Randomness in Cryptography: Theory Meets Practice
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Optimal Discrete Uniform Generation from Coin Flips, and Applications
Optimal Discrete Uniform Generation from Coin Flips, and Applications Jérémie Lumbroso April 9, 2013 Abstract This article introduces an algorithm to draw random discrete uniform va- riables within a given range of size n from a source of random bits. The al- gorithm aims to be simple to implement and optimal both with regards to the amount of random bits consumed, and from a computational perspective— allowing for faster and more efficient Monte-Carlo simulations in computa- tional physics and biology. I also provide a detailed analysis of the number of bits that are spent per variate, and offer some extensions and applications, in particular to the optimal random generation of permutations. Now that simulations can be run extremely fast, they are routinely able to consume over a billion random variates an hour—and several orders of magnitude more throughout an execution. At such a point, the amount of pseudo-randomness at our disposal may eventually become a real issue, and it is pertinent to devise techniques that are economical with respect to the amount of randomness consumed, while remaining as or more efficient than existing techniques with regards to speed and space usage. The random-bit model. Much research has gone into simulating probability dis- arXiv:1304.1916v1 [cs.DS] 6 Apr 2013 tributions, with most algorithms designed using infinitely precise continuous uni- form random variables (see [1, II.3.7]). But because (pseudo-)randomness on com- puters is typically provided as 32-bit integers—and even bypassing issues of true randomness and bias—this model is questionable. Indeed as these integers have a fixed precision, two questions arise: when are they not precise enough? when are they too precise? These are questions which are usually ignored in typical fixed- precision implementations of the aforementioned algorithms. -
Cryptography Whitepaper
Cryptography Whitepaper Threema uses modern cryptography based on open source components that strike an optimal balance between security, performance and message size. In this whitepaper, the algorithms and design decisions behind the cryptography in Threema are explained. VERSION: JUNE 21, 2021 Contents Overview 4 Open Source 5 End-to-End Encryption 5 Key Generation and Registration 5 Key Distribution and Trust 6 Message Encryption 7 Group Messaging 8 Key Backup 8 Client-Server Protocol Description 10 Chat Protocol (Message Transport Layer) 10 Directory Access Protocol 11 Media Access Protocol 11 Cryptography Details 12 Key Lengths 12 Random Number Generation 13 Forward Secrecy 14 Padding 14 Repudiability 15 Replay Prevention 15 Local Data Encryption 15 iOS 15 Android 16 Key Storage 16 iOS 16 Android 16 Push Notifications 17 iOS 17 Android 17 Threema • Cryptography Whitepaper Address Book Synchronization 17 Linking 18 ID Revocation 19 An Example 19 Profile Pictures 19 Web Client 20 Architecture 20 Connection Buildup 21 WebRTC Signaling 22 WebRTC Connection Buildup 22 Trusted Keys / Stored Sessions 23 Push Service 23 Self Hosting 24 Links 24 Threema Calls 24 Signaling 24 Call Encryption 24 Audio Encoding 25 Video Encoding 25 Privacy / IP Exposure 25 Threema Safe 26 Overview 26 Backup Format 27 Encryption 27 Upload/Storage 27 Backup Intervals 28 Restore/Decryption 28 Running a Custom Threema Safe Server 28 Threema • Cryptography Whitepaper Overview Threema uses two different encryption layers to protect messages between the sender and the recipient. • End-to-end encryption layer: this layer is between the sender and the recipient. • Transport layer: each end-to-end encrypted message is encrypted again for transport between the client and the server, in order to protect the header information. -
Balanced Permutations Even–Mansour Ciphers
Article Balanced Permutations Even–Mansour Ciphers Shoni Gilboa 1, Shay Gueron 2,3 ∗ and Mridul Nandi 4 1 Department of Mathematics and Computer Science, The Open University of Israel, Raanana 4353701, Israel; [email protected] 2 Department of Mathematics, University of Haifa, Haifa 3498838, Israel 3 Intel Corporation, Israel Development Center, Haifa 31015, Israel 4 Indian Statistical Institute, Kolkata 700108, India; [email protected] * Correspondence: [email protected]; Tel.: +04-824-0161 Academic Editor: Kwangjo Kim Received: 2 February 2016; Accepted: 30 March 2016; Published: 1 April 2016 Abstract: The r-rounds Even–Mansour block cipher is a generalization of the well known Even–Mansour block cipher to r iterations. Attacks on this construction were described by Nikoli´c et al. and Dinur et al. for r = 2, 3. These attacks are only marginally better than brute force but are based on an interesting observation (due to Nikoli´c et al.): for a “typical” permutation P, the distribution of P(x) ⊕ x is not uniform. This naturally raises the following question. Let us call permutations for which the distribution of P(x) ⊕ x is uniformly “balanced” — is there a sufficiently large family of balanced permutations, and what is the security of the resulting Even–Mansour block cipher? We show how to generate families of balanced permutations from the Luby–Rackoff construction and use them to define a 2n-bit block cipher from the 2-round Even–Mansour scheme. We prove that this cipher is indistinguishable from a random permutation of f0, 1g2n, for any adversary who has oracle access to the public permutations and to an encryption/decryption oracle, as long as the number of queries is o(2n/2). -
ERHARD-RNG: a Random Number Generator Built from Repurposed Hardware in Embedded Systems
ERHARD-RNG: A Random Number Generator Built from Repurposed Hardware in Embedded Systems Jacob Grycel and Robert J. Walls Department of Computer Science Worcester Polytechnic Institute Worcester, MA Email: jtgrycel, [email protected] Abstract—Quality randomness is fundamental to crypto- only an external 4 MHz crystal oscillator and power supply. graphic operations but on embedded systems good sources are We chose this platform due to its numerous programmable pe- (seemingly) hard to find. Rather than use expensive custom hard- ripherals, its commonality in embedded systems development, ware, our ERHARD-RNG Pseudo-Random Number Generator (PRNG) utilizes entropy sources that are already common in a and its affordability. Many microcontrollers and Systems On a range of low-cost embedded platforms. We empirically evaluate Chip (SoC) include similar hardware that allows our PRNG to the entropy provided by three sources—SRAM startup state, be implemented, including chips from Atmel, Xilinx, Cypress oscillator jitter, and device temperature—and integrate those Semiconductor, and other chips from Texas Instruments. sources into a full Pseudo-Random Number Generator imple- ERHARD-RNG is based on three key insights. First, we mentation based on Fortuna [1]. Our system addresses a number of fundamental challenges affecting random number generation can address the challenge of collecting entropy at runtime by on embedded systems. For instance, we propose SRAM startup sampling the jitter of the low-power/low-precision oscillator. state as a means to efficiently generate the initial seed—even for Coupled with measurements of the internal temperature sensor systems that do not have writeable storage. Further, the system’s we can effectively re-seed our PRNG with minimal overhead. -
How to Eat Your Entropy and Have It Too — Optimal Recovery Strategies for Compromised Rngs
How to Eat Your Entropy and Have it Too — Optimal Recovery Strategies for Compromised RNGs Yevgeniy Dodis1?, Adi Shamir2, Noah Stephens-Davidowitz1, and Daniel Wichs3?? 1 Dept. of Computer Science, New York University. { [email protected], [email protected] } 2 Dept. of Computer Science and Applied Mathematics, Weizmann Institute. [email protected] 3 Dept. of Computer Science, Northeastern University. [email protected] Abstract. We study random number generators (RNGs) with input, RNGs that regularly update their internal state according to some aux- iliary input with additional randomness harvested from the environment. We formalize the problem of designing an efficient recovery mechanism from complete state compromise in the presence of an active attacker. If we knew the timing of the last compromise and the amount of entropy gathered since then, we could stop producing any outputs until the state becomes truly random again. However, our challenge is to recover within a time proportional to this optimal solution even in the hardest (and most realistic) case in which (a) we know nothing about the timing of the last state compromise, and the amount of new entropy injected since then into the state, and (b) any premature production of outputs leads to the total loss of all the added entropy used by the RNG. In other words, the challenge is to develop recovery mechanisms which are guaranteed to save the day as quickly as possible after a compromise we are not even aware of. The dilemma is that any entropy used prematurely will be lost, and any entropy which is kept unused will delay the recovery. -
Definition of PRF 4 Review: Security Against Chosen-Plaintext Attacks
1 Announcements – Paper presentation sign up sheet is up. Please sign up for papers by next class. – Lecture summaries and notes now up on course webpage 2 Recap and Overview Previous lecture: – Symmetric key encryption: various security defintions and constructions. This lecture: – Review definition of PRF, construction (and proof) of symmetric key encryption from PRF – Block ciphers, modes of operation – Public Key Encryption – Digital Signature Schemes – Additional background for readings 3 Review: Definition of PRF Definition 1. Let F : f0; 1g∗ × f0; 1g∗ ! f0; 1g∗ be an efficient, length-preserving, keyed function. We say that F is a pseudorandom function if for all probabilistic polynomial-time distinguishers D, there exists a negligible function neg such that: FSK (·) n f(·) n Pr[D (1 ) = 1] − Pr[D (1 ) = 1] ≤ neg(n); where SK f0; 1gn is chosen uniformly at random and f is chosen uniformly at random from the set of functions mapping n-bit strings to n-bit strings. 4 Review: Security Against Chosen-Plaintext Attacks (CPA) The experiment is defined for any private-key encryption scheme E = (Gen; Enc; Dec), any adversary A, and any value n for the security parameter: cpa The CPA indistinguishability experiment PrivKA;E (n): 1. A key SK is generated by running Gen(1n). n 2. The adversary A is given input 1 and oracle access to EncSK(·) and outputs a pair of messages m0; m1 of the same length. 3. A random bit b f0; 1g is chosen and then a ciphertext C EncSK(mb) is computed and given to A. We call C the challenge ciphertext. -
Cs 255 (Introduction to Cryptography)
CS 255 (INTRODUCTION TO CRYPTOGRAPHY) DAVID WU Abstract. Notes taken in Professor Boneh’s Introduction to Cryptography course (CS 255) in Winter, 2012. There may be errors! Be warned! Contents 1. 1/11: Introduction and Stream Ciphers 2 1.1. Introduction 2 1.2. History of Cryptography 3 1.3. Stream Ciphers 4 1.4. Pseudorandom Generators (PRGs) 5 1.5. Attacks on Stream Ciphers and OTP 6 1.6. Stream Ciphers in Practice 6 2. 1/18: PRGs and Semantic Security 7 2.1. Secure PRGs 7 2.2. Semantic Security 8 2.3. Generating Random Bits in Practice 9 2.4. Block Ciphers 9 3. 1/23: Block Ciphers 9 3.1. Pseudorandom Functions (PRF) 9 3.2. Data Encryption Standard (DES) 10 3.3. Advanced Encryption Standard (AES) 12 3.4. Exhaustive Search Attacks 12 3.5. More Attacks on Block Ciphers 13 3.6. Block Cipher Modes of Operation 13 4. 1/25: Message Integrity 15 4.1. Message Integrity 15 5. 1/27: Proofs in Cryptography 17 5.1. Time/Space Tradeoff 17 5.2. Proofs in Cryptography 17 6. 1/30: MAC Functions 18 6.1. Message Integrity 18 6.2. MAC Padding 18 6.3. Parallel MAC (PMAC) 19 6.4. One-time MAC 20 6.5. Collision Resistance 21 7. 2/1: Collision Resistance 21 7.1. Collision Resistant Hash Functions 21 7.2. Construction of Collision Resistant Hash Functions 22 7.3. Provably Secure Compression Functions 23 8. 2/6: HMAC And Timing Attacks 23 8.1. HMAC 23 8.2. -
Cryptography for Developers.Pdf
404_CRYPTO_FM.qxd 10/30/06 2:33 PM Page i Visit us at www.syngress.com Syngress is committed to publishing high-quality books for IT Professionals and delivering those books in media and formats that fit the demands of our cus- tomers. We are also committed to extending the utility of the book you purchase via additional materials available from our Web site. SOLUTIONS WEB SITE To register your book, visit www.syngress.com/solutions. Once registered, you can access our [email protected] Web pages. There you may find an assortment of value-added features such as free e-books related to the topic of this book, URLs of related Web site, FAQs from the book, corrections, and any updates from the author(s). ULTIMATE CDs Our Ultimate CD product line offers our readers budget-conscious compilations of some of our best-selling backlist titles in Adobe PDF form. These CDs are the perfect way to extend your reference library on key topics pertaining to your area of exper- tise, including Cisco Engineering, Microsoft Windows System Administration, CyberCrime Investigation, Open Source Security, and Firewall Configuration, to name a few. DOWNLOADABLE E-BOOKS For readers who can’t wait for hard copy, we offer most of our titles in download- able Adobe PDF form. These e-books are often available weeks before hard copies, and are priced affordably. SYNGRESS OUTLET Our outlet store at syngress.com features overstocked, out-of-print, or slightly hurt books at significant savings. SITE LICENSING Syngress has a well-established program for site licensing our e-books onto servers in corporations, educational institutions, and large organizations. -
Analysis of Entropy Usage in Random Number Generators
DEGREE PROJECT IN THE FIELD OF TECHNOLOGY ENGINEERING PHYSICS AND THE MAIN FIELD OF STUDY COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2017 Analysis of Entropy Usage in Random Number Generators KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF COMPUTER SCIENCE AND COMMUNICATION Analysis of Entropy Usage in Random Number Generators JOEL GÄRTNER Master in Computer Science Date: September 16, 2017 Supervisor: Douglas Wikström Examiner: Johan Håstad Principal: Omegapoint Swedish title: Analys av entropianvändning i slumptalsgeneratorer School of Computer Science and Communication i Abstract Cryptographically secure random number generators usually require an outside seed to be initialized. Other solutions instead use a continuous entropy stream to ensure that the internal state of the generator always remains unpredictable. This thesis analyses four such generators with entropy inputs. Furthermore, different ways to estimate entropy is presented and a new method useful for the generator analy- sis is developed. The developed entropy estimator performs well in tests and is used to analyse en- tropy gathered from the different generators. Furthermore, all the analysed generators exhibit some seemingly unintentional behaviour, but most should still be safe for use. ii Sammanfattning Kryptografiskt säkra slumptalsgeneratorer behöver ofta initialiseras med ett oförutsägbart frö. En annan lösning är att istället konstant ge slumptalsgeneratorer entropi. Detta gör det möjligt att garantera att det interna tillståndet i generatorn hålls oförutsägbart. I den här rapporten analyseras fyra sådana generatorer som matas med entropi. Dess- utom presenteras olika sätt att skatta entropi och en ny skattningsmetod utvecklas för att användas till analysen av generatorerna. Den framtagna metoden för entropiskattning lyckas bra i tester och används för att analysera entropin i de olika generatorerna. -
An In-Depth Analysis of Various Steganography Techniques
International Journal of Security and Its Applications Vol.9, No.8 (2015), pp.67-94 http://dx.doi.org/10.14257/ijsia.2015.9.8.07 An In-depth Analysis of Various Steganography Techniques Sangeeta Dhall, Bharat Bhushan and Shailender Gupta YMCA University of Science and Technology [email protected], [email protected], [email protected] Abstract The Steganography is an art and technique of hiding secret data in some carrier i.e. image, audio or video file. For hiding data in an image file various steganography techniques are available with their respective pros and cons. Broadly these techniques are classified as Spatial domain techniques, Transform domain techniques, Distortion techniques and Visual cryptography. Each technique is further classified into different types depending on their actual implementation. This paper is an effort to provide comprehensive comparison of these steganography techniques based on different Performance Metrics such as PSNR, MSE, MAE, Intersection coefficient, Bhattacharyya coefficient, UIQI, NCD, Time Complexity and Qualitative analysis. For this purpose a simulator is designed in MATLAB to implement above said techniques. The techniques are compared based on performance metrics. Keywords: Steganography, Classification of Steganography Techniques, Performance Metrics and MATLAB 1. Introduction "Steganography is the art and science of communicating in a way which hides the existence of the communication. In contrast to Cryptography, where the enemy is allowed to detect, intercept and modify messages without being able to violate certain security premises guaranteed by the cover message with the embedded cryptosystem. The goal of Steganography is to hide messages inside other harmless messages in a way that does not allow any enemy to even detect that there is a second message present"[1]. -
Cryptography
Cryptography Jonathan Katz, University of Maryland, College Park, MD 20742. 1 Introduction Cryptography is a vast subject, addressing problems as diverse as e-cash, remote authentication, fault-tolerant distributed computing, and more. We cannot hope to give a comprehensive account of the ¯eld here. Instead, we will narrow our focus to those aspects of cryptography most relevant to the problem of secure communication. Broadly speaking, secure communication encompasses two complementary goals: the secrecy and integrity of communicated data. These terms can be illustrated using the simple example of a user A attempting to transmit a message m to a user B over a public channel. In the simplest sense, techniques for data secrecy ensure that an eavesdropping adversary (i.e., an adversary who sees all communication occurring on the channel) cannot learn any information about the underlying message m. Viewed in this way, such techniques protect against a passive adversary who listens to | but does not otherwise interfere with | the parties' communication. Techniques for data integrity, on the other hand, protect against an active adversary who may arbitrarily modify the information sent over the channel or may inject new messages of his own. Security in this setting requires that any such modi¯cations or insertions performed by the adversary will be detected by the receiving party. In the cases of both secrecy and integrity, two di®erent assumptions regarding the initial set-up of the communicating parties can be considered. In the private-key setting (also known as the \shared-key," \secret-key," or \symmetric-key" setting), which was the setting used exclusively for cryptography until the mid-1970s, parties A and B are assumed to have shared some secret information | a key | in advance. -
Security Levels in Steganography – Insecurity Does Not Imply Detectability
Electronic Colloquium on Computational Complexity, Report No. 10 (2015) Security Levels in Steganography { Insecurity does not Imply Detectability Maciej Li´skiewicz,R¨udigerReischuk, and Ulrich W¨olfel Institut f¨urTheoretische Informatik, Universit¨atzu L¨ubeck Ratzeburger Allee 160, 23538 L¨ubeck, Germany [email protected], [email protected], [email protected] Abstract. This paper takes a fresh look at security notions for steganography { the art of encoding secret messages into unsuspicious covertexts such that an adversary cannot distinguish the resulting stegotexts from original covertexts. Stegosystems that fulfill the security notion used so far, however, are quite inefficient. This setting is not able to quantify the power of the adversary and thus leads to extremely high requirements. We will show that there exist stegosystems that are not secure with respect to the measure considered so far, still cannot be detected by the adversary in practice. This indicates that a different notion of security is needed which we call undetectability. We propose different variants of (un)-detectability and discuss their appropriateness. By constructing concrete ex- amples of stegosystems and covertext distributions it is shown that among these measures only one manages to clearly and correctly differentiate different levels of security when compared to an intuitive understanding in real life situations. We have termed this detectability on average. As main technical contribution we design a framework for steganography that exploits the difficulty to learn the covertext distribution. This way, for the first time a tight analytical relationship between the task of discovering the use of stegosystems and the task of differentiating between possible covertext distributions is obtained.