DOCSLIB.ORG

1 Review 2 Poly-Alphabetic Classical Cryptosystems

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
1 Review 2 Poly-Alphabetic Classical Cryptosystems EE 595 (PMP) Introduction to Security and Privacy Lecutre #3 Introduction to Cryptanalysis. DES, AES and Modes of Operation. Lecture notes prepared by Professor Radha Poovendran Thursday, April 12, 2018 Tamara Bonaci Department of Electrical Engineering University of Washington, Seattle Outline: 1. Polyalphabetic classical cryptosystems { Vigenere cipher { Permutation cipher 2. Cryptanalysis. 3. Data Encryption Standard (DES) 4. Triple DES 5. Advanced Encryption Standard (AES) 6. Encrypting large plaintexts: Modes of operation { Electronic Code Book (ECB) mode { Cipher Block Chaining (CBC) mode { Counter (CTR) mode 1 Review Last time, we saw that the goal of a symmetric key cryptosystem is to ensure that two parties Alice and Bob can communicate confidentially using a shared secret key K. Equivalently, the goal is to ensure that a third party Eve, who does not have knowledge of the key K, cannot determine the plaintext sent by Alice to Bob. Let's recall that a cryptosystem is defined as a five-tuple (P; C; K; E; D). The set P is the set of possible plaintexts, C is the set of possible ciphertexts, and K is the set of possible keys. The sets E and D are the sets of possible encryption and decryption functions, respectively. In today's lecture, we will first consider how we can model and analyze a behavior of an attacker, trying to break a cryptosystem. We will then describe two widely-used current symmetric-key cryptosystems, namely DES and AES. For each cryptosystem, we will show the parameter values (e.g., key length) that are specified by standards bodies such as the National Institute of Standards and Technology for real-world use. We will then present block-chaining modes that can be used to encrypt longer messages while preserving the security guarantees of each of these cryptosystems. 2 Poly-alphabetic Classical Cryptosystems A polyalphabetic cryptosystem is a cryptosystem where multiple alphabetic characters are encrypted at a time. In other words, each plaintext element is equivalent to n alphabetic characters. The Vigen`ere cipher is the first polyalphabetic cryptosystem that we are encountering in this course. 1 2.1 The Vigen`ereCipher The idea behind this cryptosystem is to use a vector of n keys, i.e., K = (K1;K2; ::; Kn). n n P = C = K = (Z26) where (Z26) is an n-tuple. The difference between the Vigen`erecipher and the shift, substitution, and affine ciphers is that in the Vigen`erecipher each alphabetic character is not uniquely mapped to another alphabetic character. y = eK (x1; x2; ::; xn) = (x1 + K1; x2 + K2; ::; xn + Kn) mod 26; (1) dK (y1; y2; ::; yn) = (y1 − K1; y2 − K2; ::; yn − Kn) mod 26: (2) Example Let the plaintext be vector, and let n = 4; K = (2; 4; 6; 7). From the correspondence table we have x = (21; 4; 2; 19; 14; 17), and the cipher is shown in Table 2.1. PLAINTEXT: 21 4 2 19 14 17 KEY: 2 4 6 7 2 4 CIPHER: 23 8 8 0 16 21 XIIA QV To decrypt, we use the same keyword, but modulo subtraction is performed instead of modulo addition. The number of possible keywords of length n is 26n; so even for small n an exhaustive search attack requires a long time. 2.2 The Permutation Cipher The idea of the permutation cipher (also known as the transposition cipher) cryptosystem is to generate the ciphertext by altering the positions of the characters in the plaintext, i.e. to rearrange the alphabets using a permutation. In contrast to the substitution cipher, there is no replacement of characters (it is similar to just scrambling the letters of a word). Formally, we describe the permutation cipher cryptosystem as follows. n Let P = C = (Z26) , where n is a positive integer. K includes all permutations of f1; :::; ng. For each permutation π 2 K: y = eπ(x1; :::; xn) = (xπ(1); :::; xπ(n)) (3) x = dπ(y1; :::; yn) = (yπ−1(1); :::; yπ−1(n)): (4) π−1 denotes inverse permutation to π. Example: For illustration, let's consider n = 6, and permutation (the key) π is as follows: j 1 2 3 4 5 6 π(j) 3 5 1 6 4 2 To obtain π−1, interchange the rows, and sort the columns such that the first row is in ascending order. We obtain: For encryption, if the plaintext is followashore, we first partition the plaintext into groups of six letters as: follow j ashore. Using the above key π, we re-arrange each group of six alphabets as: LOFWLO j HRAEOS. Similarly, the ciphertext can be decrypted using the inverse permutation π−1. 2 j 1 2 3 4 5 6 π−1(j) 3 6 1 5 2 4 3 Cryptanalysis Now that we are familiar with some simple classical cryptosystems, we might be interested in how secure these cryptosystems are (or how could one go about breaking them). In doing so, we turn to cryptanalysis, and start by considering one of the most important assumptions in the modern cryptography, namely the Kerchoff's principle. 3.1 Kerchoff's Principle: The Kerchoff's principle was introduced in 1883 by A. Kerchoff, and it states that in assessing the security of a cryptosystem, one should always assume that an attacker know the details of the cryptosystem being used. In other words, an attacker knows the tuple (P; C; K; E; D) defining the cryptosystem. Therefore, the security of the system should always be based on the key, and not on the obscurity of a cryptographic algorithm. 3.2 Attack models An attacker can have different goals when attacking a channel between communicating parties. For example, an attacker may wish to: 1. Read one specific message. 2. Find the encryption/decryption key, and thus read all of the exchanged messages. 3. Corrupt Alice's message into another message in such a way that Bob thinks that Alice has sent the altered message. 4. Masquerade as Alice in order to communicate with Bob such that Bob believes he is communicating with Alice. For each of these goals, there are four main types of attacks that an attacker can use, and those types differ in the amount of information an attacker has available when trying to determine the key. Those four attack types are as follows. Type of attack Description Ciphertext only attack Eve only observes the ciphertext y Known plaintext attack Eve knows the ciphertext y corresponding to plaintext x Chosen plaintext attack Eve has temporary access to an encryption box. The encryption box takes as input any chosen plaintext x and outputs the ciphertext y Chosen ciphertext attack Eve has temporary access to a decryption box. The decryption box takes as input any chosen ciphertext y and outputs the plaintext x Based on these models, we can analyze the security of every cryptosystem. 3.3 Cryptanalysis of the Shift Cipher { Ciphertext only: Let K = 3 and the plaintext be shift. We then get VKLIW as the cipher (for a right shift). Assume Eve knows only the ciphertext V KLIW . Eve also knows that a shift cipher algorithm is used for encryption. Given the small cardinality of the key space, Eve can try all the possible 26 shifts in right direction. Upon shifting, the following plaintexts are obtained: 3 1stleft shift 2ndleft shift 3rdleft shift vkliw −! ujkhv −! tijgu −! shift, and so on. Since \shift" is the only dictionary word in the list of 26 possible words, Eve assumes that it is indeed the plaintext that was encrypted. Therefore, Eve can also infer the original key K = 3. { Known plaintext: If Eve knows a (plaintext, ciphertext) pair, then Eve can find the key by subtracting the plaintext from the ciphertext mod 26. For instance, if Eve knows that plaintext b corresponds to ciphertext E, then Eve can determine that K = 3. { Chosen plaintext: Choose letter a as plaintext; the resulting ciphertext will be the key. For example, if the ciphertext is P then K = 15: { Chosen cipher: Choose A as the ciphertext. The plaintext is then the negative of the key K: 3.4 Remarks on Letter Distribution of the English Language English language text has different frequencies for different alphabets. An estimate of relative frequencies (probabilities) of the 26 letters are as indicated in Table 3.4. Note that the letter e has the maximum relative frequency of 0.127. Table 1. Probabilities of occurrence of the 26 letters of the English language alphabet. A B C D E F G H I J K L M 0.082 0.015 0.028 0.043 0.127 0.022 0.020 0.061 0.070 0.002 0.008 0.040 0.024 N O P Q R S T U V W X Y Z 0.067 0.075 0.019 0.001 0.060 0.063 0.091 0.028 0.010 0.023 0.001 0.020 0.001 Similarly we can define frequencies of digrams, trigrams, initial letters, final letters, etc. More generally, we can then use the statistical properties of the English language to perform cryptanalysis. A key observation here that the vowels "a, e, i, o" and the letters "t, s, b, h, d" have relatively high probability of appearance in the English language. Table 3.4 indicates the rank order of vowels based on their frequencies, and Table 3.4 the rank order of consonants "t, s, d, n, h" based on their frequencies. Table 2. Rank order of the probabilities of occurrence of the vowels. E 0.0127 A 0.082 I 0.075 O 0.070 U 0.028 Table 3.
Load more

Recommended publications
  • Cryptanalysis of a Reduced Version of the Block Cipher E2
    Cryptanalysis of a Reduced Version of the Block Cipher E2 Mitsuru Matsui and Toshio Tokita Information Technology R&D Center Mitsubishi Electric Corporation 5-1-1, Ofuna, Kamakura, Kanagawa, 247, Japan [email protected], [email protected] Abstract. This paper deals with truncated differential cryptanalysis of the 128-bit block cipher E2, which is an AES candidate designed and submitted by NTT. Our analysis is based on byte characteristics, where a difference of two bytes is simply encoded into one bit information “0” (the same) or “1” (not the same). Since E2 is a strongly byte-oriented algorithm, this bytewise treatment of characteristics greatly simplifies a description of its probabilistic behavior and noticeably enables us an analysis independent of the structure of its (unique) lookup table. As a result, we show a non-trivial seven round byte characteristic, which leads to a possible attack of E2 reduced to eight rounds without IT and FT by a chosen plaintext scenario. We also show that by a minor modification of the byte order of output of the round function — which does not reduce the complexity of the algorithm nor violates its design criteria at all —, a non-trivial nine round byte characteristic can be established, which results in a possible attack of the modified E2 reduced to ten rounds without IT and FT, and reduced to nine rounds with IT and FT. Our analysis does not have a serious impact on the full E2, since it has twelve rounds with IT and FT; however, our results show that the security level of the modified version against differential cryptanalysis is lower than the designers’ estimation.
    [Show full text]
  • Historical Ciphers • A
    ECE 646 - Lecture 6 Required Reading • W. Stallings, Cryptography and Network Security, Chapter 2, Classical Encryption Techniques Historical Ciphers • A. Menezes et al., Handbook of Applied Cryptography, Chapter 7.3 Classical ciphers and historical development Why (not) to study historical ciphers? Secret Writing AGAINST FOR Steganography Cryptography (hidden messages) (encrypted messages) Not similar to Basic components became modern ciphers a part of modern ciphers Under special circumstances modern ciphers can be Substitution Transposition Long abandoned Ciphers reduced to historical ciphers Transformations (change the order Influence on world events of letters) Codes Substitution The only ciphers you Ciphers can break! (replace words) (replace letters) Selected world events affected by cryptology Mary, Queen of Scots 1586 - trial of Mary Queen of Scots - substitution cipher • Scottish Queen, a cousin of Elisabeth I of England • Forced to flee Scotland by uprising against 1917 - Zimmermann telegram, America enters World War I her and her husband • Treated as a candidate to the throne of England by many British Catholics unhappy about 1939-1945 Battle of England, Battle of Atlantic, D-day - a reign of Elisabeth I, a Protestant ENIGMA machine cipher • Imprisoned by Elisabeth for 19 years • Involved in several plots to assassinate Elisabeth 1944 – world’s first computer, Colossus - • Put on trial for treason by a court of about German Lorenz machine cipher 40 noblemen, including Catholics, after being implicated in the Babington Plot by her own 1950s – operation Venona – breaking ciphers of soviet spies letters sent from prison to her co-conspirators stealing secrets of the U.S. atomic bomb in the encrypted form – one-time pad 1 Mary, Queen of Scots – cont.
    [Show full text]
  • The QARMA Block Cipher Family
    The QARMA Block Cipher Family Almost MDS Matrices Over Rings With Zero Divisors, Nearly Symmetric Even-Mansour Constructions With Non-Involutory Central Rounds, and Search Heuristics for Low-Latency S-Boxes Roberto Avanzi Qualcomm Product Security, Munich, Germany [email protected], [email protected] Abstract. This paper introduces QARMA, a new family of lightweight tweakable block ciphers targeted at applications such as memory encryption, the generation of very short tags for hardware-assisted prevention of software exploitation, and the con- struction of keyed hash functions. QARMA is inspired by reflection ciphers such as PRINCE, to which it adds a tweaking input, and MANTIS. However, QARMA differs from previous reflector constructions in that it is a three-round Even-Mansour scheme instead of a FX-construction, and its middle permutation is non-involutory and keyed. We introduce and analyse a family of Almost MDS matrices defined over a ring with zero divisors that allows us to encode rotations in its operation while maintaining the minimal latency associated to {0, 1}-matrices. The purpose of all these design choices is to harden the cipher against various classes of attacks. We also describe new S-Box search heuristics aimed at minimising the critical path. QARMA exists in 64- and 128-bit block sizes, where block and tweak size are equal, and keys are twice as long as the blocks. We argue that QARMA provides sufficient security margins within the constraints de- termined by the mentioned applications, while still achieving best-in-class latency. Implementation results on a state-of-the art manufacturing process are reported.
    [Show full text]
  • On Recent Attacks Against Cryptographic Hash Functions
    On recent attacks against Cryptographic Hash Functions Martin Ekerå & Henrik Ygge 1 Outline ‣ First part ‣ Preliminaries ‣ Which cryptographic hash functions exist? ‣ What degree of security do they offer? ‣ An introduction to Wang’s attack ‣ Second part ‣ Wang’s attack applied to MD5 ‣ Demo 2 Part I 3 Operators Symbol Meaning x ⊞ y Addition modulo 2n x ⊟ y Subtraction modulo 2n x ⊕ y Exclusive OR x ⋀ y Bitwise AND x ⋁ y Bitwise OR ¬ x The negation of x. x ≪ s Shifting of x by s bits to the left. x ⋘ s Rotation of x by s bits to the left. 4 Bitwise Functions Function IF (x, y, z) (x ⋀ y) ⋁ ((¬ x) ⋀ z) XOR (x, y, z) x ⊕ y ⊕ z MAJ (x, y, z) (x ⋀ y) ⋁ (y ⋀ z) ⋁ (z ⋀ x) XNO (x, y, z) y ⊕ ((¬ z) ⋁ x) ‣ The functions above are all bitwise. 5 Hash Functions ‣ A hash function maps elements from a finite or infinite domain, into elements of a fixed size domain. 6 Attacks on Hash Functions ‣ Collision attack Find m and m’ ≠ m such that H(m) = H(m’). ‣ First pre-image attack Given h find m such that h = H(m). ‣ Second pre-image attack Given m find m’ ≠ m such that H(m) = H(m’). 7 Attack Complexities ‣ Collision attack Naïve complexity O(2n/2) due to the birthday paradox. ‣ First pre-image attack Naïve complexity O(2n) ‣ Second pre-image attack Naïve complexity O(2n) 8 Cryptographic Hash Functions ‣ It is desirable for a cryptographic hash function to be collision resistant, first pre-image resistant and second pre-image resistant.
    [Show full text]
  • The Quasigroup Block Cipher and Its Analysis Matthew .J Battey University of Nebraska at Omaha
    University of Nebraska at Omaha DigitalCommons@UNO Student Work 5-2014 The Quasigroup Block Cipher and its Analysis Matthew .J Battey University of Nebraska at Omaha Follow this and additional works at: https://digitalcommons.unomaha.edu/studentwork Part of the Computer Sciences Commons Recommended Citation Battey, Matthew J., "The Quasigroup Block Cipher and its Analysis" (2014). Student Work. 2892. https://digitalcommons.unomaha.edu/studentwork/2892 This Thesis is brought to you for free and open access by DigitalCommons@UNO. It has been accepted for inclusion in Student Work by an authorized administrator of DigitalCommons@UNO. For more information, please contact [email protected]. The Quasigroup Block Cipher and its Analysis A Thesis Presented to the Department of Computer Sience and the Faculty of the Graduate College University of Nebraska In partial satisfaction of the requirements for the degree of Masters of Science by Matthew J. Battey May, 2014 Supervisory Committee: Abhishek Parakh, Co-Chair Haifeng Guo, Co-Chair Kenneth Dick Qiuming Zhu UMI Number: 1554776 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 1554776 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O.
    [Show full text]
  • Advanced Meet-In-The-Middle Preimage Attacks: First Results on Full Tiger, and Improved Results on MD4 and SHA-2
    Advanced Meet-in-the-Middle Preimage Attacks: First Results on Full Tiger, and Improved Results on MD4 and SHA-2 Jian Guo1, San Ling1, Christian Rechberger2, and Huaxiong Wang1 1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 2 Dept. of Electrical Engineering ESAT/COSIC, K.U.Leuven, and Interdisciplinary Institute for BroadBand Technology (IBBT), Kasteelpark Arenberg 10, B–3001 Heverlee, Belgium. [email protected] Abstract. We revisit narrow-pipe designs that are in practical use, and their security against preimage attacks. Our results are the best known preimage attacks on Tiger, MD4, and reduced SHA-2, with the result on Tiger being the first cryptanalytic shortcut attack on the full hash function. Our attacks runs in time 2188.8 for finding preimages, and 2188.2 for second-preimages. Both have memory requirement of order 28, which is much less than in any other recent preimage attacks on reduced Tiger. Using pre-computation techniques, the time complexity for finding a new preimage or second-preimage for MD4 can now be as low as 278.4 and 269.4 MD4 computations, respectively. The second-preimage attack works for all messages longer than 2 blocks. To obtain these results, we extend the meet-in-the-middle framework recently developed by Aoki and Sasaki in a series of papers. In addition to various algorithm-specific techniques, we use a number of conceptually new ideas that are applicable to a larger class of constructions. Among them are (1) incorporating multi-target scenarios into the MITM framework, leading to faster preimages from pseudo-preimages, (2) a simple precomputation technique that allows for finding new preimages at the cost of a single pseudo-preimage, and (3) probabilistic initial structures, to reduce the attack time complexity.
    [Show full text]
  • DIN/ANSI Shark Line Material Specific Application Taps New Products 2017 SHARK
    DIN/ANSI Shark Line Material Specific Application Taps New Products 2017 SHARK INTRODUCTION Dormer brand material specific application-based ranges of DIN ANSI Shark Taps offer high performance and process security. Shark Line taps are easily recognizable by their color ring coding, denoting recommendation for use on specific materials. FEATURES AND BENEFITS • COLOR RING CODING • EDGE TREATMENT (Red, Yellow, Blue Shark) The color ring on the tool shank identifies suitability for Spiral flute taps incorporate a special edge treatment specific materials and enables quick and easy tool selection. to increase strength and reduce the chance • ADVANCED GEOMETRY of micro-chipping on the cutting edges. This considerably Significant reduction in axial forces and torque compared improves performance and tool life. to conventional taps. This ensures problem-free threading of blind and through holes in the selected material. • DIN/ANSI STANDARD Standard ANSI shank and square with DIN overall length, SHARK LINE for extra reach and compatability with Inch Standard Tap Holding. MATERIAL GEOMETRY AND CHAMFER Shark taps are manufactured from a unique powder metallurgy Thread geometry with optimized form generates: tool steel different from any other HSS-E-PM. This provides • Low torque an unbeatable combination of toughness and edge strength, allowing the taps to perform at higher cutting temperatures • Excellent threads at both high and low speeds while offering excellent performance and longer tool life. • Superior surface finish • HIGHER IMPACT TOUGHNESS
    [Show full text]
  • Cryptography
    What is this course about? Aims Cryptography This course provides an overview of basic modern cryptographic techniques and covers essential concepts that users of cryptographic standards need to understand to achieve their intended security goals. Markus Kuhn Objectives By the end of the course you should I be familiar with commonly used standardized cryptographic building Computer Laboratory, University of Cambridge blocks; I be able to match application requirements with concrete security definitions and identify their absence in naive schemes; https://www.cl.cam.ac.uk/teaching/1920/Crypto/ I understand various adversarial capabilities and basic attack These notes are merely provided as an aid for following the lectures. algorithms and how they affect key sizes; They are no substitute for attending the course. I understand and compare the finite groups most commonly used with discrete-logarithm schemes; Lent 2020 { CST Part II I understand the basic number theory underlying the most common public-key schemes, and some efficient implementation techniques. crypto-slides-4up.pdf 2020-04-23 20:49 b7c0c5f 1 2 1 Historic ciphers Related textbooks 2 Perfect secrecy Main reference: 3 Semantic security I Jonathan Katz, Yehuda Lindell: 4 Block ciphers Introduction to Modern Cryptography 2nd ed., Chapman & Hall/CRC, 2014 5 Modes of operation Further reading: 6 Message authenticity I Christof Paar, Jan Pelzl: 7 Authenticated encryption Understanding Cryptography Springer, 2010 8 Secure hash functions http://www.springerlink.com/content/978-3-642-04100-6/ http://www.crypto-textbook.com/ 9 Secure hash applications I Douglas Stinson: 10 Key distribution problem Cryptography { Theory and Practice 3rd ed., CRC Press, 2005 11 Number theory and group theory I Menezes, van Oorschot, Vanstone: 12 Discrete logarithm problem Handbook of Applied Cryptography 13 RSA trapdoor permutation CRC Press, 1996 http://www.cacr.math.uwaterloo.ca/hac/ 14 Digital signatures The course notes and some of the exercises also contain URLs with more detailed information.
    [Show full text]
  • The LED Block Cipher
    The LED Block Cipher Jian Guo1,ThomasPeyrin2,,AxelPoschmann2,, and Matt Robshaw3, 1 Institute for Infocomm Research, Singapore 2 Nanyang Technological University, Singapore 3 Applied Cryptography Group, Orange Labs, France {ntu.guo,thomas.peyrin}@gmail.com, [email protected], [email protected] Abstract. We present a new block cipher LED. While dedicated to com- pact hardware implementation, and offering the smallest silicon footprint among comparable block ciphers, the cipher has been designed to simul- taneously tackle three additional goals. First, we explore the role of an ultra-light (in fact non-existent) key schedule. Second, we consider the resistance of ciphers, and LED in particular, to related-key attacks: we are able to derive simple yet interesting AES-like security proofs for LED regarding related- or single-key attacks. And third, while we provide a block cipher that is very compact in hardware, we aim to maintain a reasonable performance profile for software implementation. Keywords: Lightweight, block cipher, RFID tag, AES. 1 Introduction Over past years many new cryptographic primitives have been proposed for use in RFID tag deployments, sensor networks, and other applications characterised by highly-constrained devices. The pervasive deployment of tiny computational devices brings with it many interesting, and potentially difficult, security issues. Chief among recent developments has been the evolution of lightweight block ciphers where an accumulation of advances in algorithm design, together with an increased awareness of the likely application, has helped provide important developments. To some commentators the need for yet another lightweight block cipher proposal will be open to question. However, in addition to the fact that many proposals present some weaknesses [2,10,45], we feel there is still more to be said on the subject and we observe that it is in the “second generation” of work that designers might learn from the progress, and omissions, of “first generation” proposals.
    [Show full text]
  • Statistical Cryptanalysis of Block Ciphers
    STATISTICAL CRYPTANALYSIS OF BLOCK CIPHERS THÈSE NO 3179 (2005) PRÉSENTÉE À LA FACULTÉ INFORMATIQUE ET COMMUNICATIONS Institut de systèmes de communication SECTION DES SYSTÈMES DE COMMUNICATION ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR Pascal JUNOD ingénieur informaticien dilpômé EPF de nationalité suisse et originaire de Sainte-Croix (VD) acceptée sur proposition du jury: Prof. S. Vaudenay, directeur de thèse Prof. J. Massey, rapporteur Prof. W. Meier, rapporteur Prof. S. Morgenthaler, rapporteur Prof. J. Stern, rapporteur Lausanne, EPFL 2005 to Mimi and Chlo´e Acknowledgments First of all, I would like to warmly thank my supervisor, Prof. Serge Vaude- nay, for having given to me such a wonderful opportunity to perform research in a friendly environment, and for having been the perfect supervisor that every PhD would dream of. I am also very grateful to the president of the jury, Prof. Emre Telatar, and to the reviewers Prof. em. James L. Massey, Prof. Jacques Stern, Prof. Willi Meier, and Prof. Stephan Morgenthaler for having accepted to be part of the jury and for having invested such a lot of time for reviewing this thesis. I would like to express my gratitude to all my (former and current) col- leagues at LASEC for their support and for their friendship: Gildas Avoine, Thomas Baign`eres, Nenad Buncic, Brice Canvel, Martine Corval, Matthieu Finiasz, Yi Lu, Jean Monnerat, Philippe Oechslin, and John Pliam. With- out them, the EPFL (and the crypto) would not be so fun! Without their support, trust and encouragement, the last part of this thesis, FOX, would certainly not be born: I owe to MediaCrypt AG, espe- cially to Ralf Kastmann and Richard Straub many, many, many hours of interesting work.
    [Show full text]
  • Cryptanalysis of Reduced Round SKINNY Block Cipher
    Cryptanalysis of Reduced round SKINNY Block Cipher Sadegh Sadeghi1, Tahereh Mohammadi2 and Nasour Bagheri2,3 1 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran, [email protected] 2 Electrical Engineering Department, Shahid Rajaee Teacher Training University, Tehran, Iran, {T.Mohammadi,Nabgheri}@sru.ac.ir 3 School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran, [email protected] Abstract. SKINNY is a family of lightweight tweakable block ciphers designed to have the smallest hardware footprint. In this paper, we present zero-correlation linear approximations and the related-tweakey impossible differential characteristics for different versions of SKINNY .We utilize Mixed Integer Linear Programming (MILP) to search all zero-correlation linear distinguishers for all variants of SKINNY, where the longest distinguisher found reaches 10 rounds. Using a 9-round characteristic, we present 14 and 18-round zero correlation attacks on SKINNY-64-64 and SKINNY- 64-128, respectively. Also, for SKINNY-n-n and SKINNY-n-2n, we construct 13 and 15-round related-tweakey impossible differential characteristics, respectively. Utilizing these characteristics, we propose 23-round related-tweakey impossible differential cryptanalysis by applying the key recovery attack for SKINNY-n-2n and 19-round attack for SKINNY-n-n. To the best of our knowledge, the presented zero-correlation characteristics in this paper are the first attempt to investigate the security of SKINNY against this attack and the results on the related-tweakey impossible differential attack are the best reported ones. Keywords: SKINNY · Zero-correlation linear cryptanalysis · Related-tweakey impos- sible differential cryptanalysis · MILP 1 Introduction Because of the growing use of small computing devices such as RFID tags, the new challenge in the past few years has been the application of conventional cryptographic standards to small devices.
    [Show full text]
  • New Observations on Impossible Differential Cryptanalysis Of
    New Observations on Impossible Differential Cryptanalysis of Reduced-Round Camellia⋆ Ya Liu1, Leibo Li2,3⋆⋆, Dawu Gu1, Xiaoyun Wang2,3,4, Zhiqiang Liu1, Jiazhe Chen2,3, Wei Li5,6 1 Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China {liuya0611,dwgu,ilu zq}@sjtu.edu.cn 2 Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan 250100, China 3 School of Mathematics, Shandong University, Jinan 250100, China {lileibo, jiazhechen}@mail.sdu.edu.cn 4 Institute for Advanced Study, Tsinghua University, Beijing 100084, China [email protected] 5 School of Computer Science and Technology, Donghua University, Shanghai 201620, China 6 Shanghai Key Laboratory of Integrate Administration Technologies for Information Security, Shanghai 200240, China [email protected] Abstract. Camellia is one of the widely used block ciphers, which has been selected as an in- ternational standard by ISO/IEC. In this paper, by studying the properties of the key-dependent transformations F L/F L−1, we improve the previous results on impossible differential cryptanalysis of reduced-round Camellia and gain some new observations. First, we introduce some new 7-round impossible differentials of Camellia for weak keys. These weak keys that work for the impossible differential take 3/4 of the whole key space, therefore, we further get rid of the weak-key assump- tion and leverage the attacks on reduced-round Camellia to all keys by utilizing a method that is called the multiplied method. Second, we build a set of differentials which contains at least one 8-round impossible differential of Camellia with two F L/F L−1 layers.
    [Show full text]