PLANETARY SCIENCES American and Soviet Research
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Tuto Documentation Release 0.1.0
Tuto Documentation Release 0.1.0 DevOps people 2020-05-09 09H16 CONTENTS 1 Documentation news 3 1.1 Documentation news 2020........................................3 1.1.1 New features of sphinx.ext.autodoc (typing) in sphinx 2.4.0 (2020-02-09)..........3 1.1.2 Hypermodern Python Chapter 5: Documentation (2020-01-29) by https://twitter.com/cjolowicz/..................................3 1.2 Documentation news 2018........................................4 1.2.1 Pratical sphinx (2018-05-12, pycon2018)...........................4 1.2.2 Markdown Descriptions on PyPI (2018-03-16)........................4 1.2.3 Bringing interactive examples to MDN.............................5 1.3 Documentation news 2017........................................5 1.3.1 Autodoc-style extraction into Sphinx for your JS project...................5 1.4 Documentation news 2016........................................5 1.4.1 La documentation linux utilise sphinx.............................5 2 Documentation Advices 7 2.1 You are what you document (Monday, May 5, 2014)..........................8 2.2 Rédaction technique...........................................8 2.2.1 Libérez vos informations de leurs silos.............................8 2.2.2 Intégrer la documentation aux processus de développement..................8 2.3 13 Things People Hate about Your Open Source Docs.........................9 2.4 Beautiful docs.............................................. 10 2.5 Designing Great API Docs (11 Jan 2012)................................ 10 2.6 Docness................................................. -
Cryptanalysis of Substitution-Permutation Networks Using Key-Dependent Degeneracy*
Cryptanalysis of Substitution-Permutation Networks Using Key-Dependent Degeneracy* Howard M. Heys Electrical Engineering, Faculty of Engineering and Applied Science Memorial University of Newfoundland St. John’s, Newfoundland, Canada A1B 3X5 Stafford E.Tavares Department of Electrical and Computer Engineering Queen’s University Kingston, Ontario, Canada K7L 3N6 * This research was supported by the Natural Sciences and Engineering Research Council of Canada and the Telecommunications Research Institute of Ontario and was completed during the first author’s doctoral studies at Queen’s University. Cryptanalysis of Substitution-Permutation Networks Using Key-Dependent Degeneracy Keywords Ð Cryptanalysis, Substitution-Permutation Network, S-box Abstract Ð This paper presents a novel cryptanalysis of Substitution- Permutation Networks using a chosen plaintext approach. The attack is based on the highly probable occurrence of key-dependent degeneracies within the network and is applicable regardless of the method of S-box keying. It is shown that a large number of rounds are required before a network is re- sistant to the attack. Experimental results have found 64-bit networks to be cryptanalyzable for as many as 8 to 12 rounds depending on the S-box properties. ¡ . Introduction The concept of Substitution-Permutation Networks (SPNs) for use in block cryp- tosystem design originates from the “confusion” and “diffusion” principles in- troduced by Shannon [1]. The SPN architecture considered in this paper was first suggested by Feistel [2] and consists of rounds of non-linear substitutions (S-boxes) connected by bit permutations. Such a cryptosystem structure, referred 1 to as LUCIFER1 by Feistel, is a simple, efficient implementation of Shannon’s concepts. -
物理雙月刊29-3 621-772.Pdf
ᒳृݧ ʳ ౨ᄭઝݾറᙀ ᚮࣔᏕ/֮ ΔࢨუԵᛵᇞݺଚشଶಬߨጿጿլឰऱਞ ၦऱࠌ ౨ᄭऱ࣠Δኙ٤شॸΔ᠏ณհၴԾࠩԱքΕԮִ መ৫ࠌ ഏᎾၴऱڇऱᐙګԳพஒऱ ᛩቼࢬທח᥆࣍ङऱֲΔ עء۶ΔլោᥦԫՀڕټᚰۖࠐΖ ඈچᑷԫंंլឰ Δᑷ รԼᒧറ֮ΚψൕഏᎾᛩቼਐᑇࡌ௧ᛩ៥ऱ ऱ࿇ሽ౨ᄭऱᛘΔ ֗ IEA อૠװထԫैཀհլ݈ ωΔᇠᒧ֮ີტխᘋՕᖂ܉ऱՕհխΔᨃԳ ։ᗺ៥࣍ ᤚຑ़Εຑ௧ຟआᤴ ढߓ୪ւࣳඒ࣍ඒᖂઔߒ խࢼ़ݺଚᐷᐊΖڦۍऱ ᎩհᎾΔڼԱΖՈࠌଖ ᆖᛎࡉഏԺऱ࿇୶זᆏᆏՂ چሽլឰشڞऱ ᎅ࠷ެ࣍౨ᄭױሽ ፖᑓΔ༓شڇΔኚ໌ΖྥۖΔ֒ Δޡݾऱၞشࠡሎ֗شழΔݺଚՈՕ ऱࠌٵཚऱ ᎅਢԫഏᆖᛎ࿇୶ऱױCO2 ऱඈ࣋ၦࡉᄵயᚨ ౨ᄭ ٺΔ౨ᄭᤜᠲኙ࣍ڼڂऱ༞֏ΔထኔఎՀԱլ֟լߜ ೯ԺΖ ࡳࢤެڶᏆऱ࿇୶ࠠٺڇᄊ֏ ഏچຒףԱګऱધᙕΔՈ ߪᣂএࠩԫषᄎՕฒऱ壂ઘࡉֲൄढ֊ޓயᚨऱං֫հԫΖ ऱᐙΔ ฒاڇवኙ࣍ Ꮭऱं೯ΖᅝഏᎾईᏝՂཆΔഏփढᏝঁஓஓױݺଚࠆ࠹ԫաऱ堚ළፖঁ൸հᎾΔڇ ՂይΖچΔ ऱৼᜢխᆥྤݲᐫᇷᄭᤖ៲ຆΔ౨ᄭ༓٤ᑇٛᘸၞՑऱྥ֚ 9 ڣ ࣍ 2005ޓࠐΔईᏝᆏᆏ֒Δڣၦথբ २༓شࢬऱؓ݁ሽၦࡉ౨ᄭࠌڣޢԳޢݺଚ ද࣍ US$70 ऱ໌ޢࠐऱᖵᄅΔሒڣۍሽ ִٝડధڇ౨ᄭΕڇऱছૄΜૉ൞უڇټਢඈ ᄭ۞ᖏञࡉైڂຝ։ڶᄅધᙕΖईᏝऱं೯ឈ ᚮࣔᏕ ౨ᄭفՂ֏چլ؆ਢڂԫ܀ਙएࠃٙΔ 堚ဎՕᖂढߓمഏ ڶईΕ֚ྥࡉᅁ౨ᄭᗏற)ऱᤖ៲ၦึߒفऑਐ) E-mail: [email protected] ࢤΔૉشऱ౨ᄭࠌڶૻΖറ୮ေ۷ૉᖕԳᣊ Ϯ621Ϯʳ քִʳڣ ˊ˃˃˅ʻ֥࠴Կཚʼʳעढᠨִ ᒳृݧ ༚ྼऱႨΖᅝᓫᓵᇠ֘ுΛࢨਢᇠᖑுΛംᠲڶۖ ࠩބயऱᆏ౨ֱூΔࢨլᕣݶ༈ڶإటנ༼౨آᙈᙈ ᇞு౨ᗏறऱ፹ທመچհছΔषᄎՕฒᚨᇠ٣堚ᄑ ڶՂೈᅁᇷᄭࡸچ౨ᄭऱᇩΔঞזࠠயհཙ ؆ਜ਼ழऱۆுᘿ୴֗אΔ܂࿓ࡉு౨࿇ሽऱՠ فईࡉ֚ྥ֏فڕהऱᤖ៲ၦ؆Δࠡ׳ؐڣ 200 ࢤড়ᨠऱኪ৫אթ౨ڼڕୌࠄΔڶՂऱ ᥨൻਜࠩࢍאڣ ౨ྤऄ֭ᐶመ 50ױၦቃ۷ژᗏறऱᚏ ཚءΔڼڂᖗΖހᒔऱإԫנு౨࿇ሽشࠌܡၦΖ ਢޣ౨ᄭ᜔Ꮑ ሽֆுԿᐗૠቤิ९ದ໑Փऱᑷ֧֨ᗏ ܑຘመف᠏ངயለհႚอ֏܅ءګΔᆖᛎۖྥ ሽֆு౨࿇ሽኔ೭ᆖ᧭ऱڣڍڶࠩԱٍࠠބऱሽ౨ Δشऴ൷ࠌאԫՕฒګ᠏ངڇΔشறऱࠌ ،ݺଚ֮റ૪ψࢢسࢨᑷ౨ऱመ࿓խΔᄎ ு֨ᛜሎᓰᓰ९׆ᐚᆠ٣(شԺ࿇ሽ)Ε೯౨(ሎᙁ־อጠ) ॺൄ᧩࣐ᚩऱאԱᇞ،--ு౨࿇ሽᓫωΔᇠ֮ڕլ ۆᎨॸΔᖄીᣤૹऱᛩቼګඈ࣋Օၦऱᄵ᧯ࡉݮ ຝٺᎅࣔԱு౨࿇ሽऱچᦰृ堚ᄑڗऱؓ݁ᄵ৫ 壄֮چࡉֲᣤૹऱᄵயᚨΔၞۖᖄી ኪؓᘝ ੌ࿓ࡉுᗏறՄऱ፹ທመ࿓Δਢԫᒧॺൄଖԫᦰऱسऱڶऱ۞ྥᛩቼࡉچኙۖڂດዬՂ֒Ζ ኪᛩቼ૿ ֮ີΖسऱچऱᣤૹᓢᚰΔࠌڃனױլګؘലທ ٤ᤜᠲǵഏᎾईᏝࡺլڜईفᜯ؎ՕऱਗᖏΖ ࠹ࠩ٤ ՂഏᎾၴᒤᄵ᧯ඈ࣋྇ၦࢭᘭհᛩঅֆףࡉଢऱ᧢ᔢࢬທ ՀΔ᧢ޏኙᛩቼऱشᣂ౨ᄭሎڶ ڂᛩঅრᢝይ֗אඔ೯ΔڤإऱᐙຍଡૹᤜᠲΔݺଚܑࡡᓮՠᄐݾઔߒ પψࠇຟᤜࡳωګ ԳᣊؘߨհሁΖ۶ᘯګ౨ᄭسᡖᐚ ైऱᓢᚰՀΔං೯٦ۂ(Հ១ጠՠઔೃ౨ᛩࢬא)ೃ౨ᄭፖᛩቼઔߒࢬ ౨ᄭ࿇ሽωٍᆖسรքᒧറ֮ψ٦עء౨ᄭΛس٦ -
Physical Processes in the Interstellar Medium
Physical Processes in the Interstellar Medium Ralf S. Klessen and Simon C. O. Glover Abstract Interstellar space is filled with a dilute mixture of charged particles, atoms, molecules and dust grains, called the interstellar medium (ISM). Understand- ing its physical properties and dynamical behavior is of pivotal importance to many areas of astronomy and astrophysics. Galaxy formation and evolu- tion, the formation of stars, cosmic nucleosynthesis, the origin of large com- plex, prebiotic molecules and the abundance, structure and growth of dust grains which constitute the fundamental building blocks of planets, all these processes are intimately coupled to the physics of the interstellar medium. However, despite its importance, its structure and evolution is still not fully understood. Observations reveal that the interstellar medium is highly tur- bulent, consists of different chemical phases, and is characterized by complex structure on all resolvable spatial and temporal scales. Our current numerical and theoretical models describe it as a strongly coupled system that is far from equilibrium and where the different components are intricately linked to- gether by complex feedback loops. Describing the interstellar medium is truly a multi-scale and multi-physics problem. In these lecture notes we introduce the microphysics necessary to better understand the interstellar medium. We review the relations between large-scale and small-scale dynamics, we con- sider turbulence as one of the key drivers of galactic evolution, and we review the physical processes that lead to the formation of dense molecular clouds and that govern stellar birth in their interior. Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany e-mail: [email protected], [email protected] 1 Contents Physical Processes in the Interstellar Medium ............... -
An Introduction to Cryptography Copyright © 1990-1999 Network Associates, Inc
An Introduction to Cryptography Copyright © 1990-1999 Network Associates, Inc. and its Affiliated Companies. All Rights Reserved. PGP*, Version 6.5.1 6-99. Printed in the United States of America. PGP, Pretty Good, and Pretty Good Privacy are registered trademarks of Network Associates, Inc. and/or its Affiliated Companies in the US and other countries. All other registered and unregistered trademarks in this document are the sole property of their respective owners. Portions of this software may use public key algorithms described in U.S. Patent numbers 4,200,770, 4,218,582, 4,405,829, and 4,424,414, licensed exclusively by Public Key Partners; the IDEA(tm) cryptographic cipher described in U.S. patent number 5,214,703, licensed from Ascom Tech AG; and the Northern Telecom Ltd., CAST Encryption Algorithm, licensed from Northern Telecom, Ltd. IDEA is a trademark of Ascom Tech AG. Network Associates Inc. may have patents and/or pending patent applications covering subject matter in this software or its documentation; the furnishing of this software or documentation does not give you any license to these patents. The compression code in PGP is by Mark Adler and Jean-Loup Gailly, used with permission from the free Info-ZIP implementation. LDAP software provided courtesy University of Michigan at Ann Arbor, Copyright © 1992-1996 Regents of the University of Michigan. All rights reserved. This product includes software developed by the Apache Group for use in the Apache HTTP server project (http://www.apache.org/). Copyright © 1995-1999 The Apache Group. All rights reserved. See text files included with the software or the PGP web site for further information. -
Differential Cryptanalysis of the Data Encryption Standard
Differential Cryptanalysis of the Data Encryption Standard Eli Biham1 Adi Shamir2 December 7, 2009 1Computer Science Department, Technion – Israel Institute of Technology, Haifa 32000, Israel. Email: [email protected], WWW: http://www.cs.technion.ac.il/˜biham/. 2Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel. Email: [email protected]. This versionofthebookisprocessedfromtheauthor’soriginalLaTeXfiles,andmaybe differentlypaginatedthantheprintedbookbySpringer(1993). Copyright:EliBihamandAdiShamir. Preface The security of iterated cryptosystems and hash functions has been an active research area for many years. The best known and most widely used function of this type is the Data Encryption Standard (DES). It was developed at IBM and adopted by the National Bureau of Standards in the mid 70’s, and has successfully withstood all the attacks published so far in the open literature. Since the introduction of DES, many other iterated cryptosystems were developed, but their design and analysis were based on ad-hoc heuristic arguments, with no theoretical justification. In this book, we develop a new type of cryptanalytic attack which can be successfully applied to many iterated cryptosystems and hash functions. It is primarily a chosen plaintext attack but under certain circumstances, it can also be applied as a known plaintext attack. We call it “differen- tial cryptanalysis”, since it analyzes the evolution of differences when two related plaintexts are encrypted under the same key. Differential cryptanalysis is the first published attack which is capable of breaking the full 16-round DES in less than 255 complexity. The data analysis phase computes the key by analyzing about 236 ciphertexts in 237 time. -
Oregon Star Party Advanced Observing List
Welcome to the OSP Advanced Observing List In a sincere attempt to lure more of you into trying the Advanced List, each object has a page telling you what it is, why it’s interesting to observe, and the minimum size telescope you might need to see it. I’ve included coordinates, the constellation each object is located in, and either a chart or photo (or both) showing what the object looks like and how it’s situated in the sky. All you have to do is observe and enjoy the challenge. Stretch your skill and imagination - see something new, something unimaginably old, something unexpected Even though this is a challenging list, you don’t need 20 years of observing experience or a 20 inch telescope to be successful – although in some cases that will help. The only way to see these cool objects for yourself is to give them a go. Howard Banich, The minimum aperture listed for each object is a rough estimate. The idea is to Chuck Dethloff and show approximately what size telescope might be needed to successfully observe Matt Vartanian that particular object. The range is 3 to 28 inches. collaborated on this The visibility of each object assumes decently good OSP observing conditions. year’s list. Requirements to receive a certificate 1. There are 14 objects to choose from. Descriptive notes and/or sketches that clearly show you observed 10 objects are needed to receive the observing certificate. For instance, you can mark up these photos and charts with lines and arrows, and add a few notes describing what you saw. -
Differential Cryptanalysis of the Data Encryption Standard Eli Biham Adi Shamir
Differential Cryptanalysis of the Data Encryption Standard Eli Biham Adi Shamir Differential Cryptanalysis of the Data Encryption Standard With 56 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest Eli Biham Computer Science Department Technion-Israel Institute of Technology Haifa 32000 Israel Adi Shamir Department of Applied Mathematics and Computer Science The Weizmann Institute of Science Rehovot 76100 Israel Library of Congress Cataloging-in-Publication Data Biham,Eli. Differential cryptanalysis of the Data Encryption Standard / Eli Biham, Adi Shamir. p.cm. Includes bibliographical references and index. ISBN-13 :978-1-4613-9316-0 e- ISBN-13: 978-1-4613-9314-6 DOl: 10.1007/978-1-4613-9314-6 1. Computer - Access control. 2. Cryptography. I. Shamir, Adi. II. Title. QA76.9.A25B54 1993 005.8'2 - dc20 92-44581 Printed on acid-free paper. © 1993 by Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1993 All rights reserved. This work may not be translated or copied in whole or in part without the writ ten permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in con nection with any form of information storage and retrieval, electronic adaptation, computer soft ware, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. -
Cryptanalysis of White-Box DES Implementations with Arbitrary External Encodings
Cryptanalysis of White-Box DES Implementations with Arbitrary External Encodings Brecht Wyseur1, Wil Michiels2, Paul Gorissen2, and Bart Preneel1 1 Katholieke Universiteit Leuven Dept. Elect. Eng.-ESAT/SCD-COSIC, Kasteelpark Arenberg 10, 3001 Heverlee, Belgium fbrecht.wyseur,[email protected] 2 Philips Research Laboratories Prof. Holstlaan 4, 5656 AA, Eindhoven, The Netherlands fwil.michiels,[email protected] Abstract. At DRM 2002, Chow et al. [4] presented a method for im- plementing the DES block cipher such that it becomes hard to extract the embedded secret key in a white-box attack context. In such a con- text, an attacker has full access to the implementation and its execution environment. In order to provide an extra level of security, an implemen- tation shielded with external encodings was introduced by Chow et al. and improved by Link and Neumann [10]. In this paper, we present an algorithm to extract the secret key from such white-box DES implemen- tations. The cryptanalysis is a di®erential attack on obfuscated rounds, and works regardless of the shielding external encodings that are applied. The cryptanalysis has a average time complexity of 214 and a negligible space complexity. Keywords. White-Box Cryptography, Obfuscation, DES, Data Encryp- tion Standard, Cryptanalysis 1 Introduction White-box cryptography aims to protect secret keys by embedding them into a software implementation of a block cipher. The attack model for these implementations is de¯ned as the white-box attack model. In this model, an attacker has full control over the implementation and its ex- ecution environment. This includes static and dynamic analysis of the implementation, altering of computation, and modi¯cation of internal variables. -
OCTOBER 2009 OBSERVER Inside the the Chill’S A-Comin’ Observer
THE DENVER OBSERVER OCTOBER 2009 OBSERVER Inside the The Chill’s a-Comin’ Observer President’s Corner........................... 2 Society Directory............................. 2 Prelude Lake................................... 3 New Scope Operator......................... 5 New Members.................................. 5 Astronomical League....................... 6 NASA’S Space Place......................... 7 Schedule of Events.............. back page Calendar 4.................................................... Full moon BUT NOWHERE NEAR THE TEMPERATURE INSIDE THE MU CEPHEI NEBULA 11..................................... Last quarter moon CLOUD, IC 1396 IN CEPHEUS, WHERE A FRIGID -290ᵒ AWAITS A STELLAR ADVENTURER 17.................................................. New moon Joe used an SBIG ST-2000XM ccd camera with a 110mm Mamiya RZ lens at f/5.6. Please contact Joe for more technical details. The bright orange star is Mu Cephei, the Garnet Star; 24........................ Colorado Astronomy Day the Elephant Trunk nebula portion is right of center. 25.................................... First quarter moon Image copyright 2009 Joe Gafford OCTOBER SKIES by Dennis Cochran upiter is already up in the south when darkness descends, situated along Alpha Aquarius, the star at the top of the arc of that constellation. Above it J the top left of Capricornus’ goat-ee jester grin. Above Jupiter and the a short way and a bit west is the slightly brighter red star, Enif, at the end of Goat is the water jug of Aquarius, in case you’ve ever wondered where one of Pegasus’ legs. Just northwest of Enif is M15, one of the best globulars this elusive constellation lies. Wasn’t there an Age of Aquarius? Perhaps that on the list. If you then drop from Enif or M15, straight south about 2/3 of was when the New Age movement was born. -
Cryptanalysis of S-DES
Cryptanalysis of S-DES Dr. K. S. Ooi Brain Chin Vito ([email protected]) ([email protected]) University of Sheffield Centre, Taylor’s College 1st April 2002 Abstract This paper describes an effort to attack S-DES using differential cryptanalysis and linear cryptanalysis. S-DES is a reduced version of the Data Encryption Standard (DES). It also includes a discussion on the subject of cryptology and a literature survey of useful papers regarding cryptography and cryptanalysis. This paper is meant as a tutorial on the fundamentals of differential cryptanalysis and linear cryptanalysis of a Feistel cipher. Contents 1. Background 2. Literature Survey 3. S-DES 4. Brute Force Attack of S-DES 5. Differential Cryptanalysis of S-DES 6. Linear Cryptanalysis of S-DES 7. Reference 8. Appendix 8.1 S-DES Source Code 8.2 Automated Brute Force Attack of S-DES Source Code 8.3 Automated Differential Cryptanalysis of S-DES Source Code 8.4 Automated Linear Cryptanalysis of S-DES Source Code 8.5 Brute Force Attack of S-DES Results 8.6 Differential Cryptanalysis of S-DES Results 8.7 Linear Cryptanalysis of S-DES Results 8.8 Difference Pair Table of S0 8.9 Difference Pair Table of S1 8.10 Difference Distribution Table of S0 8.11 Difference Distribution Table of S1 8.12 Differential Characteristic of S-DES 8.13 I/0 Table for S0 8.14 Visualisation of Linear Approximation of S0 8.15 Distribution Table for S0 8.16 Notation Table 1 1. Background 1.1 Security in the Information Age 1.2 Importance of Cipher Efficiency 1.3 Cryptology 1.4 Why Cryptanalysis? 1.1 Security in the Information Age The beginning of the Information Age heralded a new kind of threat to governments, corporations and individuals. -
Cryptanalysis of the Keeloq Block Cipher
Cryptanalysis of the KeeLoq block cipher Andrey Bogdanov Chair for Communication Security Ruhr University Bochum, Germany Abstract. KeeLoq is a block cipher used in numerous widespread pas- sive entry and remote keyless entry systems as well as in various compo- nent identification applications. The KeeLoq algorithm has a 64-bit key and operates on 32-bit blocks. It is based on an NLFSR with a nonlinear feedback function of 5 variables. In this paper a key recovery attack with complexity of about 252 steps is proposed (one step is equivalent to a single KeeLoq encryption opera- tion). In our attack we use the techniques of guess-and-determine, slide, and distinguishing attacks. Several real-world applications are vulnerable to the attack. To our best knowledge this is the first paper to describe and cryptanalyze the KeeLoq block cipher. Key words: KeeLoq block cipher, cryptanalysis, slide attacks, guess- and-determine attacks, distinguishing attacks 1 Introduction A large proportion of modern block ciphers are built upon Feistel networks. Such cryptographic algorithms as DES [22], Blowfish [26], KASUMI [6], GOST [32] or RC5 [25] are based on balanced Feistel networks. Other block ciphers use source-heavy or target-heavy unbalanced Feistel networks (e.g. REDOC III [27], Skipjack [23], etc.). The most extreme case of a source-heavy unbalanced Feistel network [28] is a nonlinear feedback shift register (NLFSR), which can be applied in both stream cipher and block cipher designs. A number of NLFSR-based stream ciphers have been recently proposed (e.g. Achterbahn [8] and [7], Grain [9]) and successfully cryptanalyzed using linear [2] and nonlinear [11], [24] approximations of nonlinear feedback functions.