DOCSLIB.ORG

Deep Learning-Based Cryptanalysis of Lightweight Block Ciphers

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Deep Learning-Based Cryptanalysis of Lightweight Block Ciphers Hindawi Security and Communication Networks Volume 2020, Article ID 3701067, 11 pages https://doi.org/10.1155/2020/3701067 Research Article Deep Learning-Based Cryptanalysis of Lightweight Block Ciphers Jaewoo So Department of Electronic Engineering, Sogang University, Seoul 04107, Republic of Korea Correspondence should be addressed to Jaewoo So; [email protected] Received 5 February 2020; Revised 21 June 2020; Accepted 26 June 2020; Published 13 July 2020 Academic Editor: Umar M. Khokhar Copyright © 2020 Jaewoo So. +is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Most of the traditional cryptanalytic technologies often require a great amount of time, known plaintexts, and memory. +is paper proposes a generic cryptanalysis model based on deep learning (DL), where the model tries to find the key of block ciphers from known plaintext-ciphertext pairs. We show the feasibility of the DL-based cryptanalysis by attacking on lightweight block ciphers such as simplified DES, Simon, and Speck. +e results show that the DL-based cryptanalysis can successfully recover the key bits when the keyspace is restricted to 64 ASCII characters. +e traditional cryptanalysis is generally performed without the keyspace restriction, but only reduced-round variants of Simon and Speck are successfully attacked. Although a text-based key is applied, the proposed DL-based cryptanalysis can successfully break the full rounds of Simon32/64 and Speck32/64. +e results indicate that the DL technology can be a useful tool for the cryptanalysis of block ciphers when the keyspace is restricted. 1. Introduction space-time tradeoff, is a generic attack which weakens the security benefits of using multiple encryptions [6]. +e Cryptanalysis of block ciphers has persistently received great biclique attack, which is a variant of the MITM attack, attention. In particular, recently, many cryptanalytic tech- utilizes a biclique structure to extend the number of possibly niques have emerged. +e cryptanalysis based on the al- attacked rounds by the MITM attack [6]. In a related-key gorithm of algebraic structures can be categorized as follows: attack, an attacker can observe the operation of a cipher a differential cryptanalysis, a linear cryptanalysis, a differ- under several different keys whose values are initially un- ential-linear cryptanalysis, a meet-in-the-middle (MITM) known, but where some mathematical relationship con- attack, and a related-key attack [1, 2]. Differential crypt- necting the keys is known to the attacker [7]. analysis, which is the first general cryptanalytic technique, However, the conventional cryptanalysis might be im- analyses how differences evolve during encryption and how practical or have limitations to be generalized. First, most of differences of plaintext pairs evolve to differences of the conventional cryptanalytic technologies often require a great resultant ciphertext pairs [3]. +e differential cryptanalysis amount of time, known plaintexts, and memory. Second, has evolved to various types of differential cryptanalysis such although the traditional cryptanalysis is generally performed as an integral cryptanalysis, which is sometimes known as a without the keyspace restriction, only reduced-round vari- multiset attack, a boomerang attack, an impossible differ- ants are successfully attacked on recent block ciphers. For ential cryptanalysis, and an improbable differential crypt- example, no successful attack on the full-round Simon or the analysis [1, 2]. Linear cryptanalysis is also a general full-round Speck, which is a family of lightweight block cryptanalytic technique, where it analyses linear approxi- ciphers, is known [8–10]. +ird, we need an automated and mations between plaintexts bits, ciphertexts bits, and key generalized test tool for checking the safety of various bits. It is a known plaintext attack. +e work in [4] showed lightweight block ciphers for Internet of +ings [11]. +ere that the efficiency of the linear cryptanalysis can be im- are various automated techniques that can be used to build proved by use of chosen plaintexts. +e authors in [5] distinguishers against block ciphers [12–14]. Because re- proposed a zero-correlation linear cryptanalysis, which is a sistance against differential cryptanalysis is an important key recovery technique. +e MITM attack, which employs a design criterion for modern block ciphers, most designs rely 2 Security and Communication Networks on finding some upper bound on probability of differential +e studies on the ML-based cryptanalysis can be characteristics [12]. +e authors in [13] proposed a truncated classified as follows: first, some studies focused on finding searching algorithm which identifies differential character- the characteristics of block ciphers by using ML technolo- istics as well as high probability differential paths. +e au- gies. +e authors in [18] used a recurrent neural network to thors in [14] applied a mixed integer linear programming find the differential characteristics of block ciphers, where (MILP) to search for differential characteristics and linear the recurrent neural network represents the substitution approximations in ARX ciphers. However, most automated functions of a block cipher. +e author in [19] applied an techniques have endeavoured to search for differential artificial neural network to automate attacks on the classical characteristics and linear approximations. Hence, the ma- ciphers of a Caesar cipher, a Vigenere` cipher, and a sub- chine learning- (ML-) based cryptanalysis can be a candidate stitution cipher, by exploiting known statistical weakness. to solve the above problems. +ey trained a neural network to recover the key by pro- +is paper proposes a generic deep learning- (DL-) based viding the relative frequencies of ciphertext letters. Recent cryptanalysis model that finds the key from known plain- work [20] experimentally showed that a CipherGAN, which text-ciphertext pairs and shows the feasibility of the DL- is a tool based on a generative adversarial network (GAN), based cryptanalysis by applying it to lightweight block ci- can crack language data enciphered using shift and Vigenere` phers. Specifically, we try to utilize deep neural networks ciphers. (DNNs) to find the key from known plaintexts. +e con- Second, some studies used ML technologies to classify tribution of this paper is two-fold: first, we develop a generic encrypted traffic or to identify the cryptographic algorithm and automated cryptanalysis model based on the DL. +e from ciphertexts. In [21], an ML-based traffic classification proposed DL-based cryptanalysis is a promising step to- was introduced to identify SSH and Skype encrypted traffic. wards a more efficient and automated test for checking the +e authors in [22] constructed three ML-based classifica- safety of emerging lightweight block ciphers. Second, we tion protocols to classify encrypted data. +ey showed the perform the DL-based attacks on lightweight block ciphers, three protocols, hyperplane decision, Na¨ıve Bayes, and such as S-DES, Simon, and Speck. In our knowledge, this is decision trees, efficiently perform a classification when the first attempt to successfully break the full rounds of running on real medication data sets. +e authors in [23] Simon32/64 and Speck32/64 although we apply the text- used a support vector machine (SVM) technique to identify based key for the block ciphers. five block cryptographic algorithms, AES, Blowfish, 3DES, +e remainder of this paper is organized as follows: RC5, and DES, from ciphertexts. +e authors in [24] pro- Section 2 presents the related work; Section 3 describes the posed an unsupervised learning cost function for a sequence attack model for cryptanalysis; Section 4 introduces the DL- classifier without labelled data, and they showed how it can based approach for the cryptanalysis of lightweight block be applied in order to break the Caesar cipher. ciphers and presents the structure of the DNN model; +ird, other researchers have endeavoured to find out Section 5 describes how to learn and evaluate the model; in the mapping relationship between plaintexts, ciphertexts, Section 6, we apply the DL-based cryptanalysis to light- and the key, but there are few scientific publications. +e weight block ciphers and evaluate the performance of the work in [25] reported astonishing results for attacking the DL-based cryptanalysis; finally, Section 7 concludes this DES and the Triple DES, where a neural network was used to paper. find the plaintexts from the ciphertexts. +e authors in [26] Notations: we give some notations, which will be used in used a neural network to find out the mapping relationship the rest of this paper. A plaintext and ciphertext are, re- between plaintexts, ciphertexts, and the key in simplified spectively, denoted by p � (p0, p1, ..., pn−1) and c � (c0, c1, ..., DES (S-DES). +e author in [27] developed a feedforward cn−1), where n is the block size, pi is the ith bit of the neural network that discovers the plaintext from the ci- plaintext, ci is the ith bit of the ciphertext, and pi; ci ∈ f0; 1 g. phertext without the key in the AES cipher. +e authors in A key is denoted by k � (k0, k1, ..., km−1), where m is the key [28] attacked on the round-reduced Speck32/64 by using j length and ki is the ith bit of the key, ki ∈ f0; 1 g. Let kji deep residual neural networks, where they trained the neural denote the key bits from the ith bit to the jth bit of the key, networks to distinguish the output of Speck with a given j that is, kji ≜ (ki; ki+1; ... ; kj). A block cipher is specified by input difference based on the chosen plaintext attack. +e an encryption function, E(p, k), that is, c � E(p, k). attack in [28] is similar to the classical differential crypt- analysis. However, the previous work failed to attack the full 2. Related Work rounds of lightweight block ciphers, and moreover, they failed to develop a generic deep learning- (DL-) based ML has been successfully applied in a wide range of areas cryptanalysis model.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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]
  • Integral Cryptanalysis on Full MISTY1⋆
    Integral Cryptanalysis on Full MISTY1? Yosuke Todo NTT Secure Platform Laboratories, Tokyo, Japan [email protected] Abstract. MISTY1 is a block cipher designed by Matsui in 1997. It was well evaluated and standardized by projects, such as CRYPTREC, ISO/IEC, and NESSIE. In this paper, we propose a key recovery attack on the full MISTY1, i.e., we show that 8-round MISTY1 with 5 FL layers does not have 128-bit security. Many attacks against MISTY1 have been proposed, but there is no attack against the full MISTY1. Therefore, our attack is the first cryptanalysis against the full MISTY1. We construct a new integral characteristic by using the propagation characteristic of the division property, which was proposed in 2015. We first improve the division property by optimizing a public S-box and then construct a 6-round integral characteristic on MISTY1. Finally, we recover the secret key of the full MISTY1 with 263:58 chosen plaintexts and 2121 time complexity. Moreover, if we can use 263:994 chosen plaintexts, the time complexity for our attack is reduced to 2107:9. Note that our cryptanalysis is a theoretical attack. Therefore, the practical use of MISTY1 will not be affected by our attack. Keywords: MISTY1, Integral attack, Division property 1 Introduction MISTY [Mat97] is a block cipher designed by Matsui in 1997 and is based on the theory of provable security [Nyb94,NK95] against differential attack [BS90] and linear attack [Mat93]. MISTY has a recursive structure, and the component function has a unique structure, the so-called MISTY structure [Mat96].
    [Show full text]
  • The First Biclique Cryptanalysis of Serpent-256
    The First Biclique Cryptanalysis of Serpent-256 Gabriel C. de Carvalho1, Luis A. B. Kowada1 1Instituto de Computac¸ao˜ – Universidade Federal Fluminense (UFF) – Niteroi´ – RJ – Brazil Abstract. The Serpent cipher was one of the finalists of the AES process and as of today there is no method for finding the key with fewer attempts than that of an exhaustive search of all possible keys, even when using known or chosen plaintexts for an attack. This work presents the first two biclique attacks for the full-round Serpent-256. The first uses a dimension 4 biclique while the second uses a dimension 8 biclique. The one with lower dimension covers nearly 4 complete rounds of the cipher, which is the reason for the lower time complex- ity when compared with the other attack (which covers nearly 3 rounds of the cipher). On the other hand, the second attack needs a lot less pairs of plain- texts for it to be done. The attacks require 2255:21 and 2255:45 full computations of Serpent-256 using 288 and 260 chosen ciphertexts respectively with negligible memory. 1. Introduction The Serpent cipher is, along with MARS, RC6, Twofish and Rijindael, one of the AES process finalists [Nechvatal et al. 2001] and has not had, since its proposal, its full round versions attacked. It is a Substitution Permutation Network (SPN) with 32 rounds, 128 bit block size and accepts keys of sizes 128, 192 and 256 bits. Serpent has been targeted by several cryptanalysis [Kelsey et al. 2000, Biham et al. 2001b, Biham et al.
    [Show full text]
  • Related-Key Statistical Cryptanalysis
    Related-Key Statistical Cryptanalysis Darakhshan J. Mir∗ Poorvi L. Vora Department of Computer Science, Department of Computer Science, Rutgers, The State University of New Jersey George Washington University July 6, 2007 Abstract This paper presents the Cryptanalytic Channel Model (CCM). The model treats statistical key recovery as communication over a low capacity channel, where the channel and the encoding are determined by the cipher and the specific attack. A new attack, related-key recovery – the use of n related keys generated from k independent ones – is defined for all ciphers vulnera- ble to single-key recovery. Unlike classical related-key attacks such as differential related-key cryptanalysis, this attack does not exploit a special structural weakness in the cipher or key schedule, but amplifies the weakness exploited in the basic single key recovery. The related- key-recovery attack is shown to correspond to the use of a concatenated code over the channel, where the relationship among the keys determines the outer code, and the cipher and the attack the inner code. It is shown that there exists a relationship among keys for which the communi- cation complexity per bit of independent key is finite, for any probability of key recovery error. This may be compared to the unbounded communication complexity per bit of the single-key- recovery attack. The practical implications of this result are demonstrated through experiments on reduced-round DES. Keywords: related keys, concatenated codes, communication channel, statistical cryptanalysis, linear cryptanalysis, DES Communicating Author: Poorvi L. Vora, [email protected] ∗This work was done while the author was in the M.S.
    [Show full text]
  • Bicliques for Preimages: Attacks on Skein-512 and the SHA-2 Family
    Bicliques for Preimages: Attacks on Skein-512 and the SHA-2 family Dmitry Khovratovich1 and Christian Rechberger2 and Alexandra Savelieva3 1Microsoft Research Redmond, USA 2DTU MAT, Denmark 3National Research University Higher School of Economics, Russia Abstract. We present the new concept of biclique as a tool for preimage attacks, which employs many powerful techniques from differential cryptanalysis of block ciphers and hash functions. The new tool has proved to be widely applicable by inspiring many authors to publish new re- sults of the full versions of AES, KASUMI, IDEA, and Square. In this paper, we demonstrate how our concept results in the first cryptanalysis of the Skein hash function, and describe an attack on the SHA-2 hash function with more rounds than before. Keywords: SHA-2, SHA-256, SHA-512, Skein, SHA-3, hash function, meet-in-the-middle attack, splice-and-cut, preimage attack, initial structure, biclique. 1 Introduction The last years saw an exciting progress in preimage attacks on hash functions. In contrast to collision search [29, 26], where differential cryptanalysis has been in use since 90s, there had been no similarly powerful tool for preimages. The situation changed dramatically in 2008, when the so-called splice-and-cut framework has been applied to MD4 and MD5 [2, 24], and later to SHA-0/1/2 [1, 3], Tiger [10], and other primitives. Despite amazing results on MD5, the applications to SHA-x primitives seemed to be limited by the internal properties of the message schedule procedures. The only promising element, the so-called initial structure tool, remained very informal and complicated.
    [Show full text]
  • 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.
    [Show full text]
  • On the Related-Key Attacks Against Aes*
    THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 13, Number 4/2012, pp. 395–400 ON THE RELATED-KEY ATTACKS AGAINST AES* Joan DAEMEN1, Vincent RIJMEN2 1 STMicroElectronics, Belgium 2 KU Leuven & IBBT (Belgium), Graz University of Technology, Austria E-mail: [email protected] Alex Biryukov and Dmitry Khovratovich presented related-key attacks on AES and reduced-round versions of AES. The most impressive of these were presented at Asiacrypt 2009: related-key attacks against the full AES-256 and AES-192. We discuss the applicability of these attacks and related-key attacks in general. We model the access of the attacker to the key in the form of key access schemes. Related-key attacks should only be considered with respect to sound key access schemes. We show that defining a sound key access scheme in which the related-key attacks against AES-256 and AES- 192 can be conducted, is possible, but contrived. Key words: Advanced Encryption Standard, AES, security, related-key attacks. 1. INTRODUCTION Since the start of the process to select the Advanced Encryption Standard (AES), the block cipher Rijndael, which later became the AES, has been scrutinized extensively for security weaknesses. The initial cryptanalytic results can be grouped into three categories. The first category contains attacks variants that were weakened by reducing the number of rounds [0]. The second category contains observations on mathematical properties of sub-components of the AES, which don’t lead to a cryptanalytic attack [0]. The third category consists of side-channel attacks, which target deficiencies in hardware or software implementations [0].
    [Show full text]
  • A Practical Attack on the Fixed RC4 in the WEP Mode
    A Practical Attack on the Fixed RC4 in the WEP Mode Itsik Mantin NDS Technologies, Israel [email protected] Abstract. In this paper we revisit a known but ignored weakness of the RC4 keystream generator, where secret state info leaks to the gen- erated keystream, and show that this leakage, also known as Jenkins’ correlation or the RC4 glimpse, can be used to attack RC4 in several modes. Our main result is a practical key recovery attack on RC4 when an IV modifier is concatenated to the beginning of a secret root key to generate a session key. As opposed to the WEP attack from [FMS01] the new attack is applicable even in the case where the first 256 bytes of the keystream are thrown and its complexity grows only linearly with the length of the key. In an exemplifying parameter setting the attack recov- ersa16-bytekeyin248 steps using 217 short keystreams generated from different chosen IVs. A second attacked mode is when the IV succeeds the secret root key. We mount a key recovery attack that recovers the secret root key by analyzing a single word from 222 keystreams generated from different IVs, improving the attack from [FMS01] on this mode. A third result is an attack on RC4 that is applicable when the attacker can inject faults to the execution of RC4. The attacker derives the internal state and the secret key by analyzing 214 faulted keystreams generated from this key. Keywords: RC4, Stream ciphers, Cryptanalysis, Fault analysis, Side- channel attacks, Related IV attacks, Related key attacks. 1 Introduction RC4 is the most widely used stream cipher in software applications.
    [Show full text]
  • New Cryptanalysis of Block Ciphers with Low Algebraic Degree
    New Cryptanalysis of Block Ciphers with Low Algebraic Degree Bing Sun1,LongjiangQu1,andChaoLi1,2 1 Department of Mathematics and System Science, Science College of National University of Defense Technology, Changsha, China, 410073 2 State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, China, 10039 happy [email protected], ljqu [email protected] Abstract. Improved interpolation attack and new integral attack are proposed in this paper, and they can be applied to block ciphers using round functions with low algebraic degree. In the new attacks, we can determine not only the degree of the polynomial, but also coefficients of some special terms. Thus instead of guessing the round keys one by one, we can get the round keys by solving some algebraic equations over finite field. The new methods are applied to PURE block cipher successfully. The improved interpolation attacks can recover the first round key of 8-round PURE in less than a second; r-round PURE with r ≤ 21 is breakable with about 3r−2 chosen plaintexts and the time complexity is 3r−2 encryptions; 22-round PURE is breakable with both data and time complexities being about 3 × 320. The new integral attacks can break PURE with rounds up to 21 with 232 encryptions and 22-round with 3 × 232 encryptions. This means that PURE with up to 22 rounds is breakable on a personal computer. Keywords: block cipher, Feistel cipher, interpolation attack, integral attack. 1 Introduction For some ciphers, the round function can be described either by a low degree polynomial or by a quotient of two low degree polynomials over finite field with characteristic 2.
    [Show 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.
    [Show full text]