The AES Winner
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Impossible Differentials in Twofish
Twofish Technical Report #5 Impossible differentials in Twofish Niels Ferguson∗ October 19, 1999 Abstract We show how an impossible-differential attack, first applied to DEAL by Knudsen, can be applied to Twofish. This attack breaks six rounds of the 256-bit key version using 2256 steps; it cannot be extended to seven or more Twofish rounds. Keywords: Twofish, cryptography, cryptanalysis, impossible differential, block cipher, AES. Current web site: http://www.counterpane.com/twofish.html 1 Introduction 2.1 Twofish as a pure Feistel cipher Twofish is one of the finalists for the AES [SKW+98, As mentioned in [SKW+98, section 7.9] and SKW+99]. In [Knu98a, Knu98b] Lars Knudsen used [SKW+99, section 7.9.3] we can rewrite Twofish to a 5-round impossible differential to attack DEAL. be a pure Feistel cipher. We will demonstrate how Eli Biham, Alex Biryukov, and Adi Shamir gave the this is done. The main idea is to save up all the ro- technique the name of `impossible differential', and tations until just before the output whitening, and applied it with great success to Skipjack [BBS99]. apply them there. We will use primes to denote the In this report we show how Knudsen's attack can values in our new representation. We start with the be applied to Twofish. We use the notation from round values: [SKW+98] and [SKW+99]; readers not familiar with R0 = ROL(Rr;0; (r + 1)=2 ) the notation should consult one of these references. r;0 b c R0 = ROR(Rr;1; (r + 1)=2 ) r;1 b c R0 = ROL(Rr;2; r=2 ) 2 The attack r;2 b c R0 = ROR(Rr;3; r=2 ) r;3 b c Knudsen's 5-round impossible differential works for To get the same output we update the rule to com- any Feistel cipher where the round function is in- pute the output whitening. -
Miss in the Middle
Miss in the middle By: Gal Leonard Keret Miss in the Middle Attacks on IDEA, Khufu and Khafre • Written by: – Prof. Eli Biham. – Prof. Alex Biryukov. – Prof. Adi Shamir. Introduction • So far we used traditional differential which predict and detect statistical events of highest possible probability. Introduction • A new approach is to search for events with probability one, whose condition cannot be met together (events that never happen). Impossible Differential • Random permutation: 휎 푀0 = 푎푛푦 퐶 표푓 푠푖푧푒 푀0. • Cipher (not perfect): 퐸 푀0 = 푠표푚푒 퐶 표푓 푠푖푧푒 푀0. • Events (푚 ↛ 푐) that never happen distinguish a cipher from a random permutation. Impossible Differential • Impossible events (푚 ↛ 푐) can help performing key elimination. • All the keys that lead to impossibility are obviously wrong. • This way we can filter wrong key guesses and leaving the correct key. Enigma – for example • Some of the attacks on Enigma were based on the observation that letters can not be encrypted to themselves. 퐸푛푖푔푚푎(푀0) ≠ 푀0 In General • (푀0, 퐶1) is a pair. If 푀0 푀0 → 퐶1. • 푀 ↛ 퐶 . 0 0 Some rounds For any key • ∀ 푘푒푦| 퐶1 → 퐶0 ↛ is an impossible key. Cannot lead to 퐶0. Some rounds Find each keys Decrypt 퐶1back to 퐶0. IDEA • International Data Encryption Algorithm. • First described in 1991. • Block cipher. • Symmetric. • Key sizes: 128 bits. • Block sizes: 64 bits. ⊕ - XOR. ⊞ - Addition modulo 216 ⊙ - Multiplication modulo 216+1 Encryption security • Combination of different mathematical groups. • Creation of "incompatibility“: ∗ • 푍216+1 → 푍216 ∗ • 푍216 → 푍216+1 ∗ ∗ Remark: 푍216+1 doesn’t contain 0 like 푍216 , so in 푍216+1 0 will be converted to 216 since 0 ≡ 216(푚표푑 216). -
Report on the AES Candidates
Rep ort on the AES Candidates 1 2 1 3 Olivier Baudron , Henri Gilb ert , Louis Granb oulan , Helena Handschuh , 4 1 5 1 Antoine Joux , Phong Nguyen ,Fabrice Noilhan ,David Pointcheval , 1 1 1 1 Thomas Pornin , Guillaume Poupard , Jacques Stern , and Serge Vaudenay 1 Ecole Normale Sup erieure { CNRS 2 France Telecom 3 Gemplus { ENST 4 SCSSI 5 Universit e d'Orsay { LRI Contact e-mail: [email protected] Abstract This do cument rep orts the activities of the AES working group organized at the Ecole Normale Sup erieure. Several candidates are evaluated. In particular we outline some weaknesses in the designs of some candidates. We mainly discuss selection criteria b etween the can- didates, and make case-by-case comments. We nally recommend the selection of Mars, RC6, Serp ent, ... and DFC. As the rep ort is b eing nalized, we also added some new preliminary cryptanalysis on RC6 and Crypton in the App endix which are not considered in the main b o dy of the rep ort. Designing the encryption standard of the rst twentyyears of the twenty rst century is a challenging task: we need to predict p ossible future technologies, and wehavetotake unknown future attacks in account. Following the AES pro cess initiated by NIST, we organized an op en working group at the Ecole Normale Sup erieure. This group met two hours a week to review the AES candidates. The present do cument rep orts its results. Another task of this group was to up date the DFC candidate submitted by CNRS [16, 17] and to answer questions which had b een omitted in previous 1 rep orts on DFC. -
State of the Art in Lightweight Symmetric Cryptography
State of the Art in Lightweight Symmetric Cryptography Alex Biryukov1 and Léo Perrin2 1 SnT, CSC, University of Luxembourg, [email protected] 2 SnT, University of Luxembourg, [email protected] Abstract. Lightweight cryptography has been one of the “hot topics” in symmetric cryptography in the recent years. A huge number of lightweight algorithms have been published, standardized and/or used in commercial products. In this paper, we discuss the different implementation constraints that a “lightweight” algorithm is usually designed to satisfy. We also present an extensive survey of all lightweight symmetric primitives we are aware of. It covers designs from the academic community, from government agencies and proprietary algorithms which were reverse-engineered or leaked. Relevant national (nist...) and international (iso/iec...) standards are listed. We then discuss some trends we identified in the design of lightweight algorithms, namely the designers’ preference for arx-based and bitsliced-S-Box-based designs and simple key schedules. Finally, we argue that lightweight cryptography is too large a field and that it should be split into two related but distinct areas: ultra-lightweight and IoT cryptography. The former deals only with the smallest of devices for which a lower security level may be justified by the very harsh design constraints. The latter corresponds to low-power embedded processors for which the Aes and modern hash function are costly but which have to provide a high level security due to their greater connectivity. Keywords: Lightweight cryptography · Ultra-Lightweight · IoT · Internet of Things · SoK · Survey · Standards · Industry 1 Introduction The Internet of Things (IoT) is one of the foremost buzzwords in computer science and information technology at the time of writing. -
The Long Road to the Advanced Encryption Standard
The Long Road to the Advanced Encryption Standard Jean-Luc Cooke CertainKey Inc. [email protected], http://www.certainkey.com/˜jlcooke Abstract 1 Introduction This paper will start with a brief background of the Advanced Encryption Standard (AES) process, lessons learned from the Data Encryp- tion Standard (DES), other U.S. government Two decades ago the state-of-the-art in cryptographic publications and the fifteen first the private sector cryptography was—we round candidate algorithms. The focus of the know now—far behind the public sector. presentation will lie in presenting the general Don Coppersmith’s knowledge of the Data design of the five final candidate algorithms, Encryption Standard’s (DES) resilience to and the specifics of the AES and how it dif- the then unknown Differential Cryptanaly- fers from the Rijndael design. A presentation sis (DC), the design principles used in the on the AES modes of operation and Secure Secure Hash Algorithm (SHA) in Digital Hash Algorithm (SHA) family of algorithms Signature Standard (DSS) being case and will follow and will include discussion about point[NISTDSS][NISTDES][DC][NISTSHA1]. how it is directly implicated by AES develop- ments. The selection and design of the DES was shrouded in controversy and suspicion. This very controversy has lead to a fantastic acceler- Intended Audience ation in private sector cryptographic advance- ment. So intrigued by the NSA’s modifica- tions to the Lucifer algorithm, researchers— This paper was written as a supplement to a academic and industry alike—powerful tools presentation at the Ottawa International Linux in assessing block cipher strength were devel- Symposium. -
Twofish Algorithm for Encryption and Decryption
© 2019 JETIR January 2019, Volume 6, Issue 1 www.jetir.org (ISSN-2349-5162) TWOFISH ALGORITHM FOR ENCRYPTION AND DECRYPTION *1 Anil G. Sawant,2 Dr. Vilas N. Nitnaware, 3Pranali Dengale, 4Sayali Garud, 5Akshay Gandewar *1 Research Scholar (Asst. Professor) ,2 Principal, 3Student, 4Student, 5Student *1 JJT University, Rajasthan, India (Trinity College of Engineering and Research, Pune), 2 D. Y. Patil School of Engineering Academy, Pune, India, 3Trinity College of Engineering and Research Pune, 4Trinity College of Engineering and Research, Pune5 Trinity College of Engineering and Research, Pune. Email:* [email protected], [email protected], [email protected], [email protected], [email protected] Abstract - In this paper, a novel VLSI architecture of the TWOFISH block cipher is presented. TWOFISH is one of the most secure cryptographic algorithm. The characteristic features of the TWOFISH Algorithm are good security margin and has fast encryption/decryption in software, moderately fast in hardware and moderate flexibility. Based on the loop-folding technique combined with efficient hardware mapping, the architecture of twofish Algorithm can make data encryption/ decryption more efficient and secure. To demonstrate the correctness of our Algorithm , a prototype chip for the architecture has been implemented. The chip can achieve an encryption rate and low power consumption while operating clock rate. Designed TWOFISH cryptographic algorithm improved the MDS block that improved a process speed, and decreased complexity and power consumption. Therefore, the chip can be applied to encryption in high-speed networking protocols like ATM networks. This paper will be implemented in Xilinx 14.2 in Verilog HDL. Keywords - Verilog , MDS, PHT, DES, Function F and h. -
Bruce Schneier 2
Committee on Energy and Commerce U.S. House of Representatives Witness Disclosure Requirement - "Truth in Testimony" Required by House Rule XI, Clause 2(g)(5) 1. Your Name: Bruce Schneier 2. Your Title: none 3. The Entity(ies) You are Representing: none 4. Are you testifying on behalf of the Federal, or a State or local Yes No government entity? X 5. Please list any Federal grants or contracts, or contracts or payments originating with a foreign government, that you or the entity(ies) you represent have received on or after January 1, 2015. Only grants, contracts, or payments related to the subject matter of the hearing must be listed. 6. Please attach your curriculum vitae to your completed disclosure form. Signatur Date: 31 October 2017 Bruce Schneier Background Bruce Schneier is an internationally renowned security technologist, called a security guru by the Economist. He is the author of 14 books—including the New York Times best-seller Data and Goliath: The Hidden Battles to Collect Your Data and Control Your World—as well as hundreds of articles, essays, and academic papers. His influential newsletter Crypto-Gram and blog Schneier on Security are read by over 250,000 people. Schneier is a fellow at the Berkman Klein Center for Internet and Society at Harvard University, a Lecturer in Public Policy at the Harvard Kennedy School, a board member of the Electronic Frontier Foundation and the Tor Project, and an advisory board member of EPIC and VerifiedVoting.org. He is also a special advisor to IBM Security and the Chief Technology Officer of IBM Resilient. -
Data Encryption Standard
Data Encryption Standard The Data Encryption Standard (DES /ˌdiːˌiːˈɛs, dɛz/) is a Data Encryption Standard symmetric-key algorithm for the encryption of electronic data. Although insecure, it was highly influential in the advancement of modern cryptography. Developed in the early 1970s atIBM and based on an earlier design by Horst Feistel, the algorithm was submitted to the National Bureau of Standards (NBS) following the agency's invitation to propose a candidate for the protection of sensitive, unclassified electronic government data. In 1976, after consultation with theNational Security Agency (NSA), the NBS eventually selected a slightly modified version (strengthened against differential cryptanalysis, but weakened against brute-force attacks), which was published as an official Federal Information Processing Standard (FIPS) for the United States in 1977. The publication of an NSA-approved encryption standard simultaneously resulted in its quick international adoption and widespread academic scrutiny. Controversies arose out of classified The Feistel function (F function) of DES design elements, a relatively short key length of the symmetric-key General block cipher design, and the involvement of the NSA, nourishing Designers IBM suspicions about a backdoor. Today it is known that the S-boxes that had raised those suspicions were in fact designed by the NSA to First 1975 (Federal Register) actually remove a backdoor they secretly knew (differential published (standardized in January 1977) cryptanalysis). However, the NSA also ensured that the key size was Derived Lucifer drastically reduced such that they could break it by brute force from [2] attack. The intense academic scrutiny the algorithm received over Successors Triple DES, G-DES, DES-X, time led to the modern understanding of block ciphers and their LOKI89, ICE cryptanalysis. -
Mars Pathfinder
NASA Facts National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109 Mars Pathfinder Mars Pathfinder was the first completed mission events, ending in a touchdown which left all systems in NASAs Discovery Program of low-cost, rapidly intact. developed planetary missions with highly focused sci- The landing site, an ancient flood plain in Mars ence goals. With a development time of only three northern hemisphere known as Ares Vallis, is among years and a total cost of $265 million, Pathfinder was the rockiest parts of Mars. It was chosen because sci- originally designed entists believed it to as a technology be a relatively safe demonstration of a surface to land on way to deliver an and one which con- instrumented lander tained a wide vari- and a free-ranging ety of rocks robotic rover to the deposited during a surface of the red catastrophic flood. planet. Pathfinder In the event early in not only accom- Mars history, sci- plished this goal but entists believe that also returned an the flood plain was unprecedented cut by a volume of amount of data and water the size of outlived its primary North Americas design life. Great Lakes in Pathfinder used about two weeks. an innovative The lander, for- method of directly mally named the entering the Carl Sagan Martian atmos- Memorial Station phere, assisted by a following its suc- parachute to slow cessful touchdown, its descent through and the rover, the thin Martian atmosphere and a giant system of named Sojourner after American civil rights crusader airbags to cushion the impact. -
Characteristics of Key-Dependent S-Boxes: the Case of Twofish
Characteristics of Key-Dependent S-Boxes: the Case of Twofish Marco Macchetti Politecnico di Milano, Milan, Italy [email protected] Abstract. In this paper we analyze and discuss the cryptographic ro- bustness of key-dependent substitution boxes (KDSBs); these can be found in some symmetric-key algorithms such as Khufu, Blowfish, and the AES finalist Twofish. We analyze KDSBs in the framework of com- posite permutations, completing the theory developed by O’Connor. Un- der the basic assumption that KDSBs are built choosing permutations randomly from the symmetric group S2m by means of the key, the ex- pressions of their linear and differential characteristics are derived. These results are used as a statistical tool to show that Twofish KDSBs, al- though very efficient, can be easily distinguished from truly randomly built KDSBs. We also analyze the motivations that lead to this previ- ously unknown property; it can be concluded that the efficiency of the construction and the small computational complexity of Twofish KDSBs, although very desirable, cannot be easily obtained together with the highest level of security. Keywords: key-dependent s-boxes, linear cryptanalysis, differential crypt- analysis, composite permutations, Twofish. 1 Introduction Block ciphers are an important and widely studied class of cryptographic algo- rithms; the obsolete Data Encryption Standard (DES) [1] and the established Advanced Encryption Standard (AES) [2] are two well known examples. Practically all the proposed algorithms are constructed as Substitution Per- mutation Networks (SPNs) or Feistel structures; in both cases the importance of the non-linear part of the algorithm is crucial, especially considering the crypt- analytic techniques known as Differential [6] and Linear Cryptanalysis [8]. -
Miss in the Middle Attacks on IDEA and Khufu
Miss in the Middle Attacks on IDEA and Khufu Eli Biham? Alex Biryukov?? Adi Shamir??? Abstract. In a recent paper we developed a new cryptanalytic techni- que based on impossible differentials, and used it to attack the Skipjack encryption algorithm reduced from 32 to 31 rounds. In this paper we describe the application of this technique to the block ciphers IDEA and Khufu. In both cases the new attacks cover more rounds than the best currently known attacks. This demonstrates the power of the new cryptanalytic technique, shows that it is applicable to a larger class of cryptosystems, and develops new technical tools for applying it in new situations. 1 Introduction In [5,17] a new cryptanalytic technique based on impossible differentials was proposed, and its application to Skipjack [28] and DEAL [17] was described. In this paper we apply this technique to the IDEA and Khufu cryptosystems. Our new attacks are much more efficient and cover more rounds than the best previously known attacks on these ciphers. The main idea behind these new attacks is a bit counter-intuitive. Unlike tra- ditional differential and linear cryptanalysis which predict and detect statistical events of highest possible probability, our new approach is to search for events that never happen. Such impossible events are then used to distinguish the ci- pher from a random permutation, or to perform key elimination (a candidate key is obviously wrong if it leads to an impossible event). The fact that impossible events can be useful in cryptanalysis is an old idea (for example, some of the attacks on Enigma were based on the observation that letters can not be encrypted to themselves). -
Applied Cryptography and Data Security
Lecture Notes APPLIED CRYPTOGRAPHY AND DATA SECURITY (version 2.5 | January 2005) Prof. Christof Paar Chair for Communication Security Department of Electrical Engineering and Information Sciences Ruhr-Universit¨at Bochum Germany www.crypto.rub.de Table of Contents 1 Introduction to Cryptography and Data Security 2 1.1 Literature Recommendations . 3 1.2 Overview on the Field of Cryptology . 4 1.3 Symmetric Cryptosystems . 5 1.3.1 Basics . 5 1.3.2 A Motivating Example: The Substitution Cipher . 7 1.3.3 How Many Key Bits Are Enough? . 9 1.4 Cryptanalysis . 10 1.4.1 Rules of the Game . 10 1.4.2 Attacks against Crypto Algorithms . 11 1.5 Some Number Theory . 12 1.6 Simple Blockciphers . 17 1.6.1 Shift Cipher . 18 1.6.2 Affine Cipher . 20 1.7 Lessons Learned | Introduction . 21 2 Stream Ciphers 22 2.1 Introduction . 22 2.2 Some Remarks on Random Number Generators . 26 2.3 General Thoughts on Security, One-Time Pad and Practical Stream Ciphers 27 2.4 Synchronous Stream Ciphers . 31 i 2.4.1 Linear Feedback Shift Registers (LFSR) . 31 2.4.2 Clock Controlled Shift Registers . 34 2.5 Known Plaintext Attack Against Single LFSRs . 35 2.6 Lessons Learned | Stream Ciphers . 37 3 Data Encryption Standard (DES) 38 3.1 Confusion and Diffusion . 38 3.2 Introduction to DES . 40 3.2.1 Overview . 41 3.2.2 Permutations . 42 3.2.3 Core Iteration / f-Function . 43 3.2.4 Key Schedule . 45 3.3 Decryption . 47 3.4 Implementation . 50 3.4.1 Hardware .