Rotational Rebound Attacks on Reduced Skein
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Improved Cryptanalysis of the Reduced Grøstl Compression Function, ECHO Permutation and AES Block Cipher
Improved Cryptanalysis of the Reduced Grøstl Compression Function, ECHO Permutation and AES Block Cipher Florian Mendel1, Thomas Peyrin2, Christian Rechberger1, and Martin Schl¨affer1 1 IAIK, Graz University of Technology, Austria 2 Ingenico, France [email protected],[email protected] Abstract. In this paper, we propose two new ways to mount attacks on the SHA-3 candidates Grøstl, and ECHO, and apply these attacks also to the AES. Our results improve upon and extend the rebound attack. Using the new techniques, we are able to extend the number of rounds in which available degrees of freedom can be used. As a result, we present the first attack on 7 rounds for the Grøstl-256 output transformation3 and improve the semi-free-start collision attack on 6 rounds. Further, we present an improved known-key distinguisher for 7 rounds of the AES block cipher and the internal permutation used in ECHO. Keywords: hash function, block cipher, cryptanalysis, semi-free-start collision, known-key distinguisher 1 Introduction Recently, a new wave of hash function proposals appeared, following a call for submissions to the SHA-3 contest organized by NIST [26]. In order to analyze these proposals, the toolbox which is at the cryptanalysts' disposal needs to be extended. Meet-in-the-middle and differential attacks are commonly used. A recent extension of differential cryptanalysis to hash functions is the rebound attack [22] originally applied to reduced (7.5 rounds) Whirlpool (standardized since 2000 by ISO/IEC 10118-3:2004) and a reduced version (6 rounds) of the SHA-3 candidate Grøstl-256 [14], which both have 10 rounds in total. -
Basic Cryptography
Basic cryptography • How cryptography works... • Symmetric cryptography... • Public key cryptography... • Online Resources... • Printed Resources... I VP R 1 © Copyright 2002-2007 Haim Levkowitz How cryptography works • Plaintext • Ciphertext • Cryptographic algorithm • Key Decryption Key Algorithm Plaintext Ciphertext Encryption I VP R 2 © Copyright 2002-2007 Haim Levkowitz Simple cryptosystem ... ! ABCDEFGHIJKLMNOPQRSTUVWXYZ ! DEFGHIJKLMNOPQRSTUVWXYZABC • Caesar Cipher • Simple substitution cipher • ROT-13 • rotate by half the alphabet • A => N B => O I VP R 3 © Copyright 2002-2007 Haim Levkowitz Keys cryptosystems … • keys and keyspace ... • secret-key and public-key ... • key management ... • strength of key systems ... I VP R 4 © Copyright 2002-2007 Haim Levkowitz Keys and keyspace … • ROT: key is N • Brute force: 25 values of N • IDEA (international data encryption algorithm) in PGP: 2128 numeric keys • 1 billion keys / sec ==> >10,781,000,000,000,000,000,000 years I VP R 5 © Copyright 2002-2007 Haim Levkowitz Symmetric cryptography • DES • Triple DES, DESX, GDES, RDES • RC2, RC4, RC5 • IDEA Key • Blowfish Plaintext Encryption Ciphertext Decryption Plaintext Sender Recipient I VP R 6 © Copyright 2002-2007 Haim Levkowitz DES • Data Encryption Standard • US NIST (‘70s) • 56-bit key • Good then • Not enough now (cracked June 1997) • Discrete blocks of 64 bits • Often w/ CBC (cipherblock chaining) • Each blocks encr. depends on contents of previous => detect missing block I VP R 7 © Copyright 2002-2007 Haim Levkowitz Triple DES, DESX, -
IMPLEMENTATION and BENCHMARKING of PADDING UNITS and HMAC for SHA-3 CANDIDATES in FPGAS and ASICS by Ambarish Vyas a Thesis Subm
IMPLEMENTATION AND BENCHMARKING OF PADDING UNITS AND HMAC FOR SHA-3 CANDIDATES IN FPGAS AND ASICS by Ambarish Vyas A Thesis Submitted to the Graduate Faculty of George Mason University in Partial Fulfillment of The Requirements for the Degree of Master of Science Computer Engineering Committee: Dr. Kris Gaj, Thesis Director Dr. Jens-Peter Kaps. Committee Member Dr. Bernd-Peter Paris. Committee Member Dr. Andre Manitius, Department Chair of Electrical and Computer Engineering Dr. Lloyd J. Griffiths. Dean, Volgenau School of Engineering Date: ---J d. / q /9- 0 II Fall Semester 2011 George Mason University Fairfax, VA Implementation and Benchmarking of Padding Units and HMAC for SHA-3 Candidates in FPGAs and ASICs A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science at George Mason University By Ambarish Vyas Bachelor of Science University of Pune, 2009 Director: Dr. Kris Gaj, Associate Professor Department of Electrical and Computer Engineering Fall Semester 2011 George Mason University Fairfax, VA Copyright c 2011 by Ambarish Vyas All Rights Reserved ii Acknowledgments I would like to use this oppurtunity to thank the people who have supported me throughout my thesis. First and foremost my advisor Dr.Kris Gaj, without his zeal, his motivation, his patience, his confidence in me, his humility, his diverse knowledge, and his great efforts this thesis wouldn't be possible. It is difficult to exaggerate my gratitude towards him. I also thank Ekawat Homsirikamol for his contributions to this project. He has significantly contributed to the designs and implementations of the architectures. Additionally, I am indebted to my student colleagues in CERG for providing a fun environment to learn and giving invaluable tips and support. -
The Boomerang Attacks on the Round-Reduced Skein-512 *
The Boomerang Attacks on the Round-Reduced Skein-512 ? Hongbo Yu1, Jiazhe Chen3, and Xiaoyun Wang2;3 1 Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China 2 Institute for Advanced Study, Tsinghua University, Beijing 100084, China fyuhongbo,[email protected] 3 Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, School of Mathematics, Shandong University, Jinan 250100, China [email protected] Abstract. The hash function Skein is one of the ¯ve ¯nalists of the NIST SHA-3 competition; it is based on the block cipher Three¯sh which only uses three primitive operations: modular addition, rotation and bitwise XOR (ARX). This paper studies the boomerang attacks on Skein-512. Boomerang distinguishers on the compression function reduced to 32 and 36 rounds are proposed, with complexities 2104:5 and 2454 respectively. Examples of the distinguishers on 28-round and 31- round are also given. In addition, the boomerang distinguishers are applicable to the key-recovery attacks on reduced Three¯sh-512. The complexities for key-recovery attacks reduced to 32-/33- /34-round are about 2181, 2305 and 2424. Because Laurent et al. [14] pointed out that the previous boomerang distinguishers for Three¯sh-512 are in fact not compatible, our attacks are the ¯rst valid boomerang attacks for the ¯nal round Skein-512. Key words: Hash function, Boomerang attack, Three¯sh, Skein 1 Introduction Cryptographic hash functions, which provide integrity, authentication and etc., are very impor- tant in modern cryptology. In 2005, as the most widely used hash functions MD5 and SHA-1 were broken by Wang et al. -
An Analytic Attack Against ARX Addition Exploiting Standard Side-Channel Leakage
An Analytic Attack Against ARX Addition Exploiting Standard Side-Channel Leakage Yan Yan1, Elisabeth Oswald1 and Srinivas Vivek2 1University of Klagenfurt, Klagenfurt, Austria 2IIIT Bangalore, India fyan.yan, [email protected], [email protected] Keywords: ARX construction, Side-channel analysis, Hamming weight, Chosen plaintext attack Abstract: In the last few years a new design paradigm, the so-called ARX (modular addition, rotation, exclusive-or) ciphers, have gained popularity in part because of their non-linear operation’s seemingly ‘inherent resilience’ against Differential Power Analysis (DPA) Attacks: the non-linear modular addition is not only known to be a poor target for DPA attacks, but also the computational complexity of DPA-style attacks grows exponentially with the operand size and thus DPA-style attacks quickly become practically infeasible. We however propose a novel DPA-style attack strategy that scales linearly with respect to the operand size in the chosen-message attack setting. 1 Introduction ever are different: they offer a potentially ‘high reso- lution’ for the adversary. In principle, under suitably Ciphers that base their round function on the sim- strong assumptions, adversaries can not only observe ple combination of modular addition, rotation, and leaks for all instructions that are executed on a proces- exclusive-or, (short ARX) have gained recent popu- sor, but indeed attribute leakage points (more or less larity for their lightweight implementations that are accurately) to instructions (Mangard et al., 2007). suitable for resource constrained devices. Some re- Achieving security in this scenario has proven to cent examples include Chacha20 (Nir and Langley, be extremely challenging, and countermeasures such 2015) and Salsa20 (Bernstein, 2008) family stream as masking (secret sharing) are well understood but ciphers, SHA-3 finalists BLAKE (Aumasson et al., costly (Schneider et al., 2015). -
SHA-3 Conference, March 2012, Skein: More Than Just a Hash Function
Skein More than just a hash function Third SHA-3 Candidate Conference 23 March 2012 Washington DC 1 Skein is Skein-512 • Confusion is common, partially our fault • Skein has two special-purpose siblings: – Skein-256 for extreme memory constraints – Skein-1024 for the ultra-high security margin • But for SHA-3, Skein is Skein-512 – One hash function for all output sizes 2 Skein Architecture • Mix function is 64-bit ARX • Permutation: relocation of eight 64-bit words • Threefish: tweakable block cipher – Mix + Permutation – Simple key schedule – 72 rounds, subkey injection every four rounds – Tweakable-cipher design key to speed, security • Skein chains Threefish with UBI chaining mode – Tweakable mode based on MMO – Provable properties – Every hashed block is unique • Variable size output means flexible to use! – One function for any size output 3 The Skein/Threefish Mix 4 Four Threefish Rounds 5 Skein and UBI chaining 6 Fastest in Software • 5.5 cycles/byte on 64-bit reference platform • 17.4 cycles/byte on 32-bit reference platform • 4.7 cycles/byte on Itanium • 15.2 cycles/byte on ARM Cortex A8 (ARMv7) – New numbers, best finalist on ARMv7 (iOS, Samsung, etc.) 7 Fast and Compact in Hardware • Fast – Skein-512 at 32 Gbit/s in 32 nm in 58 k gates – (57 Gbit/s if processing two messages in parallel) • To maximize hardware performance: – Use a fast adder, rely on simple control structure, and exploit Threefish's opportunities for pipelining – Do not trust your EDA tool to generate an efficient implementation • Compact design: – Small FPGA -
Rotational Cryptanalysis of ARX
Rotational Cryptanalysis of ARX Dmitry Khovratovich and Ivica Nikoli´c University of Luxembourg [email protected], [email protected] Abstract. In this paper we analyze the security of systems based on modular additions, rotations, and XORs (ARX systems). We provide both theoretical support for their security and practical cryptanalysis of real ARX primitives. We use a technique called rotational cryptanalysis, that is universal for the ARX systems and is quite efficient. We illustrate the method with the best known attack on reduced versions of the block cipher Threefish (the core of Skein). Additionally, we prove that ARX with constants are functionally complete, i.e. any function can be realized with these operations. Keywords: ARX, cryptanalysis, rotational cryptanalysis. 1 Introduction A huge number of symmetric primitives using modular additions, bitwise XORs, and intraword rotations have appeared in the last 20 years. The most famous are the hash functions from MD-family (MD4, MD5) and their descendants SHA-x. While modular addition is often approximated with XOR, for random inputs these operations are quite different. Addition provides diffusion and nonlinearity, while XOR does not. Although the diffusion is relatively slow, it is compensated by a low price of addition in both software and hardware, so primitives with relatively high number of additions (tens per byte) are still fast. The intraword rotation removes disbalance between left and right bits (introduced by the ad- dition) and speeds up the diffusion. Many recently design primitives use only XOR, addition, and rotation so they are grouped into a single family ARX (Addition-Rotation-XOR). -
Authenticated Encryption with Small Stretch (Or, How to Accelerate AERO) ⋆
Authenticated Encryption with Small Stretch (or, How to Accelerate AERO) ? Kazuhiko Minematsu NEC Corporation, Japan [email protected] Abstract. Standard form of authenticated encryption (AE) requires the ciphertext to be expanded by the nonce and the authentication tag. These expansions can be problematic when messages are relatively short and communication cost is high. To overcome the problem we propose a new form of AE scheme, MiniAE, which expands the ciphertext only by the single variable integrating nonce and tag. An important feature of MiniAE is that it requires the receiver to be stateful not only for detecting replays but also for detecting forgery of any type. McGrew and Foley already proposed a scheme having this feature, called AERO, however, there is no formal security guarantee based on the provable security framework. We provide a provable security analysis for MiniAE, and show several provably-secure schemes using standard symmetric crypto primitives. This covers a generalization of AERO, hence our results imply a provable security of AERO. Moreover, one of our schemes has a similar structure as OCB mode of operation and enables rate-1 operation, i.e. only one blockcipher call to process one input block. This implies that the computation cost of MiniAE can be as small as encryption-only schemes. Keywords: Authenticated Encryption, Stateful Decryption, Provable Security, AERO, OCB 1 Introduction Authenticated encryption (AE) is a symmetric-key cryptographic function for communication which provides both confidentiality and integrity of messages. A standard form of AE requires the ciphertext to be expanded by the amount of nonce, a never-repeating value maintained by the sender, and the authentication tag. -
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. -
Efficient Hashing Using the AES Instruction
Efficient Hashing Using the AES Instruction Set Joppe W. Bos1, Onur Özen1, and Martijn Stam2 1 Laboratory for Cryptologic Algorithms, EPFL, Station 14, CH-1015 Lausanne, Switzerland {joppe.bos,onur.ozen}@epfl.ch 2 Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom [email protected] Abstract. In this work, we provide a software benchmark for a large range of 256-bit blockcipher-based hash functions. We instantiate the underlying blockci- pher with AES, which allows us to exploit the recent AES instruction set (AES- NI). Since AES itself only outputs 128 bits, we consider double-block-length constructions, as well as (single-block-length) constructions based on RIJNDAEL- 256. Although we primarily target architectures supporting AES-NI, our frame- work has much broader applications by estimating the performance of these hash functions on any (micro-)architecture given AES-benchmark results. As far as we are aware, this is the first comprehensive performance comparison of multi- block-length hash functions in software. 1 Introduction Historically, the most popular way of constructing a hash function is to iterate a com- pression function that itself is based on a blockcipher (this idea dates back to Ra- bin [49]). This approach has the practical advantage—especially on resource-constrained devices—that only a single primitive is needed to implement two functionalities (namely encrypting and hashing). Moreover, trust in the blockcipher can be conferred to the cor- responding hash function. The wisdom of blockcipher-based hashing is still valid today. Indeed, the current cryptographic hash function standard SHA-2 and some of the SHA- 3 candidates are, or can be regarded as, blockcipher-based designs. -
Modes of Operation for Compressed Sensing Based Encryption
Modes of Operation for Compressed Sensing based Encryption DISSERTATION zur Erlangung des Grades eines Doktors der Naturwissenschaften Dr. rer. nat. vorgelegt von Robin Fay, M. Sc. eingereicht bei der Naturwissenschaftlich-Technischen Fakultät der Universität Siegen Siegen 2017 1. Gutachter: Prof. Dr. rer. nat. Christoph Ruland 2. Gutachter: Prof. Dr.-Ing. Robert Fischer Tag der mündlichen Prüfung: 14.06.2017 To Verena ... s7+OZThMeDz6/wjq29ACJxERLMATbFdP2jZ7I6tpyLJDYa/yjCz6OYmBOK548fer 76 zoelzF8dNf /0k8H1KgTuMdPQg4ukQNmadG8vSnHGOVpXNEPWX7sBOTpn3CJzei d3hbFD/cOgYP4N5wFs8auDaUaycgRicPAWGowa18aYbTkbjNfswk4zPvRIF++EGH UbdBMdOWWQp4Gf44ZbMiMTlzzm6xLa5gRQ65eSUgnOoZLyt3qEY+DIZW5+N s B C A j GBttjsJtaS6XheB7mIOphMZUTj5lJM0CDMNVJiL39bq/TQLocvV/4inFUNhfa8ZM 7kazoz5tqjxCZocBi153PSsFae0BksynaA9ZIvPZM9N4++oAkBiFeZxRRdGLUQ6H e5A6HFyxsMELs8WN65SCDpQNd2FwdkzuiTZ4RkDCiJ1Dl9vXICuZVx05StDmYrgx S6mWzcg1aAsEm2k+Skhayux4a+qtl9sDJ5JcDLECo8acz+RL7/ ovnzuExZ3trm+O 6GN9c7mJBgCfEDkeror5Af4VHUtZbD4vALyqWCr42u4yxVjSj5fWIC9k4aJy6XzQ cRKGnsNrV0ZcGokFRO+IAcuWBIp4o3m3Amst8MyayKU+b94VgnrJAo02Fp0873wa hyJlqVF9fYyRX+couaIvi5dW/e15YX/xPd9hdTYd7S5mCmpoLo7cqYHCVuKWyOGw ZLu1ziPXKIYNEegeAP8iyeaJLnPInI1+z4447IsovnbgZxM3ktWO6k07IOH7zTy9 w+0UzbXdD/qdJI1rENyriAO986J4bUib+9sY/2/kLlL7nPy5Kxg3 Et0Fi3I9/+c/ IYOwNYaCotW+hPtHlw46dcDO1Jz0rMQMf1XCdn0kDQ61nHe5MGTz2uNtR3bty+7U CLgNPkv17hFPu/lX3YtlKvw04p6AZJTyktsSPjubqrE9PG00L5np1V3B/x+CCe2p niojR2m01TK17/oT1p0enFvDV8C351BRnjC86Z2OlbadnB9DnQSP3XH4JdQfbtN8 BXhOglfobjt5T9SHVZpBbzhDzeXAF1dmoZQ8JhdZ03EEDHjzYsXD1KUA6Xey03wU uwnrpTPzD99cdQM7vwCBdJnIPYaD2fT9NwAHICXdlp0pVy5NH20biAADH6GQr4Vc -
Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption
Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption Robert Granger1, Philipp Jovanovic2, Bart Mennink3, and Samuel Neves4 1 Laboratory for Cryptologic Algorithms, École polytechnique fédérale de Lausanne, Switzerland, [email protected] 2 Decentralized and Distributed Systems Lab, École polytechnique fédérale de Lausanne, Switzerland, [email protected] 3 Dept. Electrical Engineering, ESAT/COSIC, KU Leuven, and iMinds, Belgium, [email protected] 4 CISUC, Dept. of Informatics Engineering, University of Coimbra, Portugal, [email protected] Abstract. A popular approach to tweakable blockcipher design is via masking, where a certain primitive (a blockcipher or a permutation) is preceded and followed by an easy-to-compute tweak-dependent mask. In this work, we revisit the principle of masking. We do so alongside the introduction of the tweakable Even-Mansour construction MEM. Its masking function combines the advantages of word-oriented LFSR- and powering-up-based methods. We show in particular how recent advancements in computing discrete logarithms over finite fields of characteristic 2 can be exploited in a constructive way to realize highly efficient, constant-time masking functions. If the masking satisfies a set of simple conditions, then MEM is a secure tweakable blockcipher up to the birthday bound. The strengths of MEM are exhibited by the design of fully parallelizable authenticated encryption schemes OPP (nonce-respecting) and MRO (misuse-resistant). If instantiated with a reduced-round BLAKE2b permutation, OPP and MRO achieve speeds up to 0.55 and 1.06 cycles per byte on the Intel Haswell microarchitecture, and are able to significantly outperform their closest competitors.