DOCSLIB.ORG

Improved Davies-Murphy's Attack on DES Revisited

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Improved Davies-Murphy's Attack on DES Revisited Improved Davies-Murphy’s Attack on DES Revisited Yi Lu1⋆ and Yvo Desmedt2⋆⋆ 1 National Engineering Research Center of Fundamental Software, Institute of Software, Chinese Academy of Sciences, Beijing, China 2 The University of Texas at Dallas, USA & University College London, UK Abstract. DES is a famous 64-bit block cipher with balanced Feistel structure. It consists of 16 rounds. The key has 56 bits and the round key has 48 bits. Two major cryptanalysis techniques (namely, linear crypt- analysis and differential cryptanalysis) were notably developed and suc- cessfully applied to the full 16-round DES in the early 1990’s. Davies- Murphy’s attack can be seen as a special linear attack, which was devel- oped before invention of linear cryptanalysis. It was improved by Biham and Biryukov and most recently by Jacques and Muller. In this paper, we revisit the recent improved Davies-Murphy’s attack by Jacques and Muller from an algorithmic point of view. Based on Matsui’s algorithm 2, we give an improved attack algorithm. Our improved attack algorithm works in time (241) with memory (233). In contrast, Jacques-Muller’s attack takes time (243) and memory (235). It seems that our results of the time and memory complexities are optimal, due to the use of Walsh transform. Meanwhile, we generalize and further improve the results of the improved Matsui’s algorithm 2 for the case that the subkeys are XORed into the round function. Keywords: DES, block cipher, Davies-Murphy’s attack, linear crypt- analysis, Matsui’s algorithm 2, Walsh transform 1 Introduction DES is one of the most famous block ciphers [13]. It has been studied for 30 years and is still undergoing the progress of advanced cryptanaly- sis research today. Of the two major cryptanalysis techniques are linear cryptanalysis and differential cryptanalysis. They both proved to be suc- cessful to the full 16-round DES ([2,12]). Besides, another new cryptanal- ysis technique (i.e. algebraic attacks) has emerged since the last decade, which works on 6 rounds of DES [5]. ⋆ Supported by the National Science and Technology Major Project under Grant No. 2012ZX01039-004, and the National Natural Science Foundation of China under Grant No. 61170072. Part of this work done while funded by British Telecommuni- cations under Grant No. ML858284/CT506918. ⋆⋆ Part of this work was done while funded by EPSRC EP/C538285/1 and by BT, as BT Chair of Information Security. Davies-Murphy’s attack [6] can be seen as a special linear attack, which was developed in the 1980’s before invention of linear cryptanalysis (cf. [4]). It was improved by Biham and Biryukov [1] and most recently by Jacques and Muller [9]. For review on Davies-Murphy’s attacks we refer to [9], and we refer to [4] for strengthening DES against Davies-Murphy’s attacks. In this paper, we revisit the improved Davies-Murphy’s attack [9] from an algorithmic point of view. Based on Matsui’s algorithm 2 [3, 7], we give an improved attack algorithm. In summary, our improved attack algorithm works in time (241) with memory (233). In contrast, the attack [9] takes time (243) and memory (235). Due to the use of Walsh transform3, it seems that our results of the time and memory complexities are optimal. Meanwhile, our results generalize and improve the results of the improved Matsui’s algorithm 2 in [3,7] for the case that the subkeys are XORed into the round function. 2 Related Works In Fig. 1, we let 32-bit L0,R0 be the left and right half of the plaintext. Let L16,R16 be the left and right half of the ciphertext. Similarly, Li,Ri denote the left and right half of DES output at Round i. As convention, the initial and final permutation of DES is ignored. The 48-bit subkey used for Round i is denoted by Ki (omitted in Fig. 1). Due to lack of space, we omit the detailed description on DES (cf. [13]). Let α = 0xa100c21 in hexadecimal representation 4. Let the 32-bit Ai be the output of DES round function f at Round i. Define the bias (also called imbalance [8]) of a binary random variable X by | Pr(X = 0)− Pr(X = 1)|. Recall due to Davies and Murphy [6], the bit α·A1 ⊕β ·K1 = −3.4 5 α · (L0 ⊕ L1) ⊕ β · K1 has bias 2 , with the subkey’s mask β = 0xf0. As DES consists of 16 rounds, this one-round characteristics is iterated 8 times in the original Davies-Murphy’s attack [6]. That makes a total bias 2−3.4×8 = 2−27.2 by Piling-up Lemma [12]. Later, Biham and Biryukov [1] proposed to use the technique of partial decryption to work with 15-round DES instead. Thus, the one-round characteristics is iterated 7 times. It makes an enlarged total bias of 2−3.4×7 = 2−23.8. Recently, with the trick 3 Note that Walsh transform and Fourier transform have been useful tools to aid linear cryptanalysis, e.g., [10, 11]. 4 Throughout the paper, we always let bit 0 be the least significant bit. 5 The subkey’s mask β corresponds to the highest 2 bits of the subkey’s 6-bit input to S-box S8 and the lowest 2 bits of the subkey’s 6-bit input to S-box S7. 2 of chosen-plaintext strategy, Jacques and Muller [9] showed that partial decryption actually allows to work with further reduced 13-round DES. It thus makes the increased bias of 2−3.4×6 = 2−20.4. L0 R0 A1 f A2 f f f . f f f A16 f L16 R16 Fig. 1. The untwisted view of DES 3 Our Improved Algorithm for Jacques-Muller’s Core Attack As α·Ai equals the XOR of the four output bits of S-box S7 and the output bit 0,2,3 of S-box S8, let the Boolean function g(ℓ16 ⊕k16) compute the bit α · A16. Here, the 12-bit ℓ16,k16 denote inputs to S-box S7,S8 at Round 16. And ℓ16 is obtained by bit expansion from 10 bits of L16. 3 On the other hand, we let the 24-bit r0,k1 denote inputs to S-boxes S5 − S8 at Round 1. And r0 is obtained by bit expansion from 18 bits of R0. Let the 12-bit ℓ0,k2 denote inputs to both S-boxes S7,S8 at Round 2. And ℓ0 is obtained by bit expansion from 10 bits of L0. We let the Boolean function ′ hk1,k2 (ℓ0,r0)= h(ℓ0 ⊕ k2 ⊕ h (r0 ⊕ k1)) (1) ′ compute the bit α · A2. Here, h (r0 ⊕ k1) maps 12 bits to 12 bits, 5 bits 6 of which can be determined from k1,r0 and we define this function by ′′ h (r0 ⊕ k1). Further, the trick of chosen-plaintext strategy [9] allows to ′ have that the remaining 7 bits of the 12-bit output of h (r0⊕k1) are always fixed, which was considered an intermediate variable of 7 bits (denoted by x herein7) in [9]. For our convenience, we let ′ ′′ h (r0 ⊕ k1)= P (h (r0 ⊕ k1)kx), (2) where k denotes string concatenation and P is the bit permutation func- tion. Given the plaintext and ciphertext pair (L0,R0,L16,R16) (and we use the superscript i to denote each sample), define8 the binary function x α·(R0⊕R16)⊕g(ℓ16⊕k16)⊕hk1,k2 (ℓ0,r0) Fk1,k2,k16 (L0,L16,R0,R16)=(−1) . (3) Clearly, with the correct x,k1,k2,k16, the right-hand side of (3) is equal to (−1)α·(A4⊕A6⊕A8⊕A10⊕A12⊕A14). Jacques-Muller’s core attack idea [9] is shown in Algorithm 1, which aims at partial key-recovery of x,k1,k2,k16. As direct computation of Algorithm 1 is impractical, [9] proposed tech- niques to decompose into several steps: at each step, by guessing a few key bits, some intermediate information can be derived which allows to get rid of the old precomputation table. The optimization techniques [9, Sect. 3.4] solves Algorithm 1 with total time O(243) and the table size 35 O(2 ). It is worth noting that if x,k1,k2,k16 (of 7+24+12+12 = 55 bits in total) were linearly independent, we can apply the improved Matsui’s algorithm 2 in [7, Sect. 4] to solve Algorithm 1 with time O(3 × 55 × 255) and memory O(255). Nonetheless, from the description of DES [13], x,k1,k2,k16 are not linearly independent and [7] is not applicable. Inspired by the improved 6 Because they are bit expansion from 4 bits of S5 − S8 outputs (i.e., output bit 1 of S5, output bit 2 of S6, output bit 3 of S7, output bit 2 of S8) at Round 1. 7 Note that the 7-bit x actually is bit expansion from 6 unknown bits. 8 Note that k1, k2, k16,ℓ0,r0,ℓ16 simply is the bit selection function of K1,K2,K16,L0,R0,L16 with reduced bit length respectively. 4 Algorithm 1 The core partial key-recovery idea of Jacques-Muller’s at- tack [9] for all x, k1, k2, k16 do x uk1,k2,k16 ← 0 x x i i i i compute uk1,k2,k16 = Pi Fk1,k2,k16 (L0,L16,R0,R16), with F defined in (3) end for x output the largest uk1,k2,k16 with x, k1, k2, k16 Matsui’s algorithm 2 [3,7], based on the use of Walsh transform, we now give another algorithm for Jacques-Muller’s core attack [9] in order to compute Algorithm 1 with reduced time and memory.
Load more

Recommended publications
  • Serpent: a Proposal for the Advanced Encryption Standard
    Serpent: A Proposal for the Advanced Encryption Standard Ross Anderson1 Eli Biham2 Lars Knudsen3 1 Cambridge University, England; email [email protected] 2 Technion, Haifa, Israel; email [email protected] 3 University of Bergen, Norway; email [email protected] Abstract. We propose a new block cipher as a candidate for the Ad- vanced Encryption Standard. Its design is highly conservative, yet still allows a very efficient implementation. It uses S-boxes similar to those of DES in a new structure that simultaneously allows a more rapid avalanche, a more efficient bitslice implementation, and an easy anal- ysis that enables us to demonstrate its security against all known types of attack. With a 128-bit block size and a 256-bit key, it is as fast as DES on the market leading Intel Pentium/MMX platforms (and at least as fast on many others); yet we believe it to be more secure than three-key triple-DES. 1 Introduction For many applications, the Data Encryption Standard algorithm is nearing the end of its useful life. Its 56-bit key is too small, as shown by a recent distributed key search exercise [28]. Although triple-DES can solve the key length problem, the DES algorithm was also designed primarily for hardware encryption, yet the great majority of applications that use it today implement it in software, where it is relatively inefficient. For these reasons, the US National Institute of Standards and Technology has issued a call for a successor algorithm, to be called the Advanced Encryption Standard or AES.
    [Show full text]
  • 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.
    [Show full text]
  • Identifying Open Research Problems in Cryptography by Surveying Cryptographic Functions and Operations 1
    International Journal of Grid and Distributed Computing Vol. 10, No. 11 (2017), pp.79-98 http://dx.doi.org/10.14257/ijgdc.2017.10.11.08 Identifying Open Research Problems in Cryptography by Surveying Cryptographic Functions and Operations 1 Rahul Saha1, G. Geetha2, Gulshan Kumar3 and Hye-Jim Kim4 1,3School of Computer Science and Engineering, Lovely Professional University, Punjab, India 2Division of Research and Development, Lovely Professional University, Punjab, India 4Business Administration Research Institute, Sungshin W. University, 2 Bomun-ro 34da gil, Seongbuk-gu, Seoul, Republic of Korea Abstract Cryptography has always been a core component of security domain. Different security services such as confidentiality, integrity, availability, authentication, non-repudiation and access control, are provided by a number of cryptographic algorithms including block ciphers, stream ciphers and hash functions. Though the algorithms are public and cryptographic strength depends on the usage of the keys, the ciphertext analysis using different functions and operations used in the algorithms can lead to the path of revealing a key completely or partially. It is hard to find any survey till date which identifies different operations and functions used in cryptography. In this paper, we have categorized our survey of cryptographic functions and operations in the algorithms in three categories: block ciphers, stream ciphers and cryptanalysis attacks which are executable in different parts of the algorithms. This survey will help the budding researchers in the society of crypto for identifying different operations and functions in cryptographic algorithms. Keywords: cryptography; block; stream; cipher; plaintext; ciphertext; functions; research problems 1. Introduction Cryptography [1] in the previous time was analogous to encryption where the main task was to convert the readable message to an unreadable format.
    [Show full text]
  • Eindhoven University of Technology MASTER Renewal Periods For
    Eindhoven University of Technology MASTER Renewal periods for cryptographic keys Posea, S. Award date: 2012 Link to publication Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain Renewal Periods for Cryptographic Keys Simona Posea August 2012 Eindhoven University of Technology Department of Mathematics and Computer Science Master's Thesis Renewal Periods for Cryptographic Keys Simona Posea Supervisors: dr. ir. L.A.M. (Berry) Schoenmakers (TU/e - W&I) drs. D.M. Wieringa RE CISSP (Deloitte - S&P) H. Hambartsumyan MSc. CISA (Deloitte - S&P) Eindhoven, August 2012 Abstract Periodically changing cryptographic keys is a common practice. Standards and publications recommending how long a key may be used before it should be renewed are available for guidance.
    [Show full text]
  • On Matsui's Linear Cryptanalysis Eli Biham Computer Science Department Technion - Israel Institute of Technology Haifa 32000, Israel
    On Matsui's Linear Cryptanalysis Eli Biham Computer Science Department Technion - Israel Institute of Technology Haifa 32000, Israel Abstract In [9] Matsui introduced a new method of cryptanalysis, called Linear Crypt- analysis. This method was used to attack DES using 24z known plaintexts. In this paper we formalize this method and show that although in the details level this method is quite different from differential crypta~alysis, in the structural level they are very similar. For example, characteristics can be defined in lin- ear cryptanalysis, but the concatenation rule has several important differences from the concatenation rule of differential cryptanalysis. We show that the attack of Davies on DES is closely related to linear cryptanalysis. We describe constraints on the size of S boxes caused by linear cryptanalysis. New results to Feal are also described. 1 Introduction In EUR.OCRYPT'93 Matsui introduced a new method of cryptanalysis, called Linear Cryptanalysis [9]. This method was used to attack DES using 24r known plaintexts. In this paper we formalize this method and show that although in the details level this method is quite different from differential cryptanalysis[2,1], in the structural level they are very similar. For example, characteristics can be defined in linear cryptanalysis, but the concatenation rule has several important differences from the concatenation rule of differential cryptanalysis. We show that the attack of Davies[5] on DES is closely related to linear cryptanalysis. We describe constraints on the size of S boxes caused by linear cryptanalysis. New results to Feal[15,11] are also described. 2 Overview of Linear Cryptanalysis Linear cryptanalysis studies statistical linear relations between bits of the plaintexts, the ciphertexts and the keys they are encrypted under.
    [Show full text]
  • AES3 Presentation
    Cryptanalytic Progress: Lessons for AES John Kelsey1, Niels Ferguson1, Bruce Schneier1, and Mike Stay2 1 Counterpane Internet Security, Inc., 3031 Tisch Way, 100 Plaza East, San Jose, CA 95128, USA 2 AccessData Corp., 2500 N University Ave. Ste. 200, Provo, UT 84606, USA 1 Introduction The cryptanalytic community is currently evaluating five finalist algorithms for the AES. Within the next year, one or more ciphers will be chosen. In this note, we argue caution in selecting a finalist with a small security margin. Known attacks continuously improve over time, and it is impossible to predict future cryptanalytic advances. If an AES algorithm chosen today is to be encrypting data twenty years from now (that may need to stay secure for another twenty years after that), it needs to be a very conservative algorithm. In this paper, we review cryptanalytic progress against three well-regarded block ciphers and discuss the development of new cryptanalytic tools against these ciphers over time. This review illustrates how cryptanalytic progress erodes a cipher’s security margin. While predicting such progress in the future is clearly not possible, we claim that assuming that no such progress can or will occur is dangerous. Our three examples are DES, IDEA, and RC5. These three ciphers have fundamentally different structures and were designed by entirely different groups. They have been analyzed by many researchers using many different techniques. More to the point, each cipher has led to the development of new cryptanalytic techniques that not only have been applied to that cipher, but also to others. 2 DES DES was developed by IBM in the early 1970s, and standardized made into a standard by NBS (the predecessor of NIST) [NBS77].
    [Show full text]
  • Zgureanu Aureliu CRIPTAREA ŞI SECURITATEA INFORMAŢIEI Note
    ACADEMIA DE TRANSPORTURI, INFORMATICĂ ŞI COMUNICAŢII Zgureanu Aureliu CRIPTAREA ŞI SECURITATEA INFORMAŢIEI Note de curs CHIŞINĂU 2013 Notele de Curs la disciplina „Criptarea şi securitatea informaţiei” a fost examinat şi aprobat la şedinţa catedrei „Matematică şi Informatică”, proces verbal nr. 3 din 11.11.2013, şi la şedinţa Comisiei metodice şi de calitate a FEI, proces verbal nr. 1 din 02.12.2013. © Zgureanu Aureliu, 2013 2 Cuprins Introducere ............................................................................................................4 Tema 1. Noţiuni de bază ale Criptografiei. .........................................................6 Tema 2. Cifruri clasice. Cifruri de substituţie ..................................................12 Tema 3. Cifruri clasice. Cifrul de transpoziţii ..................................................25 Tema 4. Maşini rotor...........................................................................................30 Tema 5. Algoritmi simetrici de criptare. Cifruri bloc. Reţeaua Feistel ..........40 Tema 6. Algoritmul de cifrare Lucifer ..............................................................46 Tema 7. Algoritmul DES.....................................................................................59 Tema 8. Cifrul AES .............................................................................................69 Tema 9. Algoritmi simetrici de tip şir (stream cypher)...................................80 Tema 10. Criptarea cu cheie publică .................................................................91
    [Show full text]
  • ASBE Defeats Statistical Analysis and Other Cryptanalysis
    Introduction | Statistical Analysis ASBE Defeats Statistical Analysis and Other Cryptanalysis By: Prem Sobel, CTO, MerlinCryption LLC Introduction Anti-Statistical Block Encryption, abbreviated ASBE, uses blocks [Ref 33, p.43-82] as part of the algorithm. These blocks are manipulated in ways different from all currently known and published existing encryption algorithms in variable ways which depend on the key. The ASBE algorithm is designed to be exponentially stronger than existing encryption algorithms and to defeat known Statistical Analysis, Cryptanalysis and Attacks. The purpose of this white paper is to describe how ASBE succeeds in these goals. Statistical Analysis Early encryption techniques are typically variations of substitution ciphers. Statistical analysis attempts to defeat such substitution ciphers, based on statistical knowledge of the language (for example, English) [Ref-1] [Ref-2] [Ref-3] [Ref-32, p.10-13]. These techniques include substitution ciphers such as: . Letter frequency, . Letter frequency of first letter of a word, . Most likely duplicate letter pairs (such as LL EE SS OO TT FF RR NN PP CC in English), . Most likely different letter pairs (in English: TH HE AN RE ER IN ON AT ND ST ES EN OF TE ED OR TI HI AS TO) and non-occurring letter pairs (for example, XJ QG HZ in English), . Most likely letter triples and non-occurring letter triples, . Most likely letter quadruples and non-occurring letter quadruples, and . Most frequent words. These statistics and patterns of multi-letter sequences are language-dependent and are also subject dependent. In the early days of cryptography, there were several limitations and/or assumptions made that are no longer valid today.
    [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]
  • A Pattern Recognition Approach to Block Cipher
    A PATTERN RECOGNITION APPROACH TO BLOCK CIPHER IDENTIFICATION A THESIS submitted by SREENIVASULU NAGIREDDY for the award of the degree of MASTER OF SCIENCE (by Research) DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY MADRAS. October 2008 Dedicated to my parents i THESIS CERTIFICATE This is to certify that the thesis entitled A Pattern Recognition Approach to Block Cipher Identification submitted by Sreenivasulu Nagireddy to the Indian Institute of Technology Madras, for the award of the degree of Master of Science (By Research) is a bonafide record of research work carried out by him under our supervision and guidance. The contents of this thesis, in full or in parts, have not been submitted to any other Institute or University for the award of any degree or diploma. Dr. C. Chandra Sekhar Dr. Hema A. Murthy Chennai-600036 Date: ACKNOWLEDGEMENTS I wish to express my gratitude to everyone who contributed in making this work a reality. There are persons not mentioned here but, deserve my token of appreciation, first of all, I thank them all. Let me also thank the Indian Institute of Technology Madras for giving me an opportunity to pursue my post graduation. I am grateful to Computer science department for providing the facilities for the same. This institute has given me great exposure. There has been a drastic change in my vision of life. I enjoyed every moment of my IIT life. I would like to thank my guides, Prof. Hema A. Murthy and Dr. C Chandra Sekhar whose expertise, understanding, and patience, helped me through the course.
    [Show full text]
  • LNCS 1514, Pp
    Optimal Resistance Against the Davies and Murphy Attack Thomas Pornin Ecole´ Normale Sup´erieure, 45 rue d’Ulm, 75005 Paris, France, [email protected] Abstract. In recent years, three main types of attacks have been de- veloped against Feistel-based ciphers, such as DES[1]; these attacks are linear cryptanalysis[2], differential cryptanalysis[3], and the Davies and Murphy attack[4]. Using the discrete Fourier transform, we present here a quantitative criterion of security against the Davies and Murphy attack. Similar work has been done on linear and differential cryptanalysis[5,11]. 1 Introduction The Feistel scheme is a simple design which allows, when suitably iterated, the construction of efficient block cipher, whose deciphering algorithm is implemen- ted in a similar way. The most famous block cipher using a Feistel scheme is DES, where the scheme is iterated 16 times, with 16 subkeys extracted from a unique masterkey. The deciphering algorithm is just the same; the only difference is that the subkeys are taken in reverse order. The masterkey of DES is only 56 bits long; this is vulnerable to exhaustive search. Indeed, specialized DES chips, able to calculate half a million DES ciphers per second, have been considered since 1987[6] and their cost evaluated; it is estimated that a five millions dollars machine using a few thousands of such chips could break a DES with a single plaintext/ciphertext pair in two or three hours[7]; other more recent estimates give lower prices, thanks to continuous technological progress. More recently, following a challenge proposed by RSA Inc., a 56 bits DES key was retrieved from a plaintext/ciphertext pair using only the idle time of a few thousands generic purpose workstations around the world[8].
    [Show full text]
  • An Introduction to Applied Cryptography
    SI4 { R´eseauxAvanc´es Introduction `ala s´ecurit´edes r´eseauxinformatiques An Introduction to Applied Cryptography Dr. Quentin Jacquemart [email protected] http://www.qj.be/teaching/ 1 / 129 Outline ) Introduction • Classic Cryptography and Cryptanalysis • Principles of Cryptography • Symmetric Cryptography (aka. Secret-Key Cryptography) • Asymmetric Cryptography (aka. Public-Key Cryptography) • Hashes and Message Digests • Conclusion 1 / 129 2 / 129 Introduction I • Cryptography is at the crossroads of mathematics, electronics, and computer science • The use of cryptography to provide confidentiality is self-evident • But cryptography is a cornerstone of network security • Cryptology is a (mathematical) discipline that includes | cryptography: studies how to exchange confidential messages over an unsecured/untrusted channel | cryptanalysis: studies how to extract meaning out of a confidential message, i.e. how to breach cryptography 2 / 129 3 / 129 Introduction II • Plaintext: the message to be exchanged between Alice and Bob (P) • Ciphering: a cryptographic function that encodes the plaintext into ciphertext (encrypt: E(·)) • Ciphertext: result of applying the cipher function to the plain text (unreadable) (C) • Deciphering: a cryptographic function that decodes the ciphertext into plaintext (decrypt: D(·)) • Key: a secret parameter given to the cryptographic functions (K ) 3 / 129 4 / 129 Introduction III Trudy Alice Bob plaintext ciphertext plaintext P E(P) P E(P) = D(E(P)) Encryption Decryption Algorithm Algorithm E(·) D(·)
    [Show full text]