DOCSLIB.ORG

Public Evaluation Report UEA2/UIA2

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Public Evaluation Report UEA2/UIA2 ETSI/SAGE Version: 2.0 Technical report Date: 9th September, 2011 Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. Document 4: Design and Evaluation Report LTE Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. page 1 of 43 Document 4: Design and Evaluation report. Version 2.0 Document History 0.1 20th June 2010 First draft of main technical text 1.0 11th August 2010 First public release 1.1 11th August 2010 A few typos corrected and text improved 1.2 4th January 2011 A modification of ZUC and 128-EIA3 and text improved 1.3 18th January 2011 Further text improvements including better reference to different historic versions of the algorithms 1.4 1st July 2011 Add a new section on timing attacks 2.0 9th September 2011 Final deliverable LTE Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. page 2 of 43 Document 4: Design and Evaluation report. Version 2.0 Reference Keywords 3GPP, security, SAGE, algorithm ETSI Secretariat Postal address F-06921 Sophia Antipolis Cedex - FRANCE Office address 650 Route des Lucioles - Sophia Antipolis Valbonne - FRANCE Tel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16 Siret N° 348 623 562 00017 - NAF 742 C Association à but non lucratif enregistrée à la Sous-Préfecture de Grasse (06) N° 7803/88 X.400 c= fr; a=atlas; p=etsi; s=secretariat Internet [email protected] http://www.etsi.fr Copyright Notification No part may be reproduced except as authorized by written permission. The copyright and the foregoing restriction extend to reproduction in all media. © European Telecommunications Standards Institute 2006. All rights reserved. LTE Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. page 3 of 43 Document 4: Design and Evaluation report. Version 2.0 Contents 1 Scope .................................................................................................................................. 7 2 References .......................................................................................................................... 7 3 Abbreviations ...................................................................................................................... 7 4 Structure of this report ........................................................................................................ 9 5 Background to the design and evaluation work .................................................................. 9 6 Versions of these algorithms / evaluation history ............................................................. 10 7 Algorithm parameters ....................................................................................................... 10 7.1 EEA – Encryption algorithm .................................................................................... 11 7.2 EIA – Integrity algorithm ......................................................................................... 11 8 Summary of the 128-EEA3 and 128-EIA3 algorithms ..................................................... 13 8.1 The stream cipher ZUC ............................................................................................. 13 8.2 Confidentiality function 128-EEA3 .......................................................................... 14 8.3 Integrity function 128-EIA3 ..................................................................................... 15 9 Overall design rationale for ZUC ..................................................................................... 16 10 Design and evaluation of ZUC components ..................................................................... 17 10.1 Design of the LFSR .................................................................................................. 17 10.2 Design of the bit-reorganization ............................................................................... 21 10.3 Design of the nonlinear function F ........................................................................... 23 11 128-EEA3 and 128-EIA3 constructions ........................................................................... 27 11.1 128-EEA3 construction ............................................................................................. 27 11.2 128-EIA3 construction .............................................................................................. 27 12 Resistance against cryptanalytic attacks ........................................................................... 30 12.1 Weak key attacks ...................................................................................................... 30 12.2 Guess-and-Determine Attacks .................................................................................. 31 12.3 BDD Attacks (from evaluation report [32]) .............................................................. 31 12.4 Inversion Attacks (from evaluation report [32]) ....................................................... 31 12.5 Linear Distinguishing Attacks .................................................................................. 31 12.6 Algebraic Attacks ..................................................................................................... 33 12.7 Chosen IV Attacks .................................................................................................... 36 12.8 Time-Memory-Data Trade-Off Attacks .................................................................... 37 12.9 Timing Attacks ......................................................................................................... 38 13 Conclusion of the evaluation ............................................................................................ 39 14 Acknowledgements .......................................................................................................... 40 Annex A - External references ................................................................................................. 41 LTE Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. page 4 of 43 Document 4: Design and Evaluation report. Version 2.0 Intellectual Property Rights IPRs essential or potentially essential to the present document may have been declared to ETSI. The information pertaining to these essential IPRs, if any, is publicly available for ETSI members and non-members, and can be found in SR 000 314: "Intellectual Property Rights (IPRs); Essential, or potentially Essential, IPRs notified to ETSI in respect of ETSI standards", which is available from the ETSI Secretariat. Latest updates are available on the ETSI Web server (http://www.etsi.org/ipr). At the time of writing of this report, no information of any Intellectual Property Rights (IPRs) has been drawn to the attention neither to the Task Force nor to ETSI. No guarantee can be given as to the existence of other IPRs not referenced in SR 000 314 (or the updates on the ETSI Web server (http://www.etsi.org/ipr) which are, or may be, or may become, essential to the present document. LTE Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. page 5 of 43 Document 4: Design and Evaluation report. Version 2.0 Foreword This Report has been produced by the ETSI SAGE Task Force on the Design of the third LTE encryption and integrity protection algorithms 128-EEA3 and 128-EIA3 (SAGE TF 3GPP). The work described in this report was undertaken in response to a request made by 3GPP. LTE Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. page 6 of 43 Document 4: Design and Evaluation report. Version 2.0 1 Scope This public report contains a detailed summary of the design and evaluation work performed during the development of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 and 128-EIA3. The report also includes summaries of evaluations made by independent external evaluators, and reflects modifications that amend the security flaws found by Bing Sun et al. [35] at the 2010 ZUC workshop, by Hongjun Wu [36] at the rump session of ASIACRYPT 2010, and by Thomas Fuhr et al. at the 2010 ZUC workshop/eprint [37]. 2 References For the purposes of this report, the following references apply: [1] 3G TS 33.401 V 9.3.1 (2010-04) 3rd Generation Partnership Project; Technical Specification Group Services and System Aspects; 3GPP System Architecture Evolution (SAE); Security architecture (Release 9). [2] ETSI/SAGE Specification. Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. Document 1: 128-EEA3 and 128-EIA3 Specification; Version: 1.6; Date: 1st July 2011. [3] ETSI/SAGE Specification. Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. Document 2: ZUC Specification; Version: 1.6; Date: 28th June 2011. Additional references to external documents are provided in Annex A. 3 Abbreviations For the purposes of the present report, the following abbreviations apply: AES Advanced Encryption Standard CK Cipher Key ETSI European Telecommunications Standards Institute GF(q) The Galois field with q elements 3GPP 3rd Generation Partnership Project EPS Evolved Packet System (comprising LTE and SAE) EEA EPS Encryption Algorithm EIA EPS Integrity Algorithm 128-EEA3 Proposed third algorithm fulfilling the EEA requirement 128-EIA3 Proposed third algorithm fulfilling the EIA requirement IBS Input Bit Stream IK Integrity Key IPR Intellectual Property Rights IV Initialization Vector LFSR Linear Feedback Shift Register LTE Long Term Evolution (radio network) MAC Message Authentication Code OBS Output Bit Stream OTP One Time Pad SA3 3GPP Systems
Load more

Recommended publications
  • Improved Related-Key Attacks on DESX and DESX+
    Improved Related-key Attacks on DESX and DESX+ Raphael C.-W. Phan1 and Adi Shamir3 1 Laboratoire de s´ecurit´eet de cryptographie (LASEC), Ecole Polytechnique F´ed´erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland [email protected] 2 Faculty of Mathematics & Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel [email protected] Abstract. In this paper, we present improved related-key attacks on the original DESX, and DESX+, a variant of the DESX with its pre- and post-whitening XOR operations replaced with addition modulo 264. Compared to previous results, our attack on DESX has reduced text complexity, while our best attack on DESX+ eliminates the memory requirements at the same processing complexity. Keywords: DESX, DESX+, related-key attack, fault attack. 1 Introduction Due to the DES’ small key length of 56 bits, variants of the DES under multiple encryption have been considered, including double-DES under one or two 56-bit key(s), and triple-DES under two or three 56-bit keys. Another popular variant based on the DES is the DESX [15], where the basic keylength of single DES is extended to 120 bits by wrapping this DES with two outer pre- and post-whitening keys of 64 bits each. Also, the endorsement of single DES had been officially withdrawn by NIST in the summer of 2004 [19], due to its insecurity against exhaustive search. Future use of single DES is recommended only as a component of the triple-DES. This makes it more important to study the security of variants of single DES which increase the key length to avoid this attack.
    [Show full text]
  • Models and Algorithms for Physical Cryptanalysis
    MODELS AND ALGORITHMS FOR PHYSICAL CRYPTANALYSIS Dissertation zur Erlangung des Grades eines Doktor-Ingenieurs der Fakult¨at fur¨ Elektrotechnik und Informationstechnik an der Ruhr-Universit¨at Bochum von Kerstin Lemke-Rust Bochum, Januar 2007 ii Thesis Advisor: Prof. Dr.-Ing. Christof Paar, Ruhr University Bochum, Germany External Referee: Prof. Dr. David Naccache, Ecole´ Normale Sup´erieure, Paris, France Author contact information: [email protected] iii Abstract This thesis is dedicated to models and algorithms for the use in physical cryptanalysis which is a new evolving discipline in implementation se- curity of information systems. It is based on physically observable and manipulable properties of a cryptographic implementation. Physical observables, such as the power consumption or electromag- netic emanation of a cryptographic device are so-called `side channels'. They contain exploitable information about internal states of an imple- mentation at runtime. Physical effects can also be used for the injec- tion of faults. Fault injection is successful if it recovers internal states by examining the effects of an erroneous state propagating through the computation. This thesis provides a unified framework for side channel and fault cryptanalysis. Its objective is to improve the understanding of physi- cally enabled cryptanalysis and to provide new models and algorithms. A major motivation for this work is that methodical improvements for physical cryptanalysis can also help in developing efficient countermea- sures for securing cryptographic implementations. This work examines differential side channel analysis of boolean and arithmetic operations which are typical primitives in cryptographic algo- rithms. Different characteristics of these operations can support a side channel analysis, even of unknown ciphers.
    [Show full text]
  • Cache-Timing Attack Against Aes Crypto System - Countermeasures Review
    Edith Cowan University Research Online Australian Information Security Management Conference Conferences, Symposia and Campus Events 2014 Cache-timing attack against aes crypto system - countermeasures review Yaseen H. Taha University of Khartoum Settana M. Abdulh University of Khartoum Naila A. Sadalla University of Khartoum Huwaida Elshoush University of Khartoum Follow this and additional works at: https://ro.ecu.edu.au/ism Part of the Information Security Commons DOI: 10.4225/75/57b65fd1343d3 12th Australian Information Security Management Conference. Held on the 1-3 December, 2014 at Edith Cowan University, Joondalup Campus, Perth, Western Australia. This Conference Proceeding is posted at Research Online. https://ro.ecu.edu.au/ism/166 CACHE-TIMING ATTACK AGAINST AES CRYPTO SYSTEM - COUNTERMEASURES REVIEW Yaseen.H.Taha, Settana.M.Abdulh, Naila.A.Sadalla, Huwaida Elshoush University of Khartoum, Sudan [email protected], [email protected], [email protected], [email protected] Abstract Side channel attacks are based on side channel information, which is information that is leaked from encryption systems. Implementing side channel attacks is possible if and only if an attacker has access to a cryptosystem (victim) or can interact with cryptosystem remotely to compute time statistics of information that collected from targeted system. Cache timing attack is a special type of side channel attack. Here, timing information caused by cache effect is collected and analyzed by an attacker to guess sensitive information such as encryption key or plaintext. Cache timing attack against AES was known theoretically until Bernstein carry out a real implementation of the attack. Fortunately, this attack can be a success only by exploiting bad implementation in software or hardware, not for algorithm structure weaknesses, and that means attack could be prevented if proper implementation has been used.
    [Show full text]
  • Related-Key Cryptanalysis of 3-WAY, Biham-DES,CAST, DES-X, Newdes, RC2, and TEA
    Related-Key Cryptanalysis of 3-WAY, Biham-DES,CAST, DES-X, NewDES, RC2, and TEA John Kelsey Bruce Schneier David Wagner Counterpane Systems U.C. Berkeley kelsey,schneier @counterpane.com [email protected] f g Abstract. We present new related-key attacks on the block ciphers 3- WAY, Biham-DES, CAST, DES-X, NewDES, RC2, and TEA. Differen- tial related-key attacks allow both keys and plaintexts to be chosen with specific differences [KSW96]. Our attacks build on the original work, showing how to adapt the general attack to deal with the difficulties of the individual algorithms. We also give specific design principles to protect against these attacks. 1 Introduction Related-key cryptanalysis assumes that the attacker learns the encryption of certain plaintexts not only under the original (unknown) key K, but also under some derived keys K0 = f(K). In a chosen-related-key attack, the attacker specifies how the key is to be changed; known-related-key attacks are those where the key difference is known, but cannot be chosen by the attacker. We emphasize that the attacker knows or chooses the relationship between keys, not the actual key values. These techniques have been developed in [Knu93b, Bih94, KSW96]. Related-key cryptanalysis is a practical attack on key-exchange protocols that do not guarantee key-integrity|an attacker may be able to flip bits in the key without knowing the key|and key-update protocols that update keys using a known function: e.g., K, K + 1, K + 2, etc. Related-key attacks were also used against rotor machines: operators sometimes set rotors incorrectly.
    [Show full text]
  • GCM) for Confidentiality And
    NIST Special Publication 800-38D Recommendation for Block DRAFT (April, 2006) Cipher Modes of Operation: Galois/Counter Mode (GCM) for Confidentiality and Authentication Morris Dworkin C O M P U T E R S E C U R I T Y Abstract This Recommendation specifies the Galois/Counter Mode (GCM), an authenticated encryption mode of operation for a symmetric key block cipher. KEY WORDS: authentication; block cipher; cryptography; information security; integrity; message authentication code; mode of operation. i Table of Contents 1 PURPOSE...........................................................................................................................................................1 2 AUTHORITY.....................................................................................................................................................1 3 INTRODUCTION..............................................................................................................................................1 4 DEFINITIONS, ABBREVIATIONS, AND SYMBOLS.................................................................................2 4.1 DEFINITIONS AND ABBREVIATIONS .............................................................................................................2 4.2 SYMBOLS ....................................................................................................................................................4 4.2.1 Variables................................................................................................................................................4
    [Show full text]
  • CIT 380: Securing Computer Systems
    CIT 380: Securing Computer Systems Symmetric Cryptography Topics 1. Modular Arithmetic 2. What is Cryptography? 3. Transposition Ciphers 4. Substitution Ciphers 1. Cæsar cipher 2. Vigènere cipher 5. Cryptanalysis: frequency analysis 6. Block Ciphers 7. AES and DES 8. Stream Ciphers Modular Arithmetic Congruence – a = b (mod N) iff a = b + kN – ex: 37=27 mod 10 b is the residue of a, modulo N – Integers 0..N-1 are the set of residues mod N Modulo 12 number system What is Cryptography? Cryptography: The art and science of keeping messages secure. Cryptanalysis: the art and science of decrypting messages. Cryptology: cryptography + cryptanalysis Terminology Plaintext: message P to be encrypted. Also called Plaintext cleartext. Encryption: altering a Encryption message to keep its Procedure contents secret. Ciphertext: encrypted message C. Ciphertext Cæsar cipher Plaintext is HELLO WORLD Change each letter to the third letter following it (X goes to A, Y to B, Z to C) – Key is 3, usually written as letter ‘D’ Ciphertext is KHOOR ZRUOG ROT 13 Cæsar cipher with key of 13 13 chosen since encryption and decryption are same operation Used to hide spoilers, punchlines, and offensive material online. Kerckhoff’s Principle Security of cryptosystem should only depend on 1. Quality of shared encryption algorithm E 2. Secrecy of key K Security through obscurity tends to fail ex: DVD Content Scrambling System Cryptanalysis Goals 1. Decrypt a given message. 2. Recover encryption key. Threat models vary based on 1. Type of information available to adversary 2. Interaction with cryptosystem. Cryptanalysis Threat Models ciphertext only: adversary has only ciphertext; goal is to find plaintext, possibly key.
    [Show full text]
  • Some Comments on the First Round AES Evaluation Of
    Some Comments on the First Round AES Evaluation of RC6 1 2 1 Scott Contini , Ronald L. Rivest , M.J.B. Robshaw , 1 and Yiqun Lisa Yin 1 RSA Lab oratories, 2955 Campus Drive, San Mateo, CA 94403, USA fscontini,matt,yiqung@rsa. com 2 M.I.T. Lab oratory for Computer Science, 545 Technology Square, Cambridge, MA 02139, USA [email protected] 1 Intro duction The rst round of the AES pro cess is coming to an end. Since August of 1998, the cryptographic community has had the opp ortunity to consider each of the fteen prop osed AES candidates. In this note, we take the opp ortunity to answer some of the questions and to resp ond to some of the issues that have b een raised ab out the suitabilityofRC6 as an AES candidate. 2 Encryption/Decryption Performance of RC6 Since the publication of RC6 a variety of researchers and implementors have examined RC6 and considered its p erformance in a wide range of environments. 2.1 32-bit architectures RC6 is one of the fastest AES prop osals on 32-bit architectures, particularly so on the NIST reference platform of a 200 MHz Pentium Pro. It is argued by many that the most reasonable way to assess the p erformance of an algorithm is to consider its sp eed in an assembly language implementation. We agree that this is the case. However it is also interesting to consider how the p erformance of RC6 compares when using di erent compilers. It is imp ortant to note that to take advantage of compiler-sp eci c optimizations the source co de provided to the compiler might need to b e changed.
    [Show full text]
  • An Adaptive-Ciphertext Attack Against I XOR C Block Cipher Modes With
    A A-C A “I ⊕ C” B C M W O Jon Passki Tom Ritter [email protected] [email protected] May 24, 2012 Abstract Certain block cipher confidentiality modes are susceptible to an adaptive chosen-ciphertext attack against the underlying format of the plaintext. When the application decrypts altered ciphertext and attempts to process the manipulated plaintext, it may disclose information about intermediate values resulting in an oracle. In this paper we describe how to recognize and exploit such an oracle to decrypt ciphertext and control the decryption to result in arbitrary plaintext. We also discuss ways to mitigate and remedy the issue. 1 I Quoting from [1]: Adaptive chosen-ciphertext attacks on cryptographic protocols allow an attacker to decrypt a cipher- text C, getting the plaintext M, by submitting a series of chosen-ciphertexts C0= 6 C to an oracle which returns information on the decryption. The ciphertexts can be adaptively chosen so that information on previous decryptions is available before the next chosen ciphertext is submitted. Adaptive chosen-ciphertext attacks against different confidentiality modes are not novel. The CBC confidentiality mode can suffer from a side channel attack against padding verification [2], popularized by [3]. A variant of the Cipher Feedback (CFB) confidentiality mode has been attacked in different encryption mail protocols by [4, 5, 1], and the padding schemes of asymmetric ciphers are another source of such attacks [6, 7]. In some form, they rely on the use of an oracle that leaks or communicates information back to attackers. We examine four different confidentiality modes encrypting plaintext that is separated by a delimiter, and the absence or inclusion of that delimiter generates an oracle by the application.
    [Show full text]
  • Cs 255 (Introduction to Cryptography)
    CS 255 (INTRODUCTION TO CRYPTOGRAPHY) DAVID WU Abstract. Notes taken in Professor Boneh’s Introduction to Cryptography course (CS 255) in Winter, 2012. There may be errors! Be warned! Contents 1. 1/11: Introduction and Stream Ciphers 2 1.1. Introduction 2 1.2. History of Cryptography 3 1.3. Stream Ciphers 4 1.4. Pseudorandom Generators (PRGs) 5 1.5. Attacks on Stream Ciphers and OTP 6 1.6. Stream Ciphers in Practice 6 2. 1/18: PRGs and Semantic Security 7 2.1. Secure PRGs 7 2.2. Semantic Security 8 2.3. Generating Random Bits in Practice 9 2.4. Block Ciphers 9 3. 1/23: Block Ciphers 9 3.1. Pseudorandom Functions (PRF) 9 3.2. Data Encryption Standard (DES) 10 3.3. Advanced Encryption Standard (AES) 12 3.4. Exhaustive Search Attacks 12 3.5. More Attacks on Block Ciphers 13 3.6. Block Cipher Modes of Operation 13 4. 1/25: Message Integrity 15 4.1. Message Integrity 15 5. 1/27: Proofs in Cryptography 17 5.1. Time/Space Tradeoff 17 5.2. Proofs in Cryptography 17 6. 1/30: MAC Functions 18 6.1. Message Integrity 18 6.2. MAC Padding 18 6.3. Parallel MAC (PMAC) 19 6.4. One-time MAC 20 6.5. Collision Resistance 21 7. 2/1: Collision Resistance 21 7.1. Collision Resistant Hash Functions 21 7.2. Construction of Collision Resistant Hash Functions 22 7.3. Provably Secure Compression Functions 23 8. 2/6: HMAC And Timing Attacks 23 8.1. HMAC 23 8.2.
    [Show full text]
  • Recommendation for Block Cipher Modes of Operation Methods
    NIST Special Publication 800-38A Recommendation for Block 2001 Edition Cipher Modes of Operation Methods and Techniques Morris Dworkin C O M P U T E R S E C U R I T Y ii C O M P U T E R S E C U R I T Y Computer Security Division Information Technology Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899-8930 December 2001 U.S. Department of Commerce Donald L. Evans, Secretary Technology Administration Phillip J. Bond, Under Secretary of Commerce for Technology National Institute of Standards and Technology Arden L. Bement, Jr., Director iii Reports on Information Security Technology The Information Technology Laboratory (ITL) at the National Institute of Standards and Technology (NIST) promotes the U.S. economy and public welfare by providing technical leadership for the Nation’s measurement and standards infrastructure. ITL develops tests, test methods, reference data, proof of concept implementations, and technical analyses to advance the development and productive use of information technology. ITL’s responsibilities include the development of technical, physical, administrative, and management standards and guidelines for the cost-effective security and privacy of sensitive unclassified information in Federal computer systems. This Special Publication 800-series reports on ITL’s research, guidance, and outreach efforts in computer security, and its collaborative activities with industry, government, and academic organizations. Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose.
    [Show full text]
  • Security Evaluation of GOST 28147-89 in View of International Standardisation
    Security Evaluation of GOST 28147-89 In View Of International Standardisation Nicolas T. Courtois University College London, Gower Street, London, UK, [email protected] Abstract. GOST 28147-89 is is a well-known 256-bit block cipher which is a plausible alternative for AES-256 and triple DES which is known to have a much lower implementation cost, see [31]. GOST is implemented in standard crypto libraries such as OpenSSL and Crypto++ [25, 45], and is increasingly popular and used also outside its country of origin and on the Internet [23, 24, 31]. In 2010 GOST was submitted to ISO, to become a worldwide industrial encryption standard. Until 2011 researchers unanimously agreed that GOST could or should be very secure, which was summarized in 2010 in these words: \despite considerable cryptanalytic e®orts spent in the past 20 years, GOST is still not broken", see [31]. Unhappily, it was recently discovered that GOST can be broken and is a deeply flawed cipher. There is a very con- siderable amount of recent not yet published work on cryptanalysis of GOST known to us, see [12]. One simple attack was already presented in February at FSE 2011, see [28]. In this short paper we describe an- other attack, to illustrate the fact that there is now plethora of attacks on GOST, which require much less memory, and don't even require the reflection property [29] to hold, without which the recent attack from [28] wouldn't work. We are also aware of many substantially faster at- tacks and of numerous special even weaker cases, see [12].
    [Show full text]
  • Thesis Submitted for the Degree of Doctor of Philosophy
    Optimizations in Algebraic and Differential Cryptanalysis Theodosis Mourouzis Department of Computer Science University College London A thesis submitted for the degree of Doctor of Philosophy January 2015 Title of the Thesis: Optimizations in Algebraic and Differential Cryptanalysis Ph.D. student: Theodosis Mourouzis Department of Computer Science University College London Address: Gower Street, London, WC1E 6BT E-mail: [email protected] Supervisors: Nicolas T. Courtois Department of Computer Science University College London Address: Gower Street, London, WC1E 6BT E-mail: [email protected] Committee Members: 1. Reviewer 1: Professor Kenny Paterson 2. Reviewer 2: Dr Christophe Petit Day of the Defense: Signature from head of PhD committee: ii Declaration I herewith declare that I have produced this paper without the prohibited assistance of third parties and without making use of aids other than those specified; notions taken over directly or indirectly from other sources have been identified as such. This paper has not previously been presented in identical or similar form to any other English or foreign examination board. The following thesis work was written by Theodosis Mourouzis under the supervision of Dr Nicolas T. Courtois at University College London. Signature from the author: Abstract In this thesis, we study how to enhance current cryptanalytic techniques, especially in Differential Cryptanalysis (DC) and to some degree in Al- gebraic Cryptanalysis (AC), by considering and solving some underlying optimization problems based on the general structure of the algorithm. In the first part, we study techniques for optimizing arbitrary algebraic computations in the general non-commutative setting with respect to sev- eral metrics [42, 44].
    [Show full text]