nach oben

Erschienen in:

2016 | OriginalPaper | Buchkapitel

MILP-Based Automatic Search Algorithms for Differential and Linear Trails for Speck

verfasst von : Kai Fu, Meiqin Wang, Yinghua Guo, Siwei Sun, Lei Hu

Erschienen in: Fast Software Encryption

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In recent years, Mixed Integer Linear Programming (MILP) has been successfully applied in searching for differential characteristics and linear approximations in block ciphers and has produced the significant results for some ciphers such as SIMON (a family of lightweight and hardware-optimized block ciphers designed by NSA) etc. However, in the literature, the MILP-based automatic search algorithm for differential characteristics and linear approximations is still infeasible for block ciphers such as ARX constructions. In this paper, we propose an MILP-based method for automatic search for differential characteristics and linear approximations in ARX ciphers. By researching the properties of differential characteristic and linear approximation of modular addition in ARX ciphers, we present a method to describe the differential characteristic and linear approximation with linear inequalities under the assumptions of independent inputs to the modular addition and independent rounds. We use this representation as an input to the publicly available MILP optimizer Gurobi to search for differential characteristics and linear approximations for ARX ciphers. As an illustration, we apply our method to Speck, a family of lightweight and software-optimized block ciphers designed by NSA, which results in the improved differential characteristics and linear approximations compared with the existing ones. Moreover, we provide the improved differential attacks on Speck48, Speck64, Speck96 and Speck128, which are the best attacks on them in terms of the number of rounds.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Automatic Search for Key-Bridging Technique: Applications to LBlock and TWINE

Nächstes Kapitel Automatic Search for the Best Trails in ARX: Application to Block Cipher Speck

Although SIMON has no S-box, the And and XOR operations for SIMON could be regarded as one S-box. So they also applied the method to SIMON.

ARX operation: modular addition, bit rotation and XOR.

Abed, F., List, E., Lucks, S., Wenzel, J.: Differential cryptanalysis of round-reduced simon and speck. In: Cid, C., Rechberger, C. (eds.) FSE 2014. LNCS, vol. 8540, pp. 525–545. Springer, Heidelberg (2015)

Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK famillies of lightweight block ciphers. Cryptology ePrint Archive, report 2013/543 (2013). http://eprint.iacr.org/

Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4(1), 3–72 (1991)MathSciNetCrossRefMATH

Biryukov, A., Velichkov, V.: Automatic search for differential trails in ARX ciphers. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 227–250. Springer, Heidelberg (2014)CrossRef

Biryukov, A., Velichkov, V., Corre, Y.: Automatic search for the best trails in ARX: application to block cipher speck. In: FSE 2016, Bochum, Germany, 20–23 March ( 2016, to appear)

Biryukov, A., Roy, A., Velichkov, V.: Differential analysis of block ciphers SIMON and SPECK. In: Cid, C., Rechberger, C. (eds.) FSE 2014. LNCS, vol. 8540, pp. 546–570. Springer, Heidelberg (2015)

Biryukov, A., Velichkov, V., Corre, Y.L.: Automatic search for the best trails in ARX: application to block cipher speck. In: FSE 2016. LNCS. Springer (to appear)

Cplex, I.I.: IBM software group. User-Manual CPLEX (2011)

Dinur, I.: Improved differential cryptanalysis of round-reduced speck. In: Joux, A., Youssef, A. (eds.) SAC 2014. LNCS, vol. 8781, pp. 147–164. Springer, Heidelberg (2014)CrossRef

10.

De Cannière, C., Rechberger, C.: Finding SHA-1 characteristics: general results and applications. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 1–20. Springer, Heidelberg (2006)CrossRef

11.

Gurobi Optimization: Gurobi Optimizer Reference Manual (2013). http://www.gurobi.com

12.

Leurent, G.: Construction of differential characteristics in ARX designs-application to skein. Cryptology ePrint Archive, 2012/668 (2012). https://eprint.iacr.org/

13.

Lipmaa, H., Moriai, S.: Efficient algorithms for computing differential properties of addition. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 336–350. Springer, Heidelberg (2002)CrossRef

14.

Liu, M., Chen, J.: Improved linear attacks on the chinese block cipher standard. JCST 29(6), 1123–1133 (2014). SpringerMathSciNet

15.

Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)

16.

Matsui, M.: On Correlation between the order of s-boxes and the strength of DES. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 366–375. Springer, Heidelberg (1995)

17.

Mendel, F., Nad, T., Schläffer, M.: Finding SHA-2 characteristics: searching through a minefield of contradictions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 288–307. Springer, Heidelberg (2011)CrossRef

18.

Mouha, N., Wang, Q., Gu, D., Preneel, B.: Differential and linear cryptanalysis using mixed-integer linear programming. In: Wu, C.-K., Yung, M., Lin, D. (eds.) Inscrypt 2011. LNCS, vol. 7537, pp. 57–76. Springer, Heidelberg (2012)CrossRef

19.

Nyberg, K., Wallén, J.: Improved linear distinguishers for SNOW 2.0. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 144–162. Springer, Heidelberg (2006)CrossRef

20.

Stein, W., et al.: Sage: Open Source Mathematical Software (2008)

21.

Sun, S., Hu, L., Song, L., Xie, Y., Wang, P.: Automatic security evaluation of block ciphers with S-bP structures against related-key differential attacks. In: Lin, D., Xu, S., Yung, M. (eds.) Inscrypt 2013. LNCS, vol. 8567, pp. 39–51. Springer, Heidelberg (2014)

22.

Sun, S., Hu, L., Wang, P., Qiao, K., Ma, X., Song, L.: Automatic security evaluation and (related-key) differential characteristic search: application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 158–178. Springer, Heidelberg (2014)

23.

Sun, S., Hu, L., Qiao, K., Ma, X., Song, L.: Automatic security evaluation and (related-key) differential characteristic search: application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers. Cryptology ePrint Archive, report 2013/676 (2013). https://eprint.iacr.org/

24.

Sun, S., Hu, L., Wang, M., Wang, P., Qiao, K., Ma, X., Shi, D., Song, L., Fu, K.: Towards finding the best characteristics of some bit-oriented block ciphers and automatic enumeration of (related-key) differential and linear characteristics with predefined properties. Cryptology ePrint Archive, report 2014/747 (2014). https://eprint.iacr.org/

25.

Wallén, J.: Linear approximations of addition modulo 2\(^{n}\). In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 261–273. Springer, Heidelberg (2003)CrossRef

26.

Wang, G., Keller, N., Dunkelman, O.: The delicate issues of addition with respect to XOR differences. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 212–231. Springer, Heidelberg (2007)CrossRef

27.

Winnen, L.: Sage S-box MILP toolkit. http://www.ecrypt.eu.org/tools/sage-s-box-milp-toolkit

28.

Wu, S., Wang, M.: Security Evaluation against differential cryptanalysis for block cipher structures. Cryptology ePrint Archive, report 2011/551 (2011). https://eprint.iacr.org/

29.

Wu, S., Wu, H., Huang, T., Wang, M., Wu, W.: Leaked-state-forgery attack against the authenticated encryption algorithm ALE. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 377–404. Springer, Heidelberg (2013)CrossRef

30.

Yao, Y., Zhang, B., Wu, W.: Automatic search for linear trails of the SPECK family. In: López, J., Mitchell, C.J. (eds.) ISC 2015. LNCS, vol. 9290, pp. 158–176. Springer, Heidelberg (2015)CrossRef

Titel: MILP-Based Automatic Search Algorithms for Differential and Linear Trails for Speck
verfasst von: Kai Fu
Meiqin Wang
Yinghua Guo
Siwei Sun
Lei Hu
Verlag: Springer Berlin Heidelberg
Buch: Fast Software Encryption
Print ISBN: 978-3-662-52992-8

Electronic ISBN: 978-3-662-52993-5

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-662-52993-5_14

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"