A Stream Cipher Algorithm Using Dynamic Feedback Control
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High Performance Architecture for LILI-II Stream Cipher
International Journal of Computer Applications (0975 – 8887) Volume 107 – No 13, December 2014 High Performance Architecture for LILI-II Stream Cipher N. B. Hulle R. D. Kharadkar, Ph.D. S. S. Dorle, Ph.D. GHRIEET, Pune GHRIEET, Pune GHRCE, Nagpur Domkhel Road Domkhel Road Hingana Road Wagholi, Pune Wagholi, Pune Nagpur ABSTRACT cipher. This architecture uses same clock for both LFSRs. It is Proposed work presents high performance architecture for capable of shifting LFSRD content by one to four stages, LILI-II stream cipher. This cipher uses 128 bit key and 128 bit depending on value of function FC in single clock cycle IV for initialization of two LFSR. Proposed architecture uses without losing any data from function FC. single clock for both LFSRs, so this architecture will be useful in high speed communication applications. Presented 2. LILI-II STREAM CIPHER architecture uses four bit shifting of LFSR in single clock LILI-II is synchronous stream cipher developed by A. Clark et D al. in 2002 by removing existing weaknesses of LILI-128 cycle without losing any data items from function FC. Proposed architecture is coded by using VHDL language with stream cipher. It consists of two subsystems, clock controlled CAD tool Xilinx ISE Design Suite 13.2 and targeted hardware subsystem and data generation subsystem as shown in Fig. 1. is Xilinx Virtex5 FPGA having device xc4vlx60, with KEY IV package ff1148. Proposed architecture achieved throughput of 127 128 128 224.7 Mbps at 224.7 MHz frequency. 127 General Terms Hardware implementation of stream ciphers LFSRc LFSRd ... Keywords X0 X126 X0 X1 X96 X122 LILI, Stream cipher, clock controlled, FPGA, LFSR. -
Algebraic Attacks on SOBER-T32 and SOBER-T16 Without Stuttering
Algebraic Attacks on SOBER-t32 and SOBER-t16 without stuttering Joo Yeon Cho and Josef Pieprzyk? Center for Advanced Computing – Algorithms and Cryptography, Department of Computing, Macquarie University, NSW, Australia, 2109 {jcho,josef}@ics.mq.edu.au Abstract. This paper presents algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering. For unstuttered SOBER-t32, two differ- ent attacks are implemented. In the first attack, we obtain multivariate equations of degree 10. Then, an algebraic attack is developed using a collection of output bits whose relation to the initial state of the LFSR can be described by low-degree equations. The resulting system of equa- tions contains 269 equations and monomials, which can be solved using the Gaussian elimination with the complexity of 2196.5. For the second attack, we build a multivariate equation of degree 14. We focus on the property of the equation that the monomials which are combined with output bit are linear. By applying the Berlekamp-Massey algorithm, we can obtain a system of linear equations and the initial states of the LFSR can be recovered. The complexity of attack is around O(2100) with 292 keystream observations. The second algebraic attack is applica- ble to SOBER-t16 without stuttering. The attack takes around O(285) CPU clocks with 278 keystream observations. Keywords : Algebraic attack, stream ciphers, linearization, NESSIE, SOBER-t32, SOBER-t16, modular addition, multivariate equations 1 Introduction Stream ciphers are an important class of encryption algorithms. They encrypt individual characters of a plaintext message one at a time, using a stream of pseudorandom bits. -
Optimizing the Placement of Tap Positions and Guess and Determine
Optimizing the placement of tap positions and guess and determine cryptanalysis with variable sampling S. Hodˇzi´c, E. Pasalic, and Y. Wei∗† Abstract 1 In this article an optimal selection of tap positions for certain LFSR-based encryption schemes is investigated from both design and cryptanalytic perspective. Two novel algo- rithms towards an optimal selection of tap positions are given which can be satisfactorily used to provide (sub)optimal resistance to some generic cryptanalytic techniques applicable to these schemes. It is demonstrated that certain real-life ciphers (e.g. SOBER-t32, SFINKS and Grain-128), employing some standard criteria for tap selection such as the concept of full difference set, are not fully optimized with respect to these attacks. These standard design criteria are quite insufficient and the proposed algorithms appear to be the only generic method for the purpose of (sub)optimal selection of tap positions. We also extend the framework of a generic cryptanalytic method called Generalized Filter State Guessing Attacks (GFSGA), introduced in [26] as a generalization of the FSGA method, by applying a variable sampling of the keystream bits in order to retrieve as much information about the secret state bits as possible. Two different modes that use a variable sampling of keystream blocks are presented and it is shown that in many cases these modes may outperform the standard GFSGA mode. We also demonstrate the possibility of employing GFSGA-like at- tacks to other design strategies such as NFSR-based ciphers (Grain family for instance) and filter generators outputting a single bit each time the cipher is clocked. -
VMPC-MAC: a Stream Cipher Based Authenticated Encryption Scheme
VMPC-MAC: A Stream Cipher Based Authenticated Encryption Scheme Bartosz Zoltak http://www.vmpcfunction.com [email protected] Abstract. A stream cipher based algorithm for computing Message Au- thentication Codes is described. The algorithm employs the internal state of the underlying cipher to minimize the required additional-to- encryption computational e®ort and maintain general simplicity of the design. The scheme appears to provide proper statistical properties, a comfortable level of resistance against forgery attacks in a chosen ci- phertext attack model and high e±ciency in software implementations. Keywords: Authenticated Encryption, MAC, Stream Cipher, VMPC 1 Introduction In the past few years the interest in message authentication algorithms has been concentrated mostly on modes of operation of block ciphers. Examples of some recent designs include OCB [4], OMAC [7], XCBC [6], EAX [8], CWC [9]. Par- allely a growing interest in stream cipher design can be observed, however along with a relative shortage of dedicated message authentication schemes. Regarding two recent proposals { Helix and Sober-128 stream ciphers with built-in MAC functionality { a powerful attack against the MAC algorithm of Sober-128 [10] and two weaknesses of Helix [12] were presented at FSE'04. This paper gives a proposition of a simple and software-e±cient algorithm for computing Message Authentication Codes for the presented at FSE'04 VMPC Stream Cipher [13]. The proposed scheme was designed to minimize the computational cost of the additional-to-encryption MAC-related operations by employing some data of the internal-state of the underlying cipher. This approach allowed to maintain sim- plicity of the design and achieve good performance in software implementations. -
Introduction to Public Key Cryptography and Clock Arithmetic Lecture Notes for Access 2010, by Erin Chamberlain and Nick Korevaar
1 Introduction to Public Key Cryptography and Clock Arithmetic Lecture notes for Access 2010, by Erin Chamberlain and Nick Korevaar We’ve discussed Caesar Shifts and other mono-alphabetic substitution ciphers, and we’ve seen how easy it can be to break these ciphers by using frequency analysis. If Mary Queen of Scots had known this, perhaps she would not have been executed. It was a long time from Mary Queen of Scots and substitution ciphers until the end of the 1900’s. Cryptography underwent the evolutionary and revolutionary changes which Si- mon Singh chronicles in The Code Book. If you are so inclined and have appropriate leisure time, you might enjoy reading Chapters 2-5, to learn some of these historical cryptography highlights: People came up with more complicated substitution ciphers, for example the Vigen`ere square. This Great Cipher of France baffled people for quite a while but a de- termined cryptographer Etienne Bazeries had a Eureka moment after three years of work, cracked the code, and possibly found the true identity of the Man in the Iron Mask, one of the great mysteries of the seventeeth century. Edgar Allan Poe and Sir Arthur Conan Doyle even dabbled in cryptanalysis. Secrecy was still a problem though because the key needed to be sent, and with the key anyone could encrypt and decrypt the messages. Frequency analysis was used to break all of these codes. In 1918 Scherbius invented his Enigma machine, but Alan Turing’s machine (the first computer?) helped in figuring out that supposedly unbreakable code, and hastened the end of the second World War. -
MTH6115 Cryptography 4.1 Fish
MTH6115 Cryptography Notes 4: Stream ciphers, continued Recall from the last part the definition of a stream cipher: Definition: A stream cipher over an alphabet of q symbols a1;:::;aq requires a key, a random or pseudo-random string of symbols from the alphabet with the same length as the plaintext, and a substitution table, a Latin square of order q (whose entries are symbols from the alphabet, and whose rows and columns are indexed by these symbols). If the plaintext is p = p1 p2 ::: pn and the key is k = k1k2 :::kn, then the ciphertext is z = z1z2 :::zn, where zt = pt ⊕ kt for t = 1;:::;n; the operation ⊕ is defined as follows: ai ⊕a j = ak if and only if the symbol in the row labelled ai and the column labelled a j of the substitution table is ak. We extend the definition of ⊕ to denote this coordinate-wise operation on strings: thus, we write z = p ⊕ k, where p;k;z are the plaintext, key, and ciphertext strings. We also define the operation by the rule that p = z k if z = p ⊕ k; thus, describes the operation of decryption. 4.1 Fish (largely not examinable) A simple improvement of the Vigenere` cipher is to encipher twice using two differ- ent keys k1 and k2. Because of the additive nature of the cipher, this is the same as enciphering with k1 + k2. The advantage is that the length of the new key is the least common multiple of the lengths of k1 and k2. For example, if we encrypt a message once with the key FOXES and again with the key WOLVES, the new key is obtained by encrypting a six-fold repeat of FOXES with a five-fold repeat of WOLVES, namely BCIZWXKLPNJGTSDASPAGQJBWOTZSIK 1 The new key has period 30. -
State Convergence and Keyspace Reduction of the Mixer Stream Cipher
State convergence and keyspace reduction of the Mixer stream cipher Sui-Guan Teo1, Kenneth Koon-Ho Wong1, Leonie Simpson1;2, and Ed Dawson1 1 Information Security Institute, Queensland University of Technology fsg.teo,kkwong,[email protected] 2 Faculty of Science and Technology, Queensland University of Technology GPO Box 2434, Brisbane Qld 4001, Australia [email protected] Keywords: Stream cipher, initialisation, state convergence, Mixer, LILI, Grain Abstract. This paper presents an analysis of the stream cipher Mixer, a bit-based cipher with structural components similar to the well-known Grain cipher and the LILI family of keystream generators. Mixer uses a 128-bit key and 64-bit IV to initialise a 217-bit internal state. The analysis is focused on the initialisation function of Mixer and shows that there exist multiple key-IV pairs which, after initialisation, produce the same initial state, and consequently will generate the same keystream. Furthermore, if the number of iterations of the state update function performed during initialisation is increased, then the number of distinct initial states that can be obtained decreases. It is also shown that there exist some distinct initial states which produce the same keystream, re- sulting in a further reduction of the effective key space. 1 Introduction Many keystream generators for stream ciphers are based on shift registers, partic- ularly Linear Feedback Shift Registers (LFSRs). Using the output of a regularly- clocked LFSR directly as keystream is cryptographically weak due to the linear properties of LFSR sequences. To mask this linearity, stream cipher designers use LFSRs and introduce non-linearity either explicitly through the use of nonlinear Boolean functions or implicitly through through the use of irregular clocking. -
The Mathemathics of Secrets.Pdf
THE MATHEMATICS OF SECRETS THE MATHEMATICS OF SECRETS CRYPTOGRAPHY FROM CAESAR CIPHERS TO DIGITAL ENCRYPTION JOSHUA HOLDEN PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c 2017 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR press.princeton.edu Jacket image courtesy of Shutterstock; design by Lorraine Betz Doneker All Rights Reserved Library of Congress Cataloging-in-Publication Data Names: Holden, Joshua, 1970– author. Title: The mathematics of secrets : cryptography from Caesar ciphers to digital encryption / Joshua Holden. Description: Princeton : Princeton University Press, [2017] | Includes bibliographical references and index. Identifiers: LCCN 2016014840 | ISBN 9780691141756 (hardcover : alk. paper) Subjects: LCSH: Cryptography—Mathematics. | Ciphers. | Computer security. Classification: LCC Z103 .H664 2017 | DDC 005.8/2—dc23 LC record available at https://lccn.loc.gov/2016014840 British Library Cataloging-in-Publication Data is available This book has been composed in Linux Libertine Printed on acid-free paper. ∞ Printed in the United States of America 13579108642 To Lana and Richard for their love and support CONTENTS Preface xi Acknowledgments xiii Introduction to Ciphers and Substitution 1 1.1 Alice and Bob and Carl and Julius: Terminology and Caesar Cipher 1 1.2 The Key to the Matter: Generalizing the Caesar Cipher 4 1.3 Multiplicative Ciphers 6 -
A 1 Gbps Chaos-Based Stream Cipher Implemented in 0.18 Μm CMOS Technology
electronics Article A 1 Gbps Chaos-Based Stream Cipher Implemented in 0.18 µm CMOS Technology Miguel Garcia-Bosque * , Guillermo Díez-Señorans, Adrián Pérez-Resa, Carlos Sánchez-Azqueta, Concepción Aldea and Santiago Celma Group of Electronic Design, University of Zaragoza, 50009 Zaragoza, Spain; [email protected] (G.D.-S.); [email protected] (A.P.-R.); [email protected] (C.S.-A.); [email protected] (C.A.); [email protected] (S.C.) * Correspondence: [email protected]; Tel.: +34-876-55-3539 Received: 15 May 2019; Accepted: 29 May 2019; Published: 1 June 2019 Abstract: In this work, a novel chaos-based stream cipher based on a skew tent map is proposed and implemented in a 0.18 µm CMOS (Complementary Metal-Oxide-Semiconductor) technology. The proposed ciphering algorithm uses a linear feedback shift register that perturbs the orbits generated by the skew tent map after each iteration. This way, the randomness of the generated sequences is considerably improved. The implemented stream cipher was capable of achieving encryption speeds of 1 Gbps by using an approximate area of 20, 000 2-NAND equivalent gates, with a power ∼ consumption of 24.1 mW. To test the security of the proposed cipher, the generated keystreams were subjected to National Institute of Standards and Technology (NIST) randomness tests, proving that they were undistinguishable from truly random sequences. Finally, other security aspects such as the key sensitivity, key space size, and security against reconstruction attacks were studied, proving that the stream cipher is secure. Keywords: stream cipher; PRNG; cryptography; chaotic map; skew tent map 1. Introduction Despite the large number of encryption algorithms proposed in previous decades, there is still a great interest in the field of cryptography [1,2]. -
Data Encryption with Linear Feedback Shift Register
International Journal of Scientific & Engineering Research Volume 3, Issue 6, June-2012 1 ISSN 2229-5518 Data Encryption with Linear Feedback Shift Register Subhra Mazumdar , Tannishtha Som Abstract— A data encryption technology which ensures secrecy of the data while being transferred over a long distance. It can provide about 80-85% data security as decoding of data involves inverting the feedback function or generating the binary sequence which will help in retrieving the data after some recombination operation. Index Terms— octal word time generation , linear feedback shift register, feedback function, data security, priority encoder, email server, SMTP(simple mail transfer protocol) ,POP(post office protocol) , device sensitive password check. —————————— —————————— 1 INTRODUCTION An efficient method to modify the plain text into an encoded cipher text , not easily predictable ensuring that the key value is irrecoverable when data is attacked while being transmitted. If a data is lost or extra bit gets added while transmission, the system will automatically show error as all the processes are synchronised. To avoid data being modified while transmission, different types of feedback function for 100 characters(3-bit sequence specific and different for adjacent row and column input devices in the register shown in figure 4; arranged in a 10 * 10 matrix) having different bit sequence is devised. Two stage password check(one of them being device figure 1: OCTAL WORD-TIME SIGNAL GENERATION specific) is used for decoding the message. 2 PURPOSE AND DESIGN OF THE DEVICE Converting the data to its ASCII value, one character at a time, using a 2^8 x 8 priority encoder (1 byte per character), the 8-bit sequence is stored in an 8-bit right shift register M (PARALLEL IN). -
The Enigma History and Mathematics
The Enigma History and Mathematics by Stephanie Faint A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master of Mathematics m Pure Mathematics Waterloo, Ontario, Canada, 1999 @Stephanie Faint 1999 I hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by pho tocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. 11 The University of Waterloo requires the signatures of all persons using or pho tocopying this thesis. Please sign below, and give address and date. ill Abstract In this thesis we look at 'the solution to the German code machine, the Enigma machine. This solution was originally found by Polish cryptologists. We look at the solution from a historical perspective, but most importantly, from a mathematical point of view. Although there are no complete records of the Polish solution, we try to reconstruct what was done, sometimes filling in blanks, and sometimes finding a more mathematical way than was originally found. We also look at whether the solution would have been possible without the help of information obtained from a German spy. IV Acknowledgements I would like to thank all of the people who helped me write this thesis, and who encouraged me to keep going with it. In particular, I would like to thank my friends and fellow grad students for their support, especially Nico Spronk and Philippe Larocque for their help with latex. -
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...”.