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September 28, 2016 @ASK2016 Nonlinear Invariant Attack NTT Secure Platform Laboratories and Kobe University Yosuke Todo Copyright©2016 NTT corp. All Rights Reserved. Overview. • Joint work with Gregor Leander and Yu Sasaki. • New type of cryptanalyses. ‐ This attack works on the weak-key setting. • Surprising practical extensions. ‐ Ciphertext-only message recovery attack!! • Good applications. ‐ Scream, iScream, and Midori64. Copyright©2016 NTT corp. All Rights Reserved. 2 Summary of results. Distinguishing attack under known-plaintext setting. Target # of weak keys Data complexity. Distinguishing probability. SCREAM 296 iSCREAM 296 1−푘 푘 1 − 2 Midori64 264 The distinguishing attack incidentally recovers 1 bit of secret key. Message-recovery attack under ciphertext-only setting. Target # of weak keys Maximum # of Data Time recovered bits. complexity. complexity. 96 3 15 SCREAM 2 32 bits 33 ciphertexts 32 = 2 96 3 15 iSCREAM 2 32 bits 33 ciphertexts 32 = 2 64 3 15 Midori64-CTR 2 32h bits 33h ciphertexts 32 ℎ = 2 ℎ ℎ is the number of blocks in the mode of operations. Copyright©2016 NTT corp. All Rights Reserved. 3 Outline 1. Nonlinear invariant attack. ‐ Map of related attacks. • Linear and nonlinear cryptanalyses. • Invariant subspace attack. ‐ Distinguishing attack. 2. Surprising extension toward practical attack. ‐ What’s happened if vulnerable ciphers are used in well- known mode of operations? 3. How to find nonlinear invariant. ‐ Appropriate nonlinear invariants. ‐ How to find nonlinear invariant for KSP round functions. 4. Practical attack on full SCREAM. Copyright©2016 NTT corp. All Rights Reserved. 4 Two streams join in new attacks. Linear attack [Matsui 1993] Nonlinear attack [Harpes et al. 1995] Invariant subspace attack [Gregor et al. 2011] Nonlinear invariant attack [Todo, Gregor, Yu 2016] Copyright©2016 NTT corp. All Rights Reserved. 5 Stream from linear attacks. Linear attack [Matsui 1993] Nonlinear attack [Harpes et al. 1995] Invariant subspace attack [Gregor et al. 2011] Nonlinear invariant attack [Todo, Gregor, Yu 2016] Copyright©2016 NTT corp. All Rights Reserved. 6 Linear attack [Matsui 93]. Key-alternating structure. 푘푖 푥푖 F 푥푖+1 푓푖 푥푖 ⊕ 푓푖+1 푥푖+1 ≈ const 푓푖 푥푖 holds with high probability. 푓푖+1 푥푖+1 next-round 푓푖 and 푓푖+1 are linearly Boolean functions. Copyright©2016 NTT corp. All Rights Reserved. 7 Nonlinear attack [Harpes et al.95]. Key-alternating structure. 푘푖 푥푖 F 푥푖+1 푔푖 푥푖 ⊕ 푔푖+1 푥푖+1 ≈ const 푔푖 푥푖 holds with high probability. 푔푖+1 푥푖+1 next-round 푔푖 and 푔푖+1 are nonlinearly Boolean functions. Copyright©2016 NTT corp. All Rights Reserved. 8 Insurmountable problem. Key-alternating structure. 푘푖 푥푖 F 푥푖+1 • The actual propagation of nonlinear mask depends on the specific value of the state. • Therefore, we cannot join nonlinear masks for two rounds. Copyright©2016 NTT corp. All Rights Reserved. 9 Nonlinear invariant attack. Key-alternating structure. Alternatively, we limit the space of secret keys. 푘푖 푥푖 F 푥푖+1 푔푖 푥푖 ⊕ 푔푖+1 푥푖+1 = const 푔푖 푥푖 with probability one. 푔푖+1 푥푖+1 next-round 푔푖 and 푔푖+1 are nonlinearly Boolean functions. Copyright©2016 NTT corp. All Rights Reserved. 10 Stream from invariant subspace attacks. Linear attack [Matsui 1993] Nonlinear attack [Harpes et al. 1995] Invariant subspace attack [Gregor et al. 2011] Nonlinear invariant attack [Todo, Gregor, Yu 2016] Copyright©2016 NTT corp. All Rights Reserved. 11 Invariant subspace attacks Key-alternating structure. weak keys. 푘푖 푥푖 F 푥푖+1 key-add F U+a U+a U+b next-round Copyright©2016 NTT corp. All Rights Reserved. 12 Nonlinear invarinat attack. Key-alternating structure. weak keys. 푘푖 푥푖 F 푥푖+1 key-add F 푔0 푔0 푔0 푔1 푔1 푔1 next-round Copyright©2016 NTT corp. All Rights Reserved. 13 Nonlinear invarinat attack. Key-alternating structure. weak keys. 푘푖 푥푖 F 푥푖+1 key-add F 푔0 푔0 푔0 푔1 푔1 푔1 next-round Copyright©2016 NTT corp. All Rights Reserved. 14 Distinguishing attack. • If the block cipher has the nonlinear invariant, we can easily distinguish from ideal ciphers. 1. Collect 푘 known plaintexts (푝푖, 푐푖). 2. Compute 푔푝 푝푖 ⊕ 푔푐(푐푖) for 푘 pair. Then 푘 XORs are always the same. The probability that ideal ciphers have this property is 2−푘+1. • At most one bit of information leaks from 푔푝 푝푖 ⊕ 푔푐(푐푖). Copyright©2016 NTT corp. All Rights Reserved. 15 Outline 1. Nonlinear invariant attack. ‐ Map of related attacks. • Linear and nonlinear cryptanalyses. • Invariant subspace attack. ‐ Distinguishing attack. 2. Surprising extension toward practical attack. ‐ What’s happened if vulnerable ciphers are used in well- known mode of operations? 3. How to find nonlinear invariant. ‐ Appropriate nonlinear invariants. ‐ How to find nonlinear invariant for KSP round functions. 4. Practical attack on full SCREAM. Copyright©2016 NTT corp. All Rights Reserved. 16 Practical attacks. strong Chosen-plaintext attacks (CPA) is natural assumption for cryptographers. is debatable in practical case. Assumption. Known-plaintext attacks (KPA) is very weak assumption for cryptographers. sometimes holds in practical case. Ciphertext-only attacks (COA) is unlikely to happen for cryptographers. is information-theoretically impossible w/o assumptions. causes non-negligible risks in practical use if possible. weak Copyright©2016 NTT corp. All Rights Reserved. 17 Our attack assumptions. • Attackers can collect multiple ciphertext blocks whose original message is the same but the IV is different. • Then, we can recover the part of message. 퐸 푘,퐼푉1 Ciphertext block 퐸푘,퐼푉2 Plaintext 퐸푘,퐼푉3 Ciphertext block block Ciphertext block Copyright©2016 NTT corp. All Rights Reserved. 18 Is this assumption practical? • It’s very difficult questions because it depends on applications. • We believe it’s more practical than KPA. • Example of vulnerable application. ‐ Application sometimes sends the ciphertext of a password for the authentication. And, attackers know the behavior of the application. Copyright©2016 NTT corp. All Rights Reserved. 19 CBC mode. P1 P2 P3 Ph IV (C0) EK EK EK EK C1 C2 C3 Ch If Ek has nonlinear invariants, 푔푝 퐶푖−1 ⊕ 푃푖 ⊕ 푔푐 퐶푖 = const Copyright©2016 NTT corp. All Rights Reserved. 20 Message-recovery attacks. • Attackers know IV and ciphertexts, and 푔푝 퐶푖−1 ⊕ 푃푖 ⊕ 푔푐 퐶푖 is always constant. • We collect multiple (퐶푖−1, 퐶푖) whose corresponding 푃푖 is the same. • By guessing 푃푖, we can recover it only from ciphertexts. ‐ Bits of 푃푖 that involve the nonlinear term of the function 푔 can be recovered. ‐ Practically, the time complexity to recover 푡 bits 3 of 푃푖 is at most 푡 . Copyright©2016 NTT corp. All Rights Reserved. 21 Outline 1. Nonlinear invariant attack. ‐ Map of related attacks. • Linear and nonlinear cryptanalyses. • Invariant subspace attack. ‐ Distinguishing attack. 2. Surprising extension toward practical attack. ‐ What’s happened if vulnerable ciphers are used in well- known mode of operations? 3. How to find nonlinear invariant. ‐ Appropriate nonlinear invariants. ‐ How to find nonlinear invariant for KSP round functions. 4. Practical attack on full SCREAM. Copyright©2016 NTT corp. All Rights Reserved. 22 Nonlinear invariant attack. Key-alternating structure. Alternatively, we limit the space of secret keys. 푘푖 푥푖 F 푥푖+1 푔푖 푥푖 ⊕ 푔푖+1 푥푖+1 = const 푔푖 푥푖 with probability one. 푔푖+1 푥푖+1 next-round We have to search for nonlinear invariants that hold in arbitrary number of rounds. Copyright©2016 NTT corp. All Rights Reserved. 23 Nonlinear invariant attack. Key-alternating structure. Alternatively, we limit the space of secret keys. 푘푖 푥푖 F 푥푖+1 푔 푥푖 ⊕ 푔 푥푖+1 = const 푔 푥푖 with probability one. 푔 푥푖+1 next-round The property tribially holds if 푔푖 = 푔푖+1. Copyright©2016 NTT corp. All Rights Reserved. 24 Searching for nonlinear invariants. • Assume that KSP-type round function. S S L S S Copyright©2016 NTT corp. All Rights Reserved. 25 Nonlinear invariants for S-box. 푥1 S 푔푖 푥푖 ⊕ 푔푖 푆 푥푖 = cons 푥2 S L 푥3 S 푥4 S • Because the bit size of S-boxes is generally small, it’s not difficult to find nonlinear invariant for S-boxes. Copyright©2016 NTT corp. All Rights Reserved. 26 Example. • Nonlinear invariant for the S-box in Scream. 푔 푥 = 푥1푥2 ⊕ 푥0 ⊕ 푥2 ⊕ 푥5 8 Then, for all 푥 ∈ 픽2, 푔 푥 = 푔 푆 푥 ⊕ 1. • Nonlinear invariant for the S-box in Midori64. 푔 푥 = 푥2푥3 ⊕ 푥0 ⊕ 푥1 ⊕ 푥2 4 Then, for all 푥 ∈ 픽2, 푔 푥 = 푔 푆 푥 . Copyright©2016 NTT corp. All Rights Reserved. 27 Nonlinear invariant for S-box layer. 푥1 S 푔푖 푥푖 ⊕ 푔푖 푆 푥푖 = cons 푥2 S L 푥3 S 푔 푥 = 푔푖(푥푖) 푖∈Λ 푥4 S • If the function 푔푖 is nonlinear invariant for the th S-box, the function 푖∈Λ 푔푖(푥푖) becomes nonlinear invariant for the S-box layer for any set Λ. Copyright©2016 NTT corp. All Rights Reserved. 28 Nonlinear invariants for key XORing. 푥 1 S 푔 푥 ⊕ 푔 푥 ⊕ 푘 = cons 푥2 S L 푥3 S 푔 푥 = 푔푖(푥푖) 푖∈Λ 푥4 S • If “1s” in 푘 are involved in only linear term of the function 푔, 푔 푥 ⊕ 푘 = 푔 푥 ⊕ 푔(푘). • 푔 푥 ⊕ 푔 푥 ⊕ 푘 = 푔 푘 = cons. Copyright©2016 NTT corp. All Rights Reserved. 29 Example. • Nonlinear invariant for the S-box in Scream. 푔 푥 = 푥1푥2 ⊕ 푥0 ⊕ 푥2 ⊕ 푥5 If 푘1 = 푘2 = 0, 푔 푥 ⊕ 푘 = 푔 푥 ⊕ 푔(푘) • Nonlinear invariant for the S-box in Midori64. 푔 푥 = 푥2푥3 ⊕ 푥0 ⊕ 푥1 ⊕ 푥2 If 푘2 = 푘3 = 0, 푔 푥 ⊕ 푘 = 푔 푥 ⊕ 푔(푘) Copyright©2016 NTT corp. All Rights Reserved. 30 Nonlinear invariant for linear layer. 푥 1 S 푔 푥 ⊕ 푔 퐿 푥 = cons 푥2 S 푛 L 푥3 S 푔 푥 = 푔푖(푥푖) 푖=1 푥4 S • If the linear function is binary orthogonal and there is a quadratic invariant for the S-box, 푛 푔푖=1(푥푖) is nonlinear invariant for the linear layer.
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    D-DOG: Securing Sensitive Data in Distributed Storage Space by Data Division and Out-of-order keystream Generation †Jun Feng, †Yu Chen*, ‡Wei-Shinn Ku, §Zhou Su †Dept. of Electrical & Computer Engineering, SUNY - Binghamton, Binghamton, NY 13902 ‡Dept. of Computer Science & Software Engineering, Auburn University, Auburn, AL 36849 §Dept. of Computer Science, Waseda University, Ohkubo 3-4-1, Shinjyuku, Tokyo 169-8555, Japan {jfeng3, ychen }@binghamton.edu, [email protected], [email protected] ∗ Abstract - Migrating from server-attached storage to system against the attacks/intrusion from outsiders. The distributed storage brings new vulnerabilities in creating a confidentiality and integrity of data are mostly achieved secure data storage and access facility. Particularly it is a using robust cryptograph schemes. challenge on top of insecure networks or unreliable storage However, such a security system is not robust enough to service providers. For example, in applications such as cloud protect the data in distributed storage applications at the computing where data storage is transparent to the owner. It is level of wide area networks. The recent progress of network even harder to protect the data stored in unreliable hosts. technology enables global-scale collaboration over More robust security scheme is desired to prevent adversaries heterogeneous networks under different authorities. For from obtaining sensitive information when the data is in their hands. Meanwhile, the performance gap between the execution instance, in the environment of peer-to-peer (P2P) file speed of security software and the amount of data to be sharing or the distributed storage in cloud computing processed is ever widening. A common solution to close the environment, it enables the concrete data storage to be even performance gap is through hardware implementation.
  • Design and Analysis of Lightweight Block Ciphers : a Focus on the Linear

    Design and Analysis of Lightweight Block Ciphers : a Focus on the Linear

    Design and Analysis of Lightweight Block Ciphers: A Focus on the Linear Layer Christof Beierle Doctoral Dissertation Faculty of Mathematics Ruhr-Universit¨atBochum December 2017 Design and Analysis of Lightweight Block Ciphers: A Focus on the Linear Layer vorgelegt von Christof Beierle Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften an der Fakult¨atf¨urMathematik der Ruhr-Universit¨atBochum Dezember 2017 First reviewer: Prof. Dr. Gregor Leander Second reviewer: Prof. Dr. Alexander May Date of oral examination: February 9, 2018 Abstract Lots of cryptographic schemes are based on block ciphers. Formally, a block cipher can be defined as a family of permutations on a finite binary vector space. A majority of modern constructions is based on the alternation of a nonlinear and a linear operation. The scope of this work is to study the linear operation with regard to optimized efficiency and necessary security requirements. Our main topics are • the problem of efficiently implementing multiplication with fixed elements in finite fields of characteristic two. • a method for finding optimal alternatives for the ShiftRows operation in AES-like ciphers. • the tweakable block ciphers Skinny and Mantis. • the effect of the choice of the linear operation and the round constants with regard to the resistance against invariant attacks. • the derivation of a security argument for the block cipher Simon that does not rely on computer-aided methods. Zusammenfassung Viele kryptographische Verfahren basieren auf Blockchiffren. Formal kann eine Blockchiffre als eine Familie von Permutationen auf einem endlichen bin¨arenVek- torraum definiert werden. Eine Vielzahl moderner Konstruktionen basiert auf der wechselseitigen Anwendung von nicht-linearen und linearen Abbildungen.
  • Scream on MSP430 07282015

    Scream on MSP430 07282015

    Implementation of the SCREAM Tweakable Block Cipher in MSP430 Assembly Language William Diehl George Mason University, Fairfax VA 22033, USA [email protected] Abstract. The encryption mode of the Tweakable Block Cipher (TBC) of the SCREAM Authenticated Cipher is implemented in the MSP430 microcontroller. Assembly language versions of the TBC are prepared using both precomputed tweak keys and tweak keys computed “on-the-fly.” Both versions are compared against published results for the assembly language version of SCREAM on the ATMEL AVR microcontroller, and against the C reference implementation in terms of performance and size. The assembly language version using precomputed tweak keys achieves a speedup of 1.7 and memory savings of 9 percent over the reported SCREAM implementation in the ATMEL AVR. The assembly language version using tweak keys computed “on-the-fly” achieves a speedup of 1.6 over the ATMEL AVR version while reducing memory usage by 15 percent. Keywords: Cryptography, encryption, MSP430, assembly, speed, efficiency 1 Introduction Authenticated ciphers combine the functionality of confidentiality and integrity into one algorithm. In 2014 the Competition for Authenticated Encryption: Security, Applicability, and Robustness (CAESAR) called for submission of authenticated cipher candidates [1]. CAESAR candidates are evaluated in terms of security, size, robustness, flexibility, and performance. Software reference implementations written in C code are required as part of Rounds One and Two submissions. Many of the Round One submissions contained the authors’ evaluations in both hardware and software. Additionally, several Round One submissions investigated the software performance of the authors’ algorithms on various types of platforms, including high-end CPU and resource-constrained microcontrollers suitable for embedded applications.