Related-Key Cryptanalysis of 3-WAY, Biham-DES,CAST, DES-X, Newdes, RC2, and TEA
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Improved Cryptanalysis of the Reduced Grøstl Compression Function, ECHO Permutation and AES Block Cipher
Improved Cryptanalysis of the Reduced Grøstl Compression Function, ECHO Permutation and AES Block Cipher Florian Mendel1, Thomas Peyrin2, Christian Rechberger1, and Martin Schl¨affer1 1 IAIK, Graz University of Technology, Austria 2 Ingenico, France [email protected],[email protected] Abstract. In this paper, we propose two new ways to mount attacks on the SHA-3 candidates Grøstl, and ECHO, and apply these attacks also to the AES. Our results improve upon and extend the rebound attack. Using the new techniques, we are able to extend the number of rounds in which available degrees of freedom can be used. As a result, we present the first attack on 7 rounds for the Grøstl-256 output transformation3 and improve the semi-free-start collision attack on 6 rounds. Further, we present an improved known-key distinguisher for 7 rounds of the AES block cipher and the internal permutation used in ECHO. Keywords: hash function, block cipher, cryptanalysis, semi-free-start collision, known-key distinguisher 1 Introduction Recently, a new wave of hash function proposals appeared, following a call for submissions to the SHA-3 contest organized by NIST [26]. In order to analyze these proposals, the toolbox which is at the cryptanalysts' disposal needs to be extended. Meet-in-the-middle and differential attacks are commonly used. A recent extension of differential cryptanalysis to hash functions is the rebound attack [22] originally applied to reduced (7.5 rounds) Whirlpool (standardized since 2000 by ISO/IEC 10118-3:2004) and a reduced version (6 rounds) of the SHA-3 candidate Grøstl-256 [14], which both have 10 rounds in total. -
Key-Dependent Approximations in Cryptanalysis. an Application of Multiple Z4 and Non-Linear Approximations
KEY-DEPENDENT APPROXIMATIONS IN CRYPTANALYSIS. AN APPLICATION OF MULTIPLE Z4 AND NON-LINEAR APPROXIMATIONS. FX Standaert, G Rouvroy, G Piret, JJ Quisquater, JD Legat Universite Catholique de Louvain, UCL Crypto Group, Place du Levant, 3, 1348 Louvain-la-Neuve, standaert,rouvroy,piret,quisquater,[email protected] Linear cryptanalysis is a powerful cryptanalytic technique that makes use of a linear approximation over some rounds of a cipher, combined with one (or two) round(s) of key guess. This key guess is usually performed by a partial decryp- tion over every possible key. In this paper, we investigate a particular class of non-linear boolean functions that allows to mount key-dependent approximations of s-boxes. Replacing the classical key guess by these key-dependent approxima- tions allows to quickly distinguish a set of keys including the correct one. By combining different relations, we can make up a system of equations whose solu- tion is the correct key. The resulting attack allows larger flexibility and improves the success rate in some contexts. We apply it to the block cipher Q. In parallel, we propose a chosen-plaintext attack against Q that reduces the required number of plaintext-ciphertext pairs from 297 to 287. 1. INTRODUCTION In its basic version, linear cryptanalysis is a known-plaintext attack that uses a linear relation between input-bits, output-bits and key-bits of an encryption algorithm that holds with a certain probability. If enough plaintext-ciphertext pairs are provided, this approximation can be used to assign probabilities to the possible keys and to locate the most probable one. -
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. -
Basic Cryptography
Basic cryptography • How cryptography works... • Symmetric cryptography... • Public key cryptography... • Online Resources... • Printed Resources... I VP R 1 © Copyright 2002-2007 Haim Levkowitz How cryptography works • Plaintext • Ciphertext • Cryptographic algorithm • Key Decryption Key Algorithm Plaintext Ciphertext Encryption I VP R 2 © Copyright 2002-2007 Haim Levkowitz Simple cryptosystem ... ! ABCDEFGHIJKLMNOPQRSTUVWXYZ ! DEFGHIJKLMNOPQRSTUVWXYZABC • Caesar Cipher • Simple substitution cipher • ROT-13 • rotate by half the alphabet • A => N B => O I VP R 3 © Copyright 2002-2007 Haim Levkowitz Keys cryptosystems … • keys and keyspace ... • secret-key and public-key ... • key management ... • strength of key systems ... I VP R 4 © Copyright 2002-2007 Haim Levkowitz Keys and keyspace … • ROT: key is N • Brute force: 25 values of N • IDEA (international data encryption algorithm) in PGP: 2128 numeric keys • 1 billion keys / sec ==> >10,781,000,000,000,000,000,000 years I VP R 5 © Copyright 2002-2007 Haim Levkowitz Symmetric cryptography • DES • Triple DES, DESX, GDES, RDES • RC2, RC4, RC5 • IDEA Key • Blowfish Plaintext Encryption Ciphertext Decryption Plaintext Sender Recipient I VP R 6 © Copyright 2002-2007 Haim Levkowitz DES • Data Encryption Standard • US NIST (‘70s) • 56-bit key • Good then • Not enough now (cracked June 1997) • Discrete blocks of 64 bits • Often w/ CBC (cipherblock chaining) • Each blocks encr. depends on contents of previous => detect missing block I VP R 7 © Copyright 2002-2007 Haim Levkowitz Triple DES, DESX, -
Block Ciphers and the Data Encryption Standard
Lecture 3: Block Ciphers and the Data Encryption Standard Lecture Notes on “Computer and Network Security” by Avi Kak ([email protected]) January 26, 2021 3:43pm ©2021 Avinash Kak, Purdue University Goals: To introduce the notion of a block cipher in the modern context. To talk about the infeasibility of ideal block ciphers To introduce the notion of the Feistel Cipher Structure To go over DES, the Data Encryption Standard To illustrate important DES steps with Python and Perl code CONTENTS Section Title Page 3.1 Ideal Block Cipher 3 3.1.1 Size of the Encryption Key for the Ideal Block Cipher 6 3.2 The Feistel Structure for Block Ciphers 7 3.2.1 Mathematical Description of Each Round in the 10 Feistel Structure 3.2.2 Decryption in Ciphers Based on the Feistel Structure 12 3.3 DES: The Data Encryption Standard 16 3.3.1 One Round of Processing in DES 18 3.3.2 The S-Box for the Substitution Step in Each Round 22 3.3.3 The Substitution Tables 26 3.3.4 The P-Box Permutation in the Feistel Function 33 3.3.5 The DES Key Schedule: Generating the Round Keys 35 3.3.6 Initial Permutation of the Encryption Key 38 3.3.7 Contraction-Permutation that Generates the 48-Bit 42 Round Key from the 56-Bit Key 3.4 What Makes DES a Strong Cipher (to the 46 Extent It is a Strong Cipher) 3.5 Homework Problems 48 2 Computer and Network Security by Avi Kak Lecture 3 Back to TOC 3.1 IDEAL BLOCK CIPHER In a modern block cipher (but still using a classical encryption method), we replace a block of N bits from the plaintext with a block of N bits from the ciphertext. -
1 Perfect Secrecy of the One-Time Pad
1 Perfect secrecy of the one-time pad In this section, we make more a more precise analysis of the security of the one-time pad. First, we need to define conditional probability. Let’s consider an example. We know that if it rains Saturday, then there is a reasonable chance that it will rain on Sunday. To make this more precise, we want to compute the probability that it rains on Sunday, given that it rains on Saturday. So we restrict our attention to only those situations where it rains on Saturday and count how often this happens over several years. Then we count how often it rains on both Saturday and Sunday. The ratio gives an estimate of the desired probability. If we call A the event that it rains on Saturday and B the event that it rains on Sunday, then the intersection A ∩ B is when it rains on both days. The conditional probability of A given B is defined to be P (A ∩ B) P (B | A)= , P (A) where P (A) denotes the probability of the event A. This formula can be used to define the conditional probability of one event given another for any two events A and B that have probabilities (we implicitly assume throughout this discussion that any probability that occurs in a denominator has nonzero probability). Events A and B are independent if P (A ∩ B)= P (A) P (B). For example, if Alice flips a fair coin, let A be the event that the coin ends up Heads. If Bob rolls a fair six-sided die, let B be the event that he rolls a 3. -
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. -
Performance and Energy Efficiency of Block Ciphers in Personal Digital Assistants
Performance and Energy Efficiency of Block Ciphers in Personal Digital Assistants Creighton T. R. Hager, Scott F. Midkiff, Jung-Min Park, Thomas L. Martin Bradley Department of Electrical and Computer Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia 24061 USA {chager, midkiff, jungmin, tlmartin} @ vt.edu Abstract algorithms may consume more energy and drain the PDA battery faster than using less secure algorithms. Due to Encryption algorithms can be used to help secure the processing requirements and the limited computing wireless communications, but securing data also power in many PDAs, using strong cryptographic consumes resources. The goal of this research is to algorithms may also significantly increase the delay provide users or system developers of personal digital between data transmissions. Thus, users and, perhaps assistants and applications with the associated time and more importantly, software and system designers need to energy costs of using specific encryption algorithms. be aware of the benefits and costs of using various Four block ciphers (RC2, Blowfish, XTEA, and AES) were encryption algorithms. considered. The experiments included encryption and This research answers questions regarding energy decryption tasks with different cipher and file size consumption and execution time for various encryption combinations. The resource impact of the block ciphers algorithms executing on a PDA platform with the goal of were evaluated using the latency, throughput, energy- helping software and system developers design more latency product, and throughput/energy ratio metrics. effective applications and systems and of allowing end We found that RC2 encrypts faster and uses less users to better utilize the capabilities of PDA devices. -
CIT 380: Securing Computer Systems
CIT 380: Securing Computer Systems Symmetric Cryptography Topics 1. Modular Arithmetic 2. What is Cryptography? 3. Transposition Ciphers 4. Substitution Ciphers 1. Cæsar cipher 2. Vigènere cipher 5. Cryptanalysis: frequency analysis 6. Block Ciphers 7. AES and DES 8. Stream Ciphers Modular Arithmetic Congruence – a = b (mod N) iff a = b + kN – ex: 37=27 mod 10 b is the residue of a, modulo N – Integers 0..N-1 are the set of residues mod N Modulo 12 number system What is Cryptography? Cryptography: The art and science of keeping messages secure. Cryptanalysis: the art and science of decrypting messages. Cryptology: cryptography + cryptanalysis Terminology Plaintext: message P to be encrypted. Also called Plaintext cleartext. Encryption: altering a Encryption message to keep its Procedure contents secret. Ciphertext: encrypted message C. Ciphertext Cæsar cipher Plaintext is HELLO WORLD Change each letter to the third letter following it (X goes to A, Y to B, Z to C) – Key is 3, usually written as letter ‘D’ Ciphertext is KHOOR ZRUOG ROT 13 Cæsar cipher with key of 13 13 chosen since encryption and decryption are same operation Used to hide spoilers, punchlines, and offensive material online. Kerckhoff’s Principle Security of cryptosystem should only depend on 1. Quality of shared encryption algorithm E 2. Secrecy of key K Security through obscurity tends to fail ex: DVD Content Scrambling System Cryptanalysis Goals 1. Decrypt a given message. 2. Recover encryption key. Threat models vary based on 1. Type of information available to adversary 2. Interaction with cryptosystem. Cryptanalysis Threat Models ciphertext only: adversary has only ciphertext; goal is to find plaintext, possibly key. -
Hemiunu Used Numerically Tagged Surface Ratios to Mark Ceilings Inside the Great Pyramid Hinting at Designed Spaces Still Hidden Within
Archaeological Discovery, 2018, 6, 319-337 http://www.scirp.org/journal/ad ISSN Online: 2331-1967 ISSN Print: 2331-1959 Hemiunu Used Numerically Tagged Surface Ratios to Mark Ceilings inside the Great Pyramid Hinting at Designed Spaces Still Hidden Within Manu Seyfzadeh Institute for the Study of the Origins of Civilization (ISOC)1, Boston University’s College of General Studies, Boston, USA How to cite this paper: Seyfzadeh, M. Abstract (2018). Hemiunu Used Numerically Tagged Surface Ratios to Mark Ceilings inside the In 1883, W. M. Flinders Petrie noticed that the vertical thickness and height Great Pyramid Hinting at Designed Spaces of certain stone courses of the Great Pyramid2 of Khufu/Cheops at Giza, Still Hidden Within. Archaeological Dis- Egypt markedly increase compared to those immediately lower periodically covery, 6, 319-337. https://doi.org/10.4236/ad.2018.64016 and conspicuously interrupting a general trend of progressive course thinning towards the summit. Having calculated the surface area of each course, Petrie Received: September 10, 2018 further noted that the courses immediately below such discrete stone thick- Accepted: October 5, 2018 Published: October 8, 2018 ness peaks tended to mark integer multiples of 1/25th of the surface area at ground level. Here I show that the probable architect of the Great Pyramid, Copyright © 2018 by author and Khufu’s vizier Hemiunu, conceptualized its vertical construction design using Scientific Research Publishing Inc. surface areas based on the same numerical principles used to design his own This work is licensed under the Creative Commons Attribution International mastaba in Giza’s western cemetery and conspicuously used this numerical License (CC BY 4.0). -
Impossible Differential Cryptanalysis of TEA, XTEA and HIGHT
Preliminaries Impossible Differential Attacks on TEA and XTEA Impossible Differential Cryptanalysis of HIGHT Conclusion Impossible Differential Cryptanalysis of TEA, XTEA and HIGHT Jiazhe Chen1;2 Meiqin Wang1;2 Bart Preneel2 1Shangdong University, China 2KU Leuven, ESAT/COSIC and IBBT, Belgium AfricaCrypt 2012 July 10, 2012 1 / 27 Preliminaries Impossible Differential Attacks on TEA and XTEA Impossible Differential Cryptanalysis of HIGHT Conclusion Preliminaries Impossible Differential Attack TEA, XTEA and HIGHT Impossible Differential Attacks on TEA and XTEA Deriving Impossible Differentials for TEA and XTEA Key Recovery Attacks on TEA and XTEA Impossible Differential Cryptanalysis of HIGHT Impossible Differential Attacks on HIGHT Conclusion 2 / 27 I Pr(∆A ! ∆B) = 1, Pr(∆G ! ∆F) = 1, ∆B 6= ∆F, Pr(∆A ! ∆G) = 0 I Extend the impossible differential forward and backward to attack a block cipher I Guess subkeys in Part I and Part II, if there is a pair meets ∆A and ∆G, then the subkey guess must be wrong P I A B F G II C Preliminaries Impossible Differential Attacks on TEA and XTEA Impossible Differential Cryptanalysis of HIGHT Conclusion Impossible Differential Attack Impossible Differential Attack 3 / 27 I Pr(∆A ! ∆B) = 1, Pr(∆G ! ∆F) = 1, ∆B 6= ∆F, Pr(∆A ! ∆G) = 0 I Extend the impossible differential forward and backward to attack a block cipher I Guess subkeys in Part I and Part II, if there is a pair meets ∆A and ∆G, then the subkey guess must be wrong P I A B F G II C Preliminaries Impossible Differential Attacks on TEA and XTEA Impossible -
Development of the Advanced Encryption Standard
Volume 126, Article No. 126024 (2021) https://doi.org/10.6028/jres.126.024 Journal of Research of the National Institute of Standards and Technology Development of the Advanced Encryption Standard Miles E. Smid Formerly: Computer Security Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA [email protected] Strong cryptographic algorithms are essential for the protection of stored and transmitted data throughout the world. This publication discusses the development of Federal Information Processing Standards Publication (FIPS) 197, which specifies a cryptographic algorithm known as the Advanced Encryption Standard (AES). The AES was the result of a cooperative multiyear effort involving the U.S. government, industry, and the academic community. Several difficult problems that had to be resolved during the standard’s development are discussed, and the eventual solutions are presented. The author writes from his viewpoint as former leader of the Security Technology Group and later as acting director of the Computer Security Division at the National Institute of Standards and Technology, where he was responsible for the AES development. Key words: Advanced Encryption Standard (AES); consensus process; cryptography; Data Encryption Standard (DES); security requirements, SKIPJACK. Accepted: June 18, 2021 Published: August 16, 2021; Current Version: August 23, 2021 This article was sponsored by James Foti, Computer Security Division, Information Technology Laboratory, National Institute of Standards and Technology (NIST). The views expressed represent those of the author and not necessarily those of NIST. https://doi.org/10.6028/jres.126.024 1. Introduction In the late 1990s, the National Institute of Standards and Technology (NIST) was about to decide if it was going to specify a new cryptographic algorithm standard for the protection of U.S.