CAST-256 Algorithm Specification
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Vector Boolean Functions: Applications in Symmetric Cryptography
Vector Boolean Functions: Applications in Symmetric Cryptography José Antonio Álvarez Cubero Departamento de Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones Universidad Politécnica de Madrid This dissertation is submitted for the degree of Doctor Ingeniero de Telecomunicación Escuela Técnica Superior de Ingenieros de Telecomunicación November 2015 I would like to thank my wife, Isabel, for her love, kindness and support she has shown during the past years it has taken me to finalize this thesis. Furthermore I would also liketo thank my parents for their endless love and support. Last but not least, I would like to thank my loved ones such as my daughter and sisters who have supported me throughout entire process, both by keeping me harmonious and helping me putting pieces together. I will be grateful forever for your love. Declaration The following papers have been published or accepted for publication, and contain material based on the content of this thesis. 1. [7] Álvarez-Cubero, J. A. and Zufiria, P. J. (expected 2016). Algorithm xxx: VBF: A library of C++ classes for vector Boolean functions in cryptography. ACM Transactions on Mathematical Software. (In Press: http://toms.acm.org/Upcoming.html) 2. [6] Álvarez-Cubero, J. A. and Zufiria, P. J. (2012). Cryptographic Criteria on Vector Boolean Functions, chapter 3, pages 51–70. Cryptography and Security in Computing, Jaydip Sen (Ed.), http://www.intechopen.com/books/cryptography-and-security-in-computing/ cryptographic-criteria-on-vector-boolean-functions. (Published) 3. [5] Álvarez-Cubero, J. A. and Zufiria, P. J. (2010). A C++ class for analysing vector Boolean functions from a cryptographic perspective. -
Quasi-Orthogonal Sequences for Code-Division Multiple-Access Systems Kyeongcheol Yang, Member, IEEE, Young-Ky Kim, and P
982 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 46, NO. 3, MAY 2000 Quasi-Orthogonal Sequences for Code-Division Multiple-Access Systems Kyeongcheol Yang, Member, IEEE, Young-Ky Kim, and P. Vijay Kumar, Member, IEEE Abstract—In this paper, the notion of quasi-orthogonal se- correlation between two binary sequences and of quence (QOS) as a means of increasing the number of channels the same length is given by in synchronous code-division multiple-access (CDMA) systems that employ Walsh sequences for spreading information signals and separating channels is introduced. It is shown that a QOS sequence may be regarded as a class of bent (almost bent) functions possessing, in addition, a certain window property. Such sequences while increasing system capacity, minimize interference where is computed modulo for all . It is easily to the existing set of Walsh sequences. The window property gives shown that where denotes the the system the ability to handle variable data rates. A general procedure of constructing QOS's from well-known families of Hamming distance of two vectors and . Two sequences are binary sequences with good correlation, including the Kasami and said to be orthogonal if their correlation is zero. Gold sequence families, as well as from the binary Kerdock code Let be a family of binary is provided. Examples of QOS's are presented for small lengths. sequences of period . The family is said to be orthogonal if Some examples of quaternary QOS's drawn from Family are any two sequences are mutually orthogonal, that is, also included. for any and . For example, the Walsh sequence family of Index Terms—Bent functions, code-division multiple-access sys- length is orthogonal. -
A Construction of Bent Functions with Optimal Algebraic Degree and Large Symmetric Group
Advances in Mathematics of Communications doi:10.3934/amc.2020003 Volume 14, No. 1, 2020, 23{33 A CONSTRUCTION OF BENT FUNCTIONS WITH OPTIMAL ALGEBRAIC DEGREE AND LARGE SYMMETRIC GROUP Wenying Zhang and Zhaohui Xing School of Information Science and Engineering, Shandong Normal University Jinan 250014, China Keqin Feng Department of Mathematical Sciences, Tsinghua University Beijing, 100084 China State Key Lab. of Cryptology, P.O.Box 5159 Beijing 100878 China (Communicated by Sihem Mesnager) Abstract. As maximal, nonlinear Boolean functions, bent functions have many theoretical and practical applications in combinatorics, coding theory, and cryptography. In this paper, we present a construction of bent function m fa;S with n = 2m variables for any nonzero vector a 2 F2 and subset S m of F2 satisfying a + S = S. We give a simple expression of the dual bent function of fa;S and prove that fa;S has optimal algebraic degree m if and only if jSj ≡ 2(mod4). This construction provides a series of bent functions with optimal algebraic degree and large symmetric group if a and S are chosen properly. We also give some examples of those bent functions fa;S and their dual bent functions. 1. Introduction Bent functions were introduced by Rothaus [17] in 1976 and studied by Dillon [7] in 1974 with their equivalent combinatorial objects: Hadamard difference sets in elementary 2-groups. Bent functions are equidistant from all the affine func- tions, so it is equally hard to approximate with any affine function. Given such good properties, bent functions are the ideal choice for secure cryptographic func- tions. -
Hardness Evaluation of Solving MQ Problems
MQ Challenge: Hardness Evaluation of Solving MQ Problems Takanori Yasuda (ISIT), Xavier Dahan (ISIT), Yun-Ju Huang (Kyushu Univ.), Tsuyoshi Takagi (Kyushu Univ.), Kouichi Sakurai (Kyushu Univ., ISIT) This work was supported by “Strategic Information and Communications R&D Promotion Programme (SCOPE), no. 0159-0091”, Ministry of Internal Affairs and Communications, Japan. The first author is supported by Grant-in-Aid for Young Scientists (B), Grant number 24740078. Fukuoka MQ challenge MQ challenge started on April 1st. https://www.mqchallenge.org/ ETSI Quantum Safe Workshop 2015/4/3 2 Why we need MQ challenge? • Several public key cryptosystems held contests which solve the associated basic mathematical problems. o RSA challenge(RSA Laboratories), ECC challenge(Certicom), Lattice challenge(TU Darmstadt) • Lattice challenge (http://www.latticechallenge.org/) o Target: Short vector problem o 2008 – now continued • Multivariate public-key cryptsystem (MPKC) also need to evaluate the current state-of-the-art in practical MQ problem solvers. We planed to hold MQ challenge. ETSI Quantum Safe Workshop 2015/4/3 3 Multivariate Public Key Cryptosystem (MPKC) • Advantage o Candidate for post-quantum cryptography o Used for both encryption and signature schemes • Encryption: Simple Matrix scheme (ABC scheme), ZHFE scheme • Signature: UOV, Rainbow o Efficient encryption and decryption and signature generation and verification. • Problems o Exact estimate of security of MPKC schemes o Huge length of secret and public keys in comparison with RSA o New application and function ETSI Quantum Safe Workshop 2015/4/3 4 MQ problem MPKC are public key cryptosystems whose security depends on the difficulty in solving a system of multivariate quadratic polynomials with coefficients in a finite field . -
Side Channel Analysis Attacks on Stream Ciphers
Side Channel Analysis Attacks on Stream Ciphers Daehyun Strobel 23.03.2009 Masterarbeit Ruhr-Universität Bochum Lehrstuhl Embedded Security Prof. Dr.-Ing. Christof Paar Betreuer: Dipl.-Ing. Markus Kasper Erklärung Ich versichere, dass ich die Arbeit ohne fremde Hilfe und ohne Benutzung anderer als der angegebenen Quellen angefertigt habe und dass die Arbeit in gleicher oder ähnlicher Form noch keiner anderen Prüfungsbehörde vorgelegen hat und von dieser als Teil einer Prüfungsleistung angenommen wurde. Alle Ausführungen, die wörtlich oder sinngemäß übernommen wurden, sind als solche gekennzeichnet. Bochum, 23.März 2009 Daehyun Strobel ii Abstract In this thesis, we present results from practical differential power analysis attacks on the stream ciphers Grain and Trivium. While most published works on practical side channel analysis describe attacks on block ciphers, this work is among the first ones giving report on practical results of power analysis attacks on stream ciphers. Power analyses of stream ciphers require different methods than the ones used in todays most popular attacks. While for the majority of block ciphers it is sufficient to attack the first or last round only, to analyze a stream cipher typically the information leakages of many rounds have to be considered. Furthermore the analysis of hardware implementations of stream ciphers based on feedback shift registers inevitably leads to methods combining algebraic attacks with methods from the field of side channel analysis. Instead of a direct recovery of key bits, only terms composed of several key bits and bits from the initialization vector can be recovered. An attacker first has to identify a sufficient set of accessible terms to finally solve for the key bits. -
Petawatt and Exawatt Class Lasers Worldwide
Petawatt and exawatt class lasers worldwide Colin Danson, Constantin Haefner, Jake Bromage, Thomas Butcher, Jean-Christophe Chanteloup, Enam Chowdhury, Almantas Galvanauskas, Leonida Gizzi, Joachim Hein, David Hillier, et al. To cite this version: Colin Danson, Constantin Haefner, Jake Bromage, Thomas Butcher, Jean-Christophe Chanteloup, et al.. Petawatt and exawatt class lasers worldwide. High Power Laser Science and Engineering, Cambridge University Press, 2019, 7, 10.1017/hpl.2019.36. hal-03037682 HAL Id: hal-03037682 https://hal.archives-ouvertes.fr/hal-03037682 Submitted on 3 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. High Power Laser Science and Engineering, (2019), Vol. 7, e54, 54 pages. © The Author(s) 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. doi:10.1017/hpl.2019.36 Petawatt and exawatt class lasers worldwide Colin N. Danson1;2;3, Constantin Haefner4;5;6, Jake Bromage7, Thomas Butcher8, Jean-Christophe F. Chanteloup9, Enam A. Chowdhury10, Almantas Galvanauskas11, Leonida A. -
Hardware Implementation of Four Byte Per Clock RC4 Algorithm Rourab Paul, Amlan Chakrabarti, Senior Member, IEEE, and Ranjan Ghosh
JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 1 Hardware Implementation of four byte per clock RC4 algorithm Rourab Paul, Amlan Chakrabarti, Senior Member, IEEE, and Ranjan Ghosh, Abstract—In the field of cryptography till date the 2-byte in 1-clock is the best known RC4 hardware design [1], while 1-byte in 1-clock [2], and the 1-byte in 3 clocks [3][4] are the best known implementation. The design algorithm in[2] considers two consecutive bytes together and processes them in 2 clocks. The design [1] is a pipelining architecture of [2]. The design of 1-byte in 3-clocks is too much modular and clock hungry. In this paper considering the RC4 algorithm, as it is, a simpler RC4 hardware design providing higher throughput is proposed in which 6 different architecture has been proposed. In design 1, 1-byte is processed in 1-clock, design 2 is a dynamic KSA-PRGA architecture of Design 1. Design 3 can process 2 byte in a single clock, where as Design 4 is Dynamic KSA-PRGA architecture of Design 3. Design 5 and Design 6 are parallelization architecture design 2 and design 4 which can compute 4 byte in a single clock. The maturity in terms of throughput, power consumption and resource usage, has been achieved from design 1 to design 6. The RC4 encryption and decryption designs are respectively embedded on two FPGA boards as co-processor hardware, the communication between the two boards performed using Ethernet. Keywords—Computer Society, IEEEtran, journal, LATEX, paper, template. -
*UPDATED Canadian Values 07-04 201 7/26/2016 4:42:21 PM *UPDATED Canadian Values 07-04 202 COIN VALUES: CANADA 02 .0 .0 12
CANADIAN VALUES By Michael Findlay Large Cents VG-8 F-12 VF-20 EF-40 MS-60 MS-63R 1917 1.00 1.25 1.50 2.50 13. 45. CANADA COIN VALUES: 1918 1.00 1.25 1.50 2.50 13. 45. 1919 1.00 1.25 1.50 2.50 13. 45. 1920 1.00 1.25 1.50 3.00 18. 70. CANADIAN COIN VALUES Small Cents PRICE GUIDE VG-8 F-12 VF-20 EF-40 MS-60 MS-63R GEORGE V All prices are in U.S. dollars LargeL Cents C t 1920 0.20 0.35 0.75 1.50 12. 45. Canadian Coin Values is a comprehensive retail value VG-8 F-12 VF-20 EF-40 MS-60 MS-63R 1921 0.50 0.75 1.50 4.00 30. 250. guide of Canadian coins published online regularly at Coin VICTORIA 1922 20. 23. 28. 40. 200. 1200. World’s website. Canadian Coin Values is provided as a 1858 70. 90. 120. 200. 475. 1800. 1923 30. 33. 42. 55. 250. 2000. reader service to collectors desiring independent informa- 1858 Coin Turn NI NI 2500. 5000. BNE BNE 1924 6.00 8.00 11. 16. 120. 800. tion about a coin’s potential retail value. 1859 4.00 5.00 6.00 10. 50. 200. 1925 25. 28. 35. 45. 200. 900. Sources for pricing include actual transactions, public auc- 1859 Brass 16000. 22000. 30000. BNE BNE BNE 1926 3.50 4.50 7.00 12. 90. 650. tions, fi xed-price lists and any additional information acquired 1859 Dbl P 9 #1 225. -
9/11 Report”), July 2, 2004, Pp
Final FM.1pp 7/17/04 5:25 PM Page i THE 9/11 COMMISSION REPORT Final FM.1pp 7/17/04 5:25 PM Page v CONTENTS List of Illustrations and Tables ix Member List xi Staff List xiii–xiv Preface xv 1. “WE HAVE SOME PLANES” 1 1.1 Inside the Four Flights 1 1.2 Improvising a Homeland Defense 14 1.3 National Crisis Management 35 2. THE FOUNDATION OF THE NEW TERRORISM 47 2.1 A Declaration of War 47 2.2 Bin Ladin’s Appeal in the Islamic World 48 2.3 The Rise of Bin Ladin and al Qaeda (1988–1992) 55 2.4 Building an Organization, Declaring War on the United States (1992–1996) 59 2.5 Al Qaeda’s Renewal in Afghanistan (1996–1998) 63 3. COUNTERTERRORISM EVOLVES 71 3.1 From the Old Terrorism to the New: The First World Trade Center Bombing 71 3.2 Adaptation—and Nonadaptation— ...in the Law Enforcement Community 73 3.3 . and in the Federal Aviation Administration 82 3.4 . and in the Intelligence Community 86 v Final FM.1pp 7/17/04 5:25 PM Page vi 3.5 . and in the State Department and the Defense Department 93 3.6 . and in the White House 98 3.7 . and in the Congress 102 4. RESPONSES TO AL QAEDA’S INITIAL ASSAULTS 108 4.1 Before the Bombings in Kenya and Tanzania 108 4.2 Crisis:August 1998 115 4.3 Diplomacy 121 4.4 Covert Action 126 4.5 Searching for Fresh Options 134 5. -
Balanced Boolean Functions with Maximum Absolute Value In
1 Construction of n-variable (n ≡ 2 mod 4) balanced Boolean functions with maximum absolute value in n autocorrelation spectra < 2 2 Deng Tang and Subhamoy Maitra Abstract In this paper we consider the maximum absolute value ∆f in the autocorrelation spectrum (not considering the zero point) of a function f. In even number of variables n, bent functions possess the highest nonlinearity with ∆f = 0. The long standing open question (for two decades) in this area is to obtain a theoretical construction of n balanced functions with ∆f < 2 2 . So far there are only a few examples of such functions for n = 10; 14, but no general construction technique is known. In this paper, we mathematically construct an infinite class of balanced n n+6 Boolean functions on n variables having absolute indicator strictly lesser than δn = 2 2 − 2 4 , nonlinearity strictly n−1 n n −3 n−2 greater than ρn = 2 − 2 2 + 2 2 − 5 · 2 4 and algebraic degree n − 1, where n ≡ 2 (mod 4) and n ≥ 46. While the bound n ≥ 46 is required for proving the generic result, our construction starts from n = 18 and we n n−1 n could obtain balanced functions with ∆f < 2 2 and nonlinearity > 2 − 2 2 for n = 18; 22 and 26. Index Terms Absolute Indicator, Autocorrelation Spectrum, Balancedness, Boolean function, Nonlinearity. I. INTRODUCTION Symmetric-key cryptography, which includes stream ciphers and block ciphers, plays a very important role in modern cryptography. The fundamental and generally accepted design principles for symmetric-key cryptography are confusion and diffusion, introduced by Shannon [23]. -
Improved Correlation Attacks on SOSEMANUK and SOBER-128
Improved Correlation Attacks on SOSEMANUK and SOBER-128 Joo Yeon Cho Helsinki University of Technology Department of Information and Computer Science, Espoo, Finland 24th March 2009 1 / 35 SOSEMANUK Attack Approximations SOBER-128 Outline SOSEMANUK Attack Method Searching Linear Approximations SOBER-128 2 / 35 SOSEMANUK Attack Approximations SOBER-128 SOSEMANUK (from Wiki) • A software-oriented stream cipher designed by Come Berbain, Olivier Billet, Anne Canteaut, Nicolas Courtois, Henri Gilbert, Louis Goubin, Aline Gouget, Louis Granboulan, Cedric` Lauradoux, Marine Minier, Thomas Pornin and Herve` Sibert. • One of the final four Profile 1 (software) ciphers selected for the eSTREAM Portfolio, along with HC-128, Rabbit, and Salsa20/12. • Influenced by the stream cipher SNOW and the block cipher Serpent. • The cipher key length can vary between 128 and 256 bits, but the guaranteed security is only 128 bits. • The name means ”snow snake” in the Cree Indian language because it depends both on SNOW and Serpent. 3 / 35 SOSEMANUK Attack Approximations SOBER-128 Overview 4 / 35 SOSEMANUK Attack Approximations SOBER-128 Structure 1. The states of LFSR : s0,..., s9 (320 bits) −1 st+10 = st+9 ⊕ α st+3 ⊕ αst, t ≥ 1 where α is a root of the primitive polynomial. 2. The Finite State Machine (FSM) : R1 and R2 R1t+1 = R2t ¢ (rtst+9 ⊕ st+2) R2t+1 = Trans(R1t) ft = (st+9 ¢ R1t) ⊕ R2t where rt denotes the least significant bit of R1t. F 3. The trans function Trans on 232 : 32 Trans(R1t) = (R1t × 0x54655307 mod 2 )≪7 4. The output of the FSM : (zt+3, zt+2, zt+1, zt)= Serpent1(ft+3, ft+2, ft+1, ft)⊕(st+3, st+2, st+1, st) 5 / 35 SOSEMANUK Attack Approximations SOBER-128 Previous Attacks • Authors state that ”No linear relation holds after applying Serpent1 and there are too many unknown bits...”. -
Higher Order Correlation Attacks, XL Algorithm and Cryptanalysis of Toyocrypt
Higher Order Correlation Attacks, XL Algorithm and Cryptanalysis of Toyocrypt Nicolas T. Courtois Cryptography research, Schlumberger Smart Cards, 36-38 rue de la Princesse, BP 45, 78430 Louveciennes Cedex, France http://www.nicolascourtois.net [email protected] Abstract. Many stream ciphers are built of a linear sequence generator and a non-linear output function f. There is an abundant literature on (fast) correlation attacks, that use linear approximations of f to attack the cipher. In this paper we explore higher degree approximations, much less studied. We reduce the cryptanalysis of a stream cipher to solv- ing a system of multivariate equations that is overdefined (much more equations than unknowns). We adapt the XL method, introduced at Eurocrypt 2000 for overdefined quadratic systems, to solving equations of higher degree. Though the exact complexity of XL remains an open problem, there is no doubt that it works perfectly well for such largely overdefined systems as ours, and we confirm this by computer simula- tions. We show that using XL, it is possible to break stream ciphers that were known to be immune to all previously known attacks. For exam- ple, we cryptanalyse the stream cipher Toyocrypt accepted to the second phase of the Japanese government Cryptrec program. Our best attack on Toyocrypt takes 292 CPU clocks for a 128-bit cipher. The interesting feature of our XL-based higher degree correlation attacks is, their very loose requirements on the known keystream needed. For example they may work knowing ONLY that the ciphertext is in English. Key Words: Algebraic cryptanalysis, multivariate equations, overde- fined equations, Reed-Muller codes, correlation immunity, XL algorithm, Gr¨obner bases, stream ciphers, pseudo-random generators, nonlinear fil- tering, ciphertext-only attacks, Toyocrypt, Cryptrec.