Bruce Schneier
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Improved Related-Key Attacks on DESX and DESX+
Improved Related-key Attacks on DESX and DESX+ Raphael C.-W. Phan1 and Adi Shamir3 1 Laboratoire de s´ecurit´eet de cryptographie (LASEC), Ecole Polytechnique F´ed´erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland [email protected] 2 Faculty of Mathematics & Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel [email protected] Abstract. In this paper, we present improved related-key attacks on the original DESX, and DESX+, a variant of the DESX with its pre- and post-whitening XOR operations replaced with addition modulo 264. Compared to previous results, our attack on DESX has reduced text complexity, while our best attack on DESX+ eliminates the memory requirements at the same processing complexity. Keywords: DESX, DESX+, related-key attack, fault attack. 1 Introduction Due to the DES’ small key length of 56 bits, variants of the DES under multiple encryption have been considered, including double-DES under one or two 56-bit key(s), and triple-DES under two or three 56-bit keys. Another popular variant based on the DES is the DESX [15], where the basic keylength of single DES is extended to 120 bits by wrapping this DES with two outer pre- and post-whitening keys of 64 bits each. Also, the endorsement of single DES had been officially withdrawn by NIST in the summer of 2004 [19], due to its insecurity against exhaustive search. Future use of single DES is recommended only as a component of the triple-DES. This makes it more important to study the security of variants of single DES which increase the key length to avoid this attack. -
Blockchain Beyond Cryptocurrency Or Is Private Chain a Hoax Or How I Lose Money in Bitcoin but Still Decide to Get in the Research
Blockchain Beyond Cryptocurrency Or Is Private Chain a Hoax Or How I Lose Money in Bitcoin but still Decide to Get in the Research Hong Wan Edward P. Fitts Department of Industrial and Systems Engineering Sept 2019 In this talk: • Blockchain and trust • Different kinds of blockchain • Cases and Examples • Discussions First Things First https://images.app.goo.gl/JuNznV8dZKTaHWEf9 Disclaimer Block and Chain https://youtu.be/SSo_EIwHSd4 https://youtu.be/SSo_EIwHSd4 Blockchain Design Questions • Who can access data: Private vs. Public • Who can validate data/add block: Permissioned vs Permissionless • Consensus to be used: Trade-off among security and efficiency. https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=2ahUKEwinjN2s7_DkAhXlmeAKHXxhAIUQjRx6BAgBEAQ&url=ht tps%3A%2F%2F101blockchains.com%2Fconsensus-algorithms-blockchain%2F&psig=AOvVaw23pKh4qS8W_xgyajJ3aFl9&ust=1569669093339830 Bad News First • “Private blockchains are completely uninteresting… -- the only reason to operate one is to ride on the blockchain hype…” Bruce Schneier Tonight we will talk about cryptocurrencies… .everything you don’t understand money combined by everything you don’t understand about computers…. Cryptocurrencies: Last Week Tonight with John Oliver (HBO) https://www.schneier.com/blog/archives/2019/02/blockchain_and_.html http://shorturl.at/ahsRU, shorturl.at/gETV2 https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=2ahUKEwj- https://d279m997dpfwgl.cloudfront.net/wp/2017/11/Trustp72L7vDkAhVjQt8KHU18CjsQjRx6BAgBEAQ&url=https%3A%2F%2Fwww.wbur.org%2Fonpoint%2F2017%2F11%2F20%2Fwho-can-cropped.jpg-you- -
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. -
Related-Key Statistical Cryptanalysis
Related-Key Statistical Cryptanalysis Darakhshan J. Mir∗ Poorvi L. Vora Department of Computer Science, Department of Computer Science, Rutgers, The State University of New Jersey George Washington University July 6, 2007 Abstract This paper presents the Cryptanalytic Channel Model (CCM). The model treats statistical key recovery as communication over a low capacity channel, where the channel and the encoding are determined by the cipher and the specific attack. A new attack, related-key recovery – the use of n related keys generated from k independent ones – is defined for all ciphers vulnera- ble to single-key recovery. Unlike classical related-key attacks such as differential related-key cryptanalysis, this attack does not exploit a special structural weakness in the cipher or key schedule, but amplifies the weakness exploited in the basic single key recovery. The related- key-recovery attack is shown to correspond to the use of a concatenated code over the channel, where the relationship among the keys determines the outer code, and the cipher and the attack the inner code. It is shown that there exists a relationship among keys for which the communi- cation complexity per bit of independent key is finite, for any probability of key recovery error. This may be compared to the unbounded communication complexity per bit of the single-key- recovery attack. The practical implications of this result are demonstrated through experiments on reduced-round DES. Keywords: related keys, concatenated codes, communication channel, statistical cryptanalysis, linear cryptanalysis, DES Communicating Author: Poorvi L. Vora, [email protected] ∗This work was done while the author was in the M.S. -
Related-Key Cryptanalysis of 3-WAY, Biham-DES,CAST, DES-X, Newdes, RC2, and TEA
Related-Key Cryptanalysis of 3-WAY, Biham-DES,CAST, DES-X, NewDES, RC2, and TEA John Kelsey Bruce Schneier David Wagner Counterpane Systems U.C. Berkeley kelsey,schneier @counterpane.com [email protected] f g Abstract. We present new related-key attacks on the block ciphers 3- WAY, Biham-DES, CAST, DES-X, NewDES, RC2, and TEA. Differen- tial related-key attacks allow both keys and plaintexts to be chosen with specific differences [KSW96]. Our attacks build on the original work, showing how to adapt the general attack to deal with the difficulties of the individual algorithms. We also give specific design principles to protect against these attacks. 1 Introduction Related-key cryptanalysis assumes that the attacker learns the encryption of certain plaintexts not only under the original (unknown) key K, but also under some derived keys K0 = f(K). In a chosen-related-key attack, the attacker specifies how the key is to be changed; known-related-key attacks are those where the key difference is known, but cannot be chosen by the attacker. We emphasize that the attacker knows or chooses the relationship between keys, not the actual key values. These techniques have been developed in [Knu93b, Bih94, KSW96]. Related-key cryptanalysis is a practical attack on key-exchange protocols that do not guarantee key-integrity|an attacker may be able to flip bits in the key without knowing the key|and key-update protocols that update keys using a known function: e.g., K, K + 1, K + 2, etc. Related-key attacks were also used against rotor machines: operators sometimes set rotors incorrectly. -
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. -
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. -
Rotational Cryptanalysis of ARX
Rotational Cryptanalysis of ARX Dmitry Khovratovich and Ivica Nikoli´c University of Luxembourg [email protected], [email protected] Abstract. In this paper we analyze the security of systems based on modular additions, rotations, and XORs (ARX systems). We provide both theoretical support for their security and practical cryptanalysis of real ARX primitives. We use a technique called rotational cryptanalysis, that is universal for the ARX systems and is quite efficient. We illustrate the method with the best known attack on reduced versions of the block cipher Threefish (the core of Skein). Additionally, we prove that ARX with constants are functionally complete, i.e. any function can be realized with these operations. Keywords: ARX, cryptanalysis, rotational cryptanalysis. 1 Introduction A huge number of symmetric primitives using modular additions, bitwise XORs, and intraword rotations have appeared in the last 20 years. The most famous are the hash functions from MD-family (MD4, MD5) and their descendants SHA-x. While modular addition is often approximated with XOR, for random inputs these operations are quite different. Addition provides diffusion and nonlinearity, while XOR does not. Although the diffusion is relatively slow, it is compensated by a low price of addition in both software and hardware, so primitives with relatively high number of additions (tens per byte) are still fast. The intraword rotation removes disbalance between left and right bits (introduced by the ad- dition) and speeds up the diffusion. Many recently design primitives use only XOR, addition, and rotation so they are grouped into a single family ARX (Addition-Rotation-XOR). -
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. -
The Mathemathics of Secrets.Pdf
THE MATHEMATICS OF SECRETS THE MATHEMATICS OF SECRETS CRYPTOGRAPHY FROM CAESAR CIPHERS TO DIGITAL ENCRYPTION JOSHUA HOLDEN PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c 2017 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR press.princeton.edu Jacket image courtesy of Shutterstock; design by Lorraine Betz Doneker All Rights Reserved Library of Congress Cataloging-in-Publication Data Names: Holden, Joshua, 1970– author. Title: The mathematics of secrets : cryptography from Caesar ciphers to digital encryption / Joshua Holden. Description: Princeton : Princeton University Press, [2017] | Includes bibliographical references and index. Identifiers: LCCN 2016014840 | ISBN 9780691141756 (hardcover : alk. paper) Subjects: LCSH: Cryptography—Mathematics. | Ciphers. | Computer security. Classification: LCC Z103 .H664 2017 | DDC 005.8/2—dc23 LC record available at https://lccn.loc.gov/2016014840 British Library Cataloging-in-Publication Data is available This book has been composed in Linux Libertine Printed on acid-free paper. ∞ Printed in the United States of America 13579108642 To Lana and Richard for their love and support CONTENTS Preface xi Acknowledgments xiii Introduction to Ciphers and Substitution 1 1.1 Alice and Bob and Carl and Julius: Terminology and Caesar Cipher 1 1.2 The Key to the Matter: Generalizing the Caesar Cipher 4 1.3 Multiplicative Ciphers 6