santosa, University of Minnesota, Minneapolis, MN, USA Amie Wilkinson, University of Chicago, Chicago, IL, USA Undergraduate Texts in Mathematics are generally aimed at third- and fourth- year undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel approaches. The books include motivation that guides the reader to an appreciation of interre- lations among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding. More information about this series at http://www.springer.com/series/666 Jeffrey Hoffstein • Jill Pipher Joseph -
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. -
Security Analysis and Trust Models in Wireless Networks Lela Mirtskhulava
Security Analysis and Trust Models in Wireless Networks Lela Mirtskhulava [email protected] Department of Computer Sciences Faculty of Exact and Natural Sciences Iv. Javakhishvili Tbilisi State University University str., 13, Georgia In the given work, we analyse the serious weaknesses recently discovered in WPA2 (Wi-Fi Protected Access 2) in October 2017 and KRACK (Key Reinstallation Attack) attack on WPA2 announced by Computer Science Scientists. The KRACKs were introduced to abuse design flaws in cryptographic protocols to reinstall an already-in-use key. Several types of cryptographic Wi-Fi handshakes are affected by the attack. There are different forms of trust to address different types of network security problems and reduce risk in certain conditions. This paper explores the trust models applied by various cryptographic schemes: a) the web of trust employed by Pretty Good Privacy (PGP) where users using their own set of trusted public keys, b) Kerberos, a secret key distribution scheme using a trusted third party, c) certificates, which allow a set of trusted third parties to authenticate each other and, by implication, each other's users. Each of the above mentioned trust models differs in complexity, scope, scalability and general applicability. Which model of trust to apply in certain circumstances and types of wireless networks are discussed in the given paper. It describes the major security issues and their techniques of building trust model by monitoring network behavior. It is intended to use secure and faster cryptographic solution for Wi-Fi networks security by using an open source public-key NTRU cryptosystem that uses lattice-based cryptography. -
SIGMA: the 'Sign-And-Mac' Approach to Authenticated Diffie-Hellman and Its Use in the IKE Protocols
SIGMA: the `SIGn-and-MAc' Approach to Authenticated Diffie-Hellman and its Use in the IKE Protocols ∗ Hugo Krawczyky June 12, 2003 Abstract We present the SIGMA family of key-exchange protocols and the \SIGn-and-MAc" approach to authenticated Diffie-Hellman underlying its design. The SIGMA protocols provide perfect forward secrecy via a Diffie-Hellman exchange authenticated with digital signatures, and are specifically designed to ensure sound cryptographic key exchange while supporting a variety of features and trade-offs required in practical scenarios (such as optional identity protection and reduced number of protocol rounds). As a consequence, the SIGMA protocols are very well suited for use in actual applications and for standardized key exchange. In particular, SIGMA serves as the cryptographic basis for the signature-based modes of the standardized Internet Key Exchange (IKE) protocol (versions 1 and 2). This paper describes the design rationale behind the SIGMA approach and protocols, and points out to many subtleties surrounding the design of secure key-exchange protocols in general, and identity-protecting protocols in particular. We motivate the design of SIGMA by comparing it to other protocols, most notable the STS protocol and its variants. In particular, it is shown how SIGMA solves some of the security shortcomings found in previous protocols. ∗A shortened version of this paper appears in the proceedings of CRYPTO'03. For further information related to the SIGMA protocols see http://www.ee.technion.ac.il/~hugo/sigma.html yEE Department, Technion, Haifa, Israel, and IBM T.J. Watson Research Center. Email: [email protected] 1 Contents 1 Introduction 1 2 Preliminaries: On the Security of Key-Exchange Protocols 4 2.1 Overview of the security model and requirements . -
11 Digital Signatures
This is a Chapter from the Handbook of Applied Cryptography, by A. Menezes, P. van Oorschot, and S. Vanstone, CRC Press, 1996. For further information, see www.cacr.math.uwaterloo.ca/hac CRC Press has granted the following specific permissions for the electronic version of this book: Permission is granted to retrieve, print and store a single copy of this chapter for personal use. This permission does not extend to binding multiple chapters of the book, photocopying or producing copies for other than personal use of the person creating the copy, or making electronic copies available for retrieval by others without prior permission in writing from CRC Press. Except where over-ridden by the specific permission above, the standard copyright notice from CRC Press applies to this electronic version: Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press for such copying. c 1997 by CRC Press, Inc. Chapter 11 Digital Signatures Contents in Brief 11.1 Introduction :::::::::::::::::::::::::::::425 11.2 A framework for digital signature mechanisms ::::::::::426 11.3 RSA and related signature schemes :::::::::::::::::433 11.4 Fiat-Shamir signature schemes :::::::::::::::::::447 11.5 The DSA and related signature schemes ::::::::::::::451 11.6 One-time digital signatures :::::::::::::::::::::462 11.7 Other signature schemes ::::::::::::::::::::::471 11.8 Signatures with additional functionality ::::::::::::::474 11.9 Notes and further references ::::::::::::::::::::481 11.1 Introduction This chapter considers techniques designed to provide the digital counterpart to a handwrit- ten signature. -
Secure Authentication Protocol for Internet of Things Achraf Fayad
Secure authentication protocol for Internet of Things Achraf Fayad To cite this version: Achraf Fayad. Secure authentication protocol for Internet of Things. Networking and Internet Archi- tecture [cs.NI]. Institut Polytechnique de Paris, 2020. English. NNT : 2020IPPAT051. tel-03135607 HAL Id: tel-03135607 https://tel.archives-ouvertes.fr/tel-03135607 Submitted on 9 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. Protocole d’authentification securis´ e´ pour les objets connectes´ These` de doctorat de l’Institut Polytechnique de Paris prepar´ ee´ a` Tel´ ecom´ Paris Ecole´ doctorale n◦626 Ecole´ doctorale de l’Institut Polytechnique de Paris (EDIPP) Specialit´ e´ de doctorat : Reseaux,´ informations et communications NNT : 2020IPPAT051 These` present´ ee´ et soutenue a` Palaiseau, le 14 decembre´ 2020, par ACHRAF FAYAD Composition du Jury : Ken CHEN Professeur, Universite´ Paris 13 Nord President´ Pascal LORENZ Professeur, Universite´ de Haute-Alsace (UHA) Rapporteur Ahmed MEHAOUA Professeur, Universite´ Paris Descartes Rapporteur Lyes KHOUKHI Professeur, Ecole´ Nationale Superieure´ d’Ingenieurs´ de Examinateur Caen-ENSICAEN Ahmad FADLALLAH Associate Professor, University of Sciences and Arts in Lebanon Examinateur (USAL) Rida KHATOUN Maˆıtre de conferences,´ Tel´ ecom´ Paris Directeur de these` Ahmed SERHROUCHNI Professeur, Tel´ ecom´ Paris Co-directeur de these` Badis HAMMI Associate Professor, Ecole´ pour l’informatique et les techniques Invite´ avancees´ (EPITA) 626 Acknowledgments First, I would like to thank my thesis supervisor Dr. -
Alternative Elliptic Curve Representations
Alternative Elliptic Curve Representations draft-struik-lwig-curve-representations-00 René Struik Struik Security Consultancy E-mail: [email protected] IETF 101draft-struik – London,-lwig-curve- representationsUK, March-002018 1 Outline 1. The ECC Algorithm Zoo – NIST curve P-256, ECDSA – Curve25519 – Ed25519 2. Implementation Detail 3. How to Reuse Code 4. How to Reuse Existing Standards 5. Conclusions draft-struik-lwig-curve-representations-00 2 ECC Algorithm Zoo (1) NIST curves: Curve model: Weierstrass curve Curve equation: y2 = x3 + ax + b (mod p) Base point: G=(Gx, Gy) Scalar multiplication: addition formulae using, e.g., mixed Jacobian coordinates Point representation: both coordinates of point P=(X, Y) (affine coordinates) 0x04 || X || Y in most-significant-bit/octet first order Examples: NIST P-256 (ANSI X9.62, NIST SP 800-56a, SECG, etc.); Brainpool256r1 (RFC 5639) ECDSA: Signature: R || s in most-significant-bit/octet first order Signing equation: e = s k + d r (mod n), where e=Hash(m) Example: ECDSA, w/ P-256 and SHA-256 (FIPS 186-4, ANSI X9.62, etc.) Note: message m pre-hashed draft-struik-lwig-curve-representations-00 3 ECC Algorithm Zoo (2) CFRG curves: Curve model: Montgomery curve Curve equation: By2 = x3 + Ax2 + x (mod p) Base point: G=(Gx, Gy) Scalar multiplication: Montgomery ladder, using projective coordinates [X: :Z] Point representation: x-coordinate of point P=(X, Y) (x-coordinate-only) X in least-significant-octet, most-significant-bit first order Examples: Curve25519, Curve448 (RFC 7748) DH Key agreement: -
Security Analysis of the Signal Protocol Student: Bc
ASSIGNMENT OF MASTER’S THESIS Title: Security Analysis of the Signal Protocol Student: Bc. Jan Rubín Supervisor: Ing. Josef Kokeš Study Programme: Informatics Study Branch: Computer Security Department: Department of Computer Systems Validity: Until the end of summer semester 2018/19 Instructions 1) Research the current instant messaging protocols, describe their properties, with a particular focus on security. 2) Describe the Signal protocol in detail, its usage, structure, and functionality. 3) Select parts of the protocol with a potential for security vulnerabilities. 4) Analyze these parts, particularly the adherence of their code to their documentation. 5) Discuss your findings. Formulate recommendations for the users. References Will be provided by the supervisor. prof. Ing. Róbert Lórencz, CSc. doc. RNDr. Ing. Marcel Jiřina, Ph.D. Head of Department Dean Prague January 27, 2018 Czech Technical University in Prague Faculty of Information Technology Department of Computer Systems Master’s thesis Security Analysis of the Signal Protocol Bc. Jan Rub´ın Supervisor: Ing. Josef Kokeˇs 1st May 2018 Acknowledgements First and foremost, I would like to express my sincere gratitude to my thesis supervisor, Ing. Josef Kokeˇs,for his guidance, engagement, extensive know- ledge, and willingness to meet at our countless consultations. I would also like to thank my brother, Tom´aˇsRub´ın,for proofreading my thesis. I cannot express enough gratitude towards my parents, Lenka and Jaroslav Rub´ınovi, who supported me both morally and financially through my whole studies. Last but not least, this thesis would not be possible without Anna who re- lentlessly supported me when I needed it most. Declaration I hereby declare that the presented thesis is my own work and that I have cited all sources of information in accordance with the Guideline for adhering to ethical principles when elaborating an academic final thesis. -
Multi-Party Encrypted Messaging Protocol Design Document, Release 0.3-2-Ge104946
Multi-Party Encrypted Messaging Protocol design document Release 0.3-2-ge104946 Mega Limited, Auckland, New Zealand Guy Kloss <[email protected]> arXiv:1606.04593v1 [cs.CR] 14 Jun 2016 11 January 2016 CONTENTS 1 Strongvelope Multi-Party Encrypted Messaging Protocol 2 1.1 Intent.......................................... ....... 2 1.2 SecurityProperties.............................. ............ 2 1.3 ScopeandLimitations ............................. ........... 3 1.4 Assumptions ..................................... ........ 3 1.5 Messages........................................ ....... 3 1.6 Terminology ..................................... ........ 4 2 Cryptographic Primitives 5 2.1 KeyPairforAuthentication . ............. 5 2.2 KeyAgreement.................................... ........ 5 2.3 (Sender)KeyEncryption. ............ 5 2.4 MessageAuthentication . ............ 6 2.5 MessageEncryption ............................... .......... 6 3 Message Encryption 7 3.1 SenderKeyExchange ............................... ......... 7 3.2 ContentEncryption............................... ........... 8 4 Protocol Encoding 9 4.1 TLVTypes ........................................ ...... 9 4.2 MessageSignatures ............................... .......... 10 4.3 MessageTypes.................................... ........ 10 4.4 KeyedMessages ................................... ........ 10 4.5 FollowupMessages ................................ ......... 10 4.6 AlterParticipantMessages. .............. 11 4.7 LegacySenderKeyEncryption . ............ 11 4.8 SenderKeystoInclude... -
Practical Fault Attack Against the Ed25519 and Eddsa Signature Schemes
Practical fault attack against the Ed25519 and EdDSA signature schemes Yolan Romailler, Sylvain Pelissier Kudelski Security Cheseaux-sur-Lausanne, Switzerland fyolan.romailler,[email protected] main advantages is that its scalar multiplication can be Abstract—The Edwards-curve Digital Signature Algorithm implemented without secret dependent branch and lookup, (EdDSA) was proposed to perform fast public-key digital avoiding the risk of side-channel leakage. More recently, a signatures as a replacement for the Elliptic Curve Digital Signature Algorithm (ECDSA). Its key advantages for em- new digital signature algorithm, namely Ed25519 [6], was bedded devices are higher performance and straightforward, proposed based on the curve edwards25519, i.e., the Edward secure implementations. Indeed, neither branch nor lookup twist of Curve25519. This algorithm was then generalized operations depending on the secret values are performed to other curves and called EdDSA [7]. Due to its various during a signature. These properties thwart many side-channel advantages [7], EdDSA was quickly implemented in many attacks. Nevertheless, we demonstrate here that a single-fault attack against EdDSA can recover enough private key material products and libraries, such as OpenSSH [8]. It was also to forge valid signatures for any message. We demonstrate a recently formally defined in RFC 8032 [9]. practical application of this attack against an implementation The authors of EdDSA did not make any claims about its on Arduino Nano. To the authors’ best knowledge this is the security against fault attacks. However, its resistance to fault first practical fault attack against EdDSA or Ed25519. attacks is discussed in [10]–[12] and taken into account by Keywords-EdDSA; Ed25519; fault attack; digital signature Perrin in [13]. -
(Not) to Design and Implement Post-Quantum Cryptography
SoK: How (not) to Design and Implement Post-Quantum Cryptography James Howe1 , Thomas Prest1 , and Daniel Apon2 1 PQShield, Oxford, UK. {james.howe,thomas.prest}@pqshield.com 2 National Institute of Standards and Technology, USA. [email protected] Abstract Post-quantum cryptography has known a Cambrian explo- sion in the last decade. What started as a very theoretical and mathe- matical area has now evolved into a sprawling research ˝eld, complete with side-channel resistant embedded implementations, large scale de- ployment tests and standardization e˙orts. This study systematizes the current state of knowledge on post-quantum cryptography. Compared to existing studies, we adopt a transversal point of view and center our study around three areas: (i) paradigms, (ii) implementation, (iii) deployment. Our point of view allows to cast almost all classical and post-quantum schemes into just a few paradigms. We highlight trends, common methodologies, and pitfalls to look for and recurrent challenges. 1 Introduction Since Shor's discovery of polynomial-time quantum algorithms for the factoring and discrete logarithm problems, researchers have looked at ways to manage the potential advent of large-scale quantum computers, a prospect which has become much more tangible of late. The proposed solutions are cryptographic schemes based on problems assumed to be resistant to quantum computers, such as those related to lattices or hash functions. Post-quantum cryptography (PQC) is an umbrella term that encompasses the design, implementation, and integration of these schemes. This document is a Systematization of Knowledge (SoK) on this diverse and progressive topic. We have made two editorial choices.