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Cryptanalysis of Feistel Networks with Secret Round Functions Alex Biryukov, Gaëtan Leurent, Léo Perrin
Cryptanalysis of Feistel Networks with Secret Round Functions Alex Biryukov, Gaëtan Leurent, Léo Perrin To cite this version: Alex Biryukov, Gaëtan Leurent, Léo Perrin. Cryptanalysis of Feistel Networks with Secret Round Functions. Selected Areas in Cryptography - SAC 2015, Aug 2015, Sackville, Canada. hal-01243130 HAL Id: hal-01243130 https://hal.inria.fr/hal-01243130 Submitted on 14 Dec 2015 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. Cryptanalysis of Feistel Networks with Secret Round Functions ? Alex Biryukov1, Gaëtan Leurent2, and Léo Perrin3 1 [email protected], University of Luxembourg 2 [email protected], Inria, France 3 [email protected], SnT,University of Luxembourg Abstract. Generic distinguishers against Feistel Network with up to 5 rounds exist in the regular setting and up to 6 rounds in a multi-key setting. We present new cryptanalyses against Feistel Networks with 5, 6 and 7 rounds which are not simply distinguishers but actually recover completely the unknown Feistel functions. When an exclusive-or is used to combine the output of the round function with the other branch, we use the so-called yoyo game which we improved using a heuristic based on particular cycle structures. -
Can We Trust Cryptographic Software? Cryptographic Flaws in GNU Privacy Guard V1.2.3
Can We Trust Cryptographic Software? Cryptographic Flaws in GNU Privacy Guard v1.2.3 Phong Q. Nguyen CNRS/Ecole´ normale sup´erieure D´epartement d’informatique 45 rue d’Ulm, 75230 Paris Cedex 05, France. [email protected] http://www.di.ens.fr/˜pnguyen Abstract. More and more software use cryptography. But how can one know if what is implemented is good cryptography? For proprietary soft- ware, one cannot say much unless one proceeds to reverse-engineering, and history tends to show that bad cryptography is much more frequent than good cryptography there. Open source software thus sounds like a good solution, but the fact that a source code can be read does not imply that it is actually read, especially by cryptography experts. In this paper, we illustrate this point by examining the case of a basic In- ternet application of cryptography: secure email. We analyze parts of thesourcecodeofthelatestversionofGNUPrivacyGuard(GnuPGor GPG), a free open source alternative to the famous PGP software, com- pliant with the OpenPGP standard, and included in most GNU/Linux distributions such as Debian, MandrakeSoft, Red Hat and SuSE. We ob- serve several cryptographic flaws in GPG v1.2.3. The most serious flaw has been present in GPG for almost four years: we show that as soon as one (GPG-generated) ElGamal signature of an arbitrary message is released, one can recover the signer’s private key in less than a second on a PC. As a consequence, ElGamal signatures and the so-called ElGamal sign+encrypt keys have recently been removed from GPG. -
A Low-Latency Block Cipher for Pervasive Computing Applications Extended Abstract?
PRINCE { A Low-latency Block Cipher for Pervasive Computing Applications Extended Abstract? Julia Borghoff1??, Anne Canteaut1;2???, Tim G¨uneysu3, Elif Bilge Kavun3, Miroslav Knezevic4, Lars R. Knudsen1, Gregor Leander1y, Ventzislav Nikov4, Christof Paar3, Christian Rechberger1, Peter Rombouts4, Søren S. Thomsen1, and Tolga Yal¸cın3 1 Technical University of Denmark 2 INRIA, Paris-Rocquencourt, France 3 Ruhr-University Bochum, Germany 4 NXP Semiconductors, Leuven, Belgium Abstract. This paper presents a block cipher that is optimized with respect to latency when implemented in hardware. Such ciphers are de- sirable for many future pervasive applications with real-time security needs. Our cipher, named PRINCE, allows encryption of data within one clock cycle with a very competitive chip area compared to known solutions. The fully unrolled fashion in which such algorithms need to be implemented calls for innovative design choices. The number of rounds must be moderate and rounds must have short delays in hardware. At the same time, the traditional need that a cipher has to be iterative with very similar round functions disappears, an observation that increases the design space for the algorithm. An important further requirement is that realizing decryption and encryption results in minimum additional costs. PRINCE is designed in such a way that the overhead for decryp- tion on top of encryption is negligible. More precisely for our cipher it holds that decryption for one key corresponds to encryption with a re- lated key. This property we refer to as α-reflection is of independent interest and we prove its soundness against generic attacks. 1 Introduction The area of lightweight cryptography, i.e., ciphers with particularly low imple- mentation costs, has drawn considerable attention over the last years. -
Lecture Notes on Error-Correcting Codes and Their Applications to Symmetric Cryptography
Lecture Notes on Error-Correcting Codes and their Applications to Symmetric Cryptography Anne Canteaut Inria [email protected] https://www.rocq.inria.fr/secret/Anne.Canteaut/ version: December 4, 2017 Contents 10 Reed-Muller Codes and Boolean Functions 5 10.1 Boolean functions and their representations . .5 10.1.1 Truth table and Algebraic normal form . .5 10.1.2 Computing the Algebraic Normal Form . .8 10.2 Reed-Muller codes . 11 10.2.1 Definition . 11 10.2.2 The (uju + v) construction . 12 10.3 Weight distributions of Reed-Muller codes . 13 10.3.1 Minimum distance of R(r; m) ........................ 13 10.3.2 Weight distribution of R(1; m) ....................... 14 10.3.3 Weight distribution of R(m − 1; m) ..................... 15 10.3.4 Weight distribution of R(2; m) ....................... 15 10.3.5 Duality . 15 10.3.6 Other properties of the weights of R(r; m) ................. 17 11 Stream Cipher Basics 19 11.1 Basic principle . 19 11.1.1 Synchronous additive stream ciphers . 19 11.1.2 Pseudo-random generators . 21 11.1.3 General functionalities of stream ciphers and usage . 22 11.2 Models of attacks . 23 11.3 Generic attacks on stream ciphers . 24 11.3.1 Period of the sequence of internal states . 24 11.3.2 Time-Memory-Data Trade-off attacks . 27 11.3.3 Statistical tests . 36 11.4 The main families of stream ciphers . 37 11.4.1 Information-theoretically generators . 37 11.4.2 Generators based on a difficult mathematical problem . 38 11.4.3 Generators based on block ciphers . -
Security Analysis and Trust Models in Wireless Networks Lela Mirtskhulava
Security Analysis and Trust Models in Wireless Networks Lela Mirtskhulava [email protected] Department of Computer Sciences Faculty of Exact and Natural Sciences Iv. Javakhishvili Tbilisi State University University str., 13, Georgia In the given work, we analyse the serious weaknesses recently discovered in WPA2 (Wi-Fi Protected Access 2) in October 2017 and KRACK (Key Reinstallation Attack) attack on WPA2 announced by Computer Science Scientists. The KRACKs were introduced to abuse design flaws in cryptographic protocols to reinstall an already-in-use key. Several types of cryptographic Wi-Fi handshakes are affected by the attack. There are different forms of trust to address different types of network security problems and reduce risk in certain conditions. This paper explores the trust models applied by various cryptographic schemes: a) the web of trust employed by Pretty Good Privacy (PGP) where users using their own set of trusted public keys, b) Kerberos, a secret key distribution scheme using a trusted third party, c) certificates, which allow a set of trusted third parties to authenticate each other and, by implication, each other's users. Each of the above mentioned trust models differs in complexity, scope, scalability and general applicability. Which model of trust to apply in certain circumstances and types of wireless networks are discussed in the given paper. It describes the major security issues and their techniques of building trust model by monitoring network behavior. It is intended to use secure and faster cryptographic solution for Wi-Fi networks security by using an open source public-key NTRU cryptosystem that uses lattice-based cryptography. -
SIGMA: the 'Sign-And-Mac' Approach to Authenticated Diffie-Hellman and Its Use in the IKE Protocols
SIGMA: the `SIGn-and-MAc' Approach to Authenticated Diffie-Hellman and its Use in the IKE Protocols ∗ Hugo Krawczyky June 12, 2003 Abstract We present the SIGMA family of key-exchange protocols and the \SIGn-and-MAc" approach to authenticated Diffie-Hellman underlying its design. The SIGMA protocols provide perfect forward secrecy via a Diffie-Hellman exchange authenticated with digital signatures, and are specifically designed to ensure sound cryptographic key exchange while supporting a variety of features and trade-offs required in practical scenarios (such as optional identity protection and reduced number of protocol rounds). As a consequence, the SIGMA protocols are very well suited for use in actual applications and for standardized key exchange. In particular, SIGMA serves as the cryptographic basis for the signature-based modes of the standardized Internet Key Exchange (IKE) protocol (versions 1 and 2). This paper describes the design rationale behind the SIGMA approach and protocols, and points out to many subtleties surrounding the design of secure key-exchange protocols in general, and identity-protecting protocols in particular. We motivate the design of SIGMA by comparing it to other protocols, most notable the STS protocol and its variants. In particular, it is shown how SIGMA solves some of the security shortcomings found in previous protocols. ∗A shortened version of this paper appears in the proceedings of CRYPTO'03. For further information related to the SIGMA protocols see http://www.ee.technion.ac.il/~hugo/sigma.html yEE Department, Technion, Haifa, Israel, and IBM T.J. Watson Research Center. Email: [email protected] 1 Contents 1 Introduction 1 2 Preliminaries: On the Security of Key-Exchange Protocols 4 2.1 Overview of the security model and requirements . -
State of the Art in Lightweight Symmetric Cryptography
State of the Art in Lightweight Symmetric Cryptography Alex Biryukov1 and Léo Perrin2 1 SnT, CSC, University of Luxembourg, [email protected] 2 SnT, University of Luxembourg, [email protected] Abstract. Lightweight cryptography has been one of the “hot topics” in symmetric cryptography in the recent years. A huge number of lightweight algorithms have been published, standardized and/or used in commercial products. In this paper, we discuss the different implementation constraints that a “lightweight” algorithm is usually designed to satisfy. We also present an extensive survey of all lightweight symmetric primitives we are aware of. It covers designs from the academic community, from government agencies and proprietary algorithms which were reverse-engineered or leaked. Relevant national (nist...) and international (iso/iec...) standards are listed. We then discuss some trends we identified in the design of lightweight algorithms, namely the designers’ preference for arx-based and bitsliced-S-Box-based designs and simple key schedules. Finally, we argue that lightweight cryptography is too large a field and that it should be split into two related but distinct areas: ultra-lightweight and IoT cryptography. The former deals only with the smallest of devices for which a lower security level may be justified by the very harsh design constraints. The latter corresponds to low-power embedded processors for which the Aes and modern hash function are costly but which have to provide a high level security due to their greater connectivity. Keywords: Lightweight cryptography · Ultra-Lightweight · IoT · Internet of Things · SoK · Survey · Standards · Industry 1 Introduction The Internet of Things (IoT) is one of the foremost buzzwords in computer science and information technology at the time of writing. -
Optimization of Core Components of Block Ciphers Baptiste Lambin
Optimization of core components of block ciphers Baptiste Lambin To cite this version: Baptiste Lambin. Optimization of core components of block ciphers. Cryptography and Security [cs.CR]. Université Rennes 1, 2019. English. NNT : 2019REN1S036. tel-02380098 HAL Id: tel-02380098 https://tel.archives-ouvertes.fr/tel-02380098 Submitted on 26 Nov 2019 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. THÈSE DE DOCTORAT DE L’UNIVERSITE DE RENNES 1 COMUE UNIVERSITE BRETAGNE LOIRE Ecole Doctorale N°601 Mathématique et Sciences et Technologies de l’Information et de la Communication Spécialité : Informatique Par Baptiste LAMBIN Optimization of Core Components of Block Ciphers Thèse présentée et soutenue à RENNES, le 22/10/2019 Unité de recherche : IRISA Rapporteurs avant soutenance : Marine Minier, Professeur, LORIA, Université de Lorraine Jacques Patarin, Professeur, PRiSM, Université de Versailles Composition du jury : Examinateurs : Marine Minier, Professeur, LORIA, Université de Lorraine Jacques Patarin, Professeur, PRiSM, Université de Versailles Jean-Louis Lanet, INRIA Rennes Virginie Lallemand, Chargée de Recherche, LORIA, CNRS Jérémy Jean, ANSSI Dir. de thèse : Pierre-Alain Fouque, IRISA, Université de Rennes 1 Co-dir. de thèse : Patrick Derbez, IRISA, Université de Rennes 1 Remerciements Je tiens à remercier en premier lieu mes directeurs de thèse, Pierre-Alain et Patrick. -
Data Encryption Standard
Data Encryption Standard The Data Encryption Standard (DES /ˌdiːˌiːˈɛs, dɛz/) is a Data Encryption Standard symmetric-key algorithm for the encryption of electronic data. Although insecure, it was highly influential in the advancement of modern cryptography. Developed in the early 1970s atIBM and based on an earlier design by Horst Feistel, the algorithm was submitted to the National Bureau of Standards (NBS) following the agency's invitation to propose a candidate for the protection of sensitive, unclassified electronic government data. In 1976, after consultation with theNational Security Agency (NSA), the NBS eventually selected a slightly modified version (strengthened against differential cryptanalysis, but weakened against brute-force attacks), which was published as an official Federal Information Processing Standard (FIPS) for the United States in 1977. The publication of an NSA-approved encryption standard simultaneously resulted in its quick international adoption and widespread academic scrutiny. Controversies arose out of classified The Feistel function (F function) of DES design elements, a relatively short key length of the symmetric-key General block cipher design, and the involvement of the NSA, nourishing Designers IBM suspicions about a backdoor. Today it is known that the S-boxes that had raised those suspicions were in fact designed by the NSA to First 1975 (Federal Register) actually remove a backdoor they secretly knew (differential published (standardized in January 1977) cryptanalysis). However, the NSA also ensured that the key size was Derived Lucifer drastically reduced such that they could break it by brute force from [2] attack. The intense academic scrutiny the algorithm received over Successors Triple DES, G-DES, DES-X, time led to the modern understanding of block ciphers and their LOKI89, ICE cryptanalysis. -
How Far Can We Go Beyond Linear Cryptanalysis?
How Far Can We Go Beyond Linear Cryptanalysis? Thomas Baign`eres, Pascal Junod, and Serge Vaudenay EPFL http://lasecwww.epfl.ch Abstract. Several generalizations of linear cryptanalysis have been pro- posed in the past, as well as very similar attacks in a statistical point of view. In this paper, we de¯ne a rigorous general statistical framework which allows to interpret most of these attacks in a simple and uni¯ed way. Then, we explicitely construct optimal distinguishers, we evaluate their performance, and we prove that a block cipher immune to classical linear cryptanalysis possesses some resistance to a wide class of general- ized versions, but not all. Finally, we derive tools which are necessary to set up more elaborate extensions of linear cryptanalysis, and to general- ize the notions of bias, characteristic, and piling-up lemma. Keywords: Block ciphers, linear cryptanalysis, statistical cryptanalysis. 1 A Decade of Linear Cryptanalysis Linear cryptanalysis is a known-plaintext attack proposed in 1993 by Matsui [21, 22] to break DES [26], exploiting speci¯c correlations between the input and the output of a block cipher. Namely, the attack traces the statistical correlation between one bit of information about the plaintext and one bit of information about the ciphertext, both obtained linearly with respect to GF(2)L (where L is the block size of the cipher), by means of probabilistic linear expressions, a concept previously introduced by Tardy-Corfdir and Gilbert [30]. Soon after, several attempts to generalize linear cryptanalysis are published: Kaliski and Robshaw [13] demonstrate how it is possible to combine several in- dependent linear correlations depending on the same key bits. -
Selecting Cryptographic Key Sizes
J. Cryptology (2001) 14: 255–293 DOI: 10.1007/s00145-001-0009-4 © 2001 International Association for Cryptologic Research Selecting Cryptographic Key Sizes Arjen K. Lenstra Citibank, N.A., 1 North Gate Road, Mendham, NJ 07945-3104, U.S.A. [email protected] and Technische Universiteit Eindhoven Eric R. Verheul PricewaterhouseCoopers, GRMS Crypto Group, Goudsbloemstraat 14, 5644 KE Eindhoven, The Netherlands eric.verheul@[nl.pwcglobal.com, pobox.com] Communicated by Andrew Odlyzko Received September 1999 and revised February 2001 Online publication 14 August 2001 Abstract. In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm-based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated parameter settings, combined with existing data points about the cryptosystems. Key words. Symmetric key length, Public key length, RSA, ElGamal, Elliptic curve cryptography, Moore’s law. 1. Introduction 1.1. The Purpose of This Paper Cryptography is one of the most important tools that enable e-commerce because cryp- tography makes it possible to protect electronic information. The effectiveness of this protection depends on a variety of mostly unrelated issues such as cryptographic key size, protocol design, and password selection. Each of these issues is equally important: if a key is too small, or if a protocol is badly designed or incorrectly used, or if a pass- word is poorly selected or protected, then the protection fails and improper access can be gained. In this article we give some guidelines for the determination of cryptographic key sizes. -
Miss in the Middle Attacks on IDEA and Khufu
Miss in the Middle Attacks on IDEA and Khufu Eli Biham? Alex Biryukov?? Adi Shamir??? Abstract. In a recent paper we developed a new cryptanalytic techni- que based on impossible differentials, and used it to attack the Skipjack encryption algorithm reduced from 32 to 31 rounds. In this paper we describe the application of this technique to the block ciphers IDEA and Khufu. In both cases the new attacks cover more rounds than the best currently known attacks. This demonstrates the power of the new cryptanalytic technique, shows that it is applicable to a larger class of cryptosystems, and develops new technical tools for applying it in new situations. 1 Introduction In [5,17] a new cryptanalytic technique based on impossible differentials was proposed, and its application to Skipjack [28] and DEAL [17] was described. In this paper we apply this technique to the IDEA and Khufu cryptosystems. Our new attacks are much more efficient and cover more rounds than the best previously known attacks on these ciphers. The main idea behind these new attacks is a bit counter-intuitive. Unlike tra- ditional differential and linear cryptanalysis which predict and detect statistical events of highest possible probability, our new approach is to search for events that never happen. Such impossible events are then used to distinguish the ci- pher from a random permutation, or to perform key elimination (a candidate key is obviously wrong if it leads to an impossible event). The fact that impossible events can be useful in cryptanalysis is an old idea (for example, some of the attacks on Enigma were based on the observation that letters can not be encrypted to themselves).