Challenges in Proving Post-Quantum Key Exchanges Based on Key Encapsulation Mechanisms
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CS 255: Intro to Cryptography 1 Introduction 2 End-To-End
Programming Assignment 2 Winter 2021 CS 255: Intro to Cryptography Prof. Dan Boneh Due Monday, March 1st, 11:59pm 1 Introduction In this assignment, you are tasked with implementing a secure and efficient end-to-end encrypted chat client using the Double Ratchet Algorithm, a popular session setup protocol that powers real- world chat systems such as Signal and WhatsApp. As an additional challenge, assume you live in a country with government surveillance. Thereby, all messages sent are required to include the session key encrypted with a fixed public key issued by the government. In your implementation, you will make use of various cryptographic primitives we have discussed in class—notably, key exchange, public key encryption, digital signatures, and authenticated encryption. Because it is ill-advised to implement your own primitives in cryptography, you should use an established library: in this case, the Stanford Javascript Crypto Library (SJCL). We will provide starter code that contains a basic template, which you will be able to fill in to satisfy the functionality and security properties described below. 2 End-to-end Encrypted Chat Client 2.1 Implementation Details Your chat client will use the Double Ratchet Algorithm to provide end-to-end encrypted commu- nications with other clients. To evaluate your messaging client, we will check that two or more instances of your implementation it can communicate with each other properly. We feel that it is best to understand the Double Ratchet Algorithm straight from the source, so we ask that you read Sections 1, 2, and 3 of Signal’s published specification here: https://signal. -
The First Collision for Full SHA-1
The first collision for full SHA-1 Marc Stevens1, Elie Bursztein2, Pierre Karpman1, Ange Albertini2, Yarik Markov2 1 CWI Amsterdam 2 Google Research [email protected] https://shattered.io Abstract. SHA-1 is a widely used 1995 NIST cryptographic hash function standard that was officially deprecated by NIST in 2011 due to fundamental security weaknesses demonstrated in various analyses and theoretical attacks. Despite its deprecation, SHA-1 remains widely used in 2017 for document and TLS certificate signatures, and also in many software such as the GIT versioning system for integrity and backup purposes. A key reason behind the reluctance of many industry players to replace SHA-1 with a safer alternative is the fact that finding an actual collision has seemed to be impractical for the past eleven years due to the high complexity and computational cost of the attack. In this paper, we demonstrate that SHA-1 collision attacks have finally become practical by providing the first known instance of a collision. Furthermore, the prefix of the colliding messages was carefully chosen so that they allow an attacker to forge two PDF documents with the same SHA-1 hash yet that display arbitrarily-chosen distinct visual contents. We were able to find this collision by combining many special cryptanalytic techniques in complex ways and improving upon previous work. In total the computational effort spent is equivalent to 263:1 SHA-1 compressions and took approximately 6 500 CPU years and 100 GPU years. As a result while the computational power spent on this collision is larger than other public cryptanalytic computations, it is still more than 100 000 times faster than a brute force search. -
FPGA Parallel-Pipelined AES-GCM Core for 100G Ethernet Applications
FPGA Parallel-Pipelined AES-GCM Core for 100G Ethernet Applications Luca Henzen and Wolfgang Fichtner Integrated Systems Laboratory, ETH Zurich, Switzerland E-mail: {henzen, fw}@iis.ee.ethz.ch Abstract—The forthcoming IEEE 802.3ba Ethernet standard Exploiting the parallelization of four cores plus the extensive will provide data transmission at a bandwidth of 100 Gbit/s. Cur- utilization of pipelining, we were able to design three different rently, the fastest cryptographic primitive approved by the U.S. National Institute for Standard and Technology, that combines 100G AES-GCM implementations for Xilinx Virtex-5 FPGAs. data encryption and authentication, is the Galois/Counter Mode (GCM) of operation. If the feasibility to increase the speed of the II. GCM AUTHENTICATED ENCRYPTION GCM up to 100 Gbit/s on ASIC technologies has already been The GCM is a block cipher mode of operation that is demonstrated, the FPGA implementation of the GCM in secure able to encrypt or decrypt data, providing at the same time 100G Ethernet network systems arises some important structural issues. In this paper, we report on an efficient FPGA architecture authentication and data integrity . In practice, it combines a of the GCM combined with the AES block cipher. With the block cipher in the counter mode with universal hashing over parallelization of four pipelined AES-GCM cores we were able the binary field GF(2128). In this work, we used the Advanced to reach the speed required by the new Ethernet standard. Encryption Standard (AES) [4] for encryption and decryption, Furthermore, the time-critical binary field multiplication of the authentication process relies on four pipelined 2-step Karatsuba- supporting key sizes of 128, 192 and 256bits. -
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.................. -
Julius: Secure Mode of Operation for Authenticated Encryption Based on ECB and Finite Field Multiplications
Julius: Secure Mode of Operation for Authenticated Encryption Based on ECB and Finite Field Multiplications Lear Bahack∗ Submission to the CAESAR competition, version 1.0, March 2014 Gaius Julius Caesar, 100 BC – 44 BC. Source: Mcleclat, GNU, Creative Commons via Wikimedia Commons. ∗Weizmann Institute of Science, Rehovot, Israel. E-mail: [email protected] 1 Abstract We present two new blockcipher modes of operation for authenti- cated encryption with associated data, designed to achieve the maxi- mal possible security in case of misused IV, while being efficient as the Galois/Counter Mode (GCM). Both of the modes are provably secure up to the birthday bound, are suitable for both software and hard- ware, and are based on GF(2128) multiplications by a secret element of the field. The Julius-CTR mode can be viewed as a certain variation combin- ing the GCM, SIV and Unbalanced Feistel Network, while the Julius- ECB mode can be viewed as a certain variation of the Naor-Reingold mode. We specify two versions for each mode: a regular version and a compact version, having different ciphertexts redundancies. Sev- eral variants aimed to achieve increased security, parallelization, and efficiency are briefly explored. Based on the two Julius modes of operation and the AES-128 block- cipher, we propose a family of four specific algorithms for authenti- cated encryption with associated data to the CAESAR competition. 1 Introduction Symmetric key authenticated encryption (AE) is in a sense the most basic and fundamental usage of cryptography. Although today’s cryptography is far broader and contains complicated algorithms aiming to achieve other (more complicated) goals, the vast majority of applications use "compli- cated" cryptographic algorithms only in addition to a "basic" symmetric key AE algorithm. -
Algebraic Frameworks for Cryptographic Primitives
Algebraic Frameworks for Cryptographic Primitives by Navid Alamati A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Computer Science and Engineering) in the University of Michigan 2020 Doctoral Committee: Associate Professor Chris Peikert, Chair Professor Jeffrey Lagarias Professor Quentin Stout Professor Martin Strauss “It must be admitted that the use of geometric intuition has no logical necessity in mathematics, and is often left out of the formal presentation of results. If one had to construct a mathematical brain, one would probably use resources more efficiently than creating a visual system. But the system is there already, it is used to great advantage by human mathematicians, and it gives a special flavor to human mathematics.” David Ruelle [Conversations on Mathematics with a Visitor from Outer Space, 1998] Navid Alamati [email protected] ORCID iD: 0000-0001-8621-7486 2020 Acknowledgments Undoubtedly, I was more than fortunate to be advised by Chris Peikert. He has guided me during the past five years with unwavering patience and unparalleled percipience. No words can adequately describe my appreciation for him. I thank the other members of the committee—Jeffrey Lagarias, Quentin Stout, and Martin Strauss. I was lucky to be interned twice at Fujitsu Labs of America, during which I have had the chance of working with wonderful researchers—Arnab Roy, Hart Montgomery, and Sikhar Patranabis. I am grateful to Hart and Sikhar for the innumerable hours of discussion and the countless moments of wonder through which I tried to do research in cryptography. I am also thankful to Luca De Feo for being a great companion for an attempt on isogenies for dummies, one of whom has written this thesis. -
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. -
Cryptographic Sponge Functions
Cryptographic sponge functions Guido B1 Joan D1 Michaël P2 Gilles V A1 http://sponge.noekeon.org/ Version 0.1 1STMicroelectronics January 14, 2011 2NXP Semiconductors Cryptographic sponge functions 2 / 93 Contents 1 Introduction 7 1.1 Roots .......................................... 7 1.2 The sponge construction ............................... 8 1.3 Sponge as a reference of security claims ...................... 8 1.4 Sponge as a design tool ................................ 9 1.5 Sponge as a versatile cryptographic primitive ................... 9 1.6 Structure of this document .............................. 10 2 Definitions 11 2.1 Conventions and notation .............................. 11 2.1.1 Bitstrings .................................... 11 2.1.2 Padding rules ................................. 11 2.1.3 Random oracles, transformations and permutations ........... 12 2.2 The sponge construction ............................... 12 2.3 The duplex construction ............................... 13 2.4 Auxiliary functions .................................. 15 2.4.1 The absorbing function and path ...................... 15 2.4.2 The squeezing function ........................... 16 2.5 Primary aacks on a sponge function ........................ 16 3 Sponge applications 19 3.1 Basic techniques .................................... 19 3.1.1 Domain separation .............................. 19 3.1.2 Keying ..................................... 20 3.1.3 State precomputation ............................ 20 3.2 Modes of use of sponge functions ......................... -
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. -
Guidelines on Cryptographic Algorithms Usage and Key Management
EPC342-08 Version 7.0 4 November 2017 [X] Public – [ ] Internal Use – [ ] Confidential – [ ] Strictest Confidence Distribution: Publicly available GUIDELINES ON CRYPTOGRAPHIC ALGORITHMS USAGE AND KEY MANAGEMENT Abstract This document defines guidelines on cryptographic algorithms usage and key management. Document Reference EPC342-08 Issue Version 7.0 Date of Issue 22 November 2017 Reason for Issue Maintenance of document Produced by EPC Authorised by EPC Document History This document was first produced by ECBS as TR 406, with its latest ECBS version published in September 2005. The document has been handed over to the EPC which is responsible for its yearly maintenance. DISCLAIMER: Whilst the European Payments Council (EPC) has used its best endeavours to make sure that all the information, data, documentation (including references) and other material in the present document are accurate and complete, it does not accept liability for any errors or omissions. EPC will not be liable for any claims or losses of any nature arising directly or indirectly from use of the information, data, documentation or other material in the present document. Conseil Européen des Paiements AISBL– Cours Saint-Michel 30A – B 1040 Brussels Tel: +32 2 733 35 33 – Fax: +32 2 736 49 88 Enterprise N° 0873.268.927 – www.epc-cep.eu – [email protected] © 2016 Copyright European Payments Council (EPC) AISBL: Reproduction for non-commercial purposes is authorised, with acknowledgement of the source Table of Content MANAGEMENT SUMMARY ............................................................. 5 1 INTRODUCTION .................................................................... 7 1.1 Scope of the document ...................................................... 7 1.2 Document structure .......................................................... 7 1.3 Recommendations ............................................................ 8 1.4 Implementation best practices ......................................... -
The Double Ratchet Algorithm
The Double Ratchet Algorithm Trevor Perrin (editor) Moxie Marlinspike Revision 1, 2016-11-20 Contents 1. Introduction 3 2. Overview 3 2.1. KDF chains . 3 2.2. Symmetric-key ratchet . 5 2.3. Diffie-Hellman ratchet . 6 2.4. Double Ratchet . 13 2.6. Out-of-order messages . 17 3. Double Ratchet 18 3.1. External functions . 18 3.2. State variables . 19 3.3. Initialization . 19 3.4. Encrypting messages . 20 3.5. Decrypting messages . 20 4. Double Ratchet with header encryption 22 4.1. Overview . 22 4.2. External functions . 26 4.3. State variables . 26 4.4. Initialization . 26 4.5. Encrypting messages . 27 4.6. Decrypting messages . 28 5. Implementation considerations 29 5.1. Integration with X3DH . 29 5.2. Recommended cryptographic algorithms . 30 6. Security considerations 31 6.1. Secure deletion . 31 6.2. Recovery from compromise . 31 6.3. Cryptanalysis and ratchet public keys . 31 1 6.4. Deletion of skipped message keys . 32 6.5. Deferring new ratchet key generation . 32 6.6. Truncating authentication tags . 32 6.7. Implementation fingerprinting . 32 7. IPR 33 8. Acknowledgements 33 9. References 33 2 1. Introduction The Double Ratchet algorithm is used by two parties to exchange encrypted messages based on a shared secret key. Typically the parties will use some key agreement protocol (such as X3DH [1]) to agree on the shared secret key. Following this, the parties will use the Double Ratchet to send and receive encrypted messages. The parties derive new keys for every Double Ratchet message so that earlier keys cannot be calculated from later ones. -
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.