Statistical Fault Analysis of Lightweight Tweakable Block Cipher QARMA in the Internet of Everything

Abstract

Based on the ciphertext-only attack(COA) assumption, the statistical fault analysis(SFA) is proposed to break all versions of QARMA in the Internet of Everything(IoE), where suitable strategies are taken into consideration for the uncertainty of tweaks to cover more rounds of fault injections. It also presents the novel double distinguishers of Cramér-von Mises test-Hamming weight(CM-HW) and Kuiper's test-maximum likelihood estimation(KT-MLE) to improve the attacking efficiency. According to the experimental results, the attackers can inject 374 and 726 random faults into the deeper antepenultimate round to recover 128-bit and 256-bit secret keys of QARMA with a reliability of at least 99%, respectively. Hence, QARMA is vulnerable to the SFA in the IoE. The results offer a valuable reference for the lightweight tweakable cryptosystems with the reflection structure and the protection of the cryptographic devices.

Keywords

Internet of Everything(IoE) / side-channel analysis / lightweight tweakable block cipher / statistical fault analysis(SFA) / QARMA

References

[1] SNYDER T, BYRD G. The Internet of Everything[J]. Computer, 2017, 50(6):8-9.

[2] DESAI S, ALHADAD R, CHILAMKURTI N, et al. A survey of privacy preserving schemes in IoE enabled smart grid advanced metering infrastructure[J]. Cluster Computing, 2019, 22(1):43-69.

[3] LIU W, WATANABE Y, SHOJI Y. Vehicle-assisted data delivery in smart city:a deep learning approach[J]. IEEE Transactions on Vehicular Technology, 2020, 69(11):13849-13860.

[4] CHINCHAWADE A J, LAMBA O S. Authentication schemes and security issues in Internet of Everything (IoE) systems[C]// 2020 12th International Conference on Computational Intelligence and Communication Networks,Bhimtal,India. New York: IEEE, 2020:342-345.

[5] PENG P, SOLJANIN E. Covert,low-delay,coded message passing in mobile (IoT) networks[J]. IEEE Transactions on Information Forensics and Security, 2022,17:599-611.

[6] NOSOUHI M R, SOOD K, GROBLER M, et al. Towards spoofing resistant next generation IoT networks[J]. IEEE Transactions on Information Forensics and Security, 2022,17:1669-1683.

[7] BOGDANOV A, KNUDSEN L R, LEANDER G, et al. PRESENT:an ultra-lightweight block cipher[C]// International Workshop on Cryptographic Hardware and Embedded Systems,Vienna,Austria. Berlin: Springer, 2007:450-466.

[8] GUO J, PEYRIN T, POSCHMANN A, et al. The LED block cipher[C]//International Workshop on Cryptographic Hardware and Embedded Systems,Nara,Japan. Berlin: Springer, 2011:326-341.

[9] WU W L, ZHANG L. LBlock:a lightweight block cipher[C]//International Conference on Applied Cryptography and Network Security,Nerja,Spain. Berlin: Springer, 2011:327-344.

[10] LARA-NINO C A, DIAZ-PEREZ A, MORALES-SANDOVAL M. Lightweight hardware architectures for the present cipher in FPGA[J]. IEEE Transactions on Circuits and Systems I:Regular Papers, 2017, 64(9):2544-2555.

[11] MOHD B J, HAYAJNEH T, AHMAD YOUSEF K M, et al. Hardware design and modeling of lightweight block ciphers for secure communications[J]. Future Generation Computer Systems, 2018,83:510-521.

[12] AVANZI R. The QARMA block cipher family:almost MDS matrices over rings with zero divisors,nearly symmetric Even-Mansour constructions with non-involutory central rounds,and search heuristics for low-latency S-boxes[J]. IACR Transactions on Symmetric Cryptology, 2017, 2017(1):4-44.

[13] CHEN Y L. Pseudorandom permutations and functions for lightweight applications[D/OL]. Belgium: KU Leuven, 2022 [2023-04-25]. https://kuleuven.limo.libis.be/discovery/fulldisplay?docid=lirias3682687&context=SearchWebhook&vid=32KUL_KUL:Lirias&search_scope=lirias_profile&tab=LIRIAS&adaptor=SearchWebhook&lang=en.

[14] BORGHOFF J, CANTEAUT A, GüNEYSU T, et al. PRINCE:a low-latency block cipher for pervasive computing applications[C]//International Conference on the Theory and Application of Cryptology and Information Security,Beijing,China. Berlin: Springer, 2012:208-225.

[15] BOURA C, CANTEAUT A, KNUDSEN L R, et al. Reflection ciphers[J]. Designs,Codes and Cryptography, 2017, 82(1):3-25.

[16] LI R J, JIN C H. Meet-in-the-middle attacks on reduced-round QARMA-64/128[J]. The Computer Journal, 2018, 61(8):1158-1165.

[17] LI M Z, HU K, WANG M Q. Related-tweak statistical saturation cryptanalysis and its application on QARMA[J]. IACR Transactions on Symmetric Cryptology, 2019(1):236-263.

[18] ZONG R, DONG X Y. MILP-aided related-tweak/key impossible differential attack and its applications to QARMA,Joltik-BC[J]. IEEE Access, 2019,7:153683-153693.

[19] LIU Y, ZANG T D, GU D W, et al. Improved cryptanalysis of reduced-version QARMA-64/128[J]. IEEE Access, 2020,8:8361-8370.

[20] DU J, WANG W, LI M Z, et al. Related-tweakey impossible differential attack on QARMA-128[J]. Science China Information Sciences, 2021, 65(2):129102.

[21] BONEH D, DEMILLO R A, LIPTON R. On the importance of checking cryptographic protocols for faults[C]//International Conference on the Theory and Applications of Cryptographic Techniques,Konstanz,Germany. Berlin: Springer, 1997:37-51.

[22] ZHANG F, ZHAO X J, GUO S Z, et al. Improved algebraic fault analysis:a case study on Piccolo and applications to other lightweight block ciphers[C]//International Workshop on Constructive Side-Channel Analysis and Secure Design,Paris,France. Berlin: Springer, 2013:62-79.

[23] MORADI A, SHALMANI M T M, SALMASIZADEH M. A generalized method of differential fault attack against AES cryptosystem[C]//International Workshop on Cryptographic Hardware and Embedded Systems,Yokohama,Japan. Berlin: Springer, 2006:91-100.

[24] BIHAM E, GRANBOULAN L, NGUYÊ N P Q. Impossible fault analysis of RC₄ and differential fault analysis of RC₄[C]//International Workshop on Fast Software Encryption,Paris,France. Berlin: Springer, 2005:359-367.

[25] DERBEZ P, FOUQUE P-A, LERESTEUX D. Meet-in-the-middle and impossible differential fault analysis on AES[C]//International Workshop on Cryptographic Hardware and Embedded Systems,Nara,Japan. Berlin: Springer, 2011:274-291.

[26] FUHR T, JAULMES E, LOMNÉ V, et al. Fault attacks on AES with faulty ciphertexts only[C]//Workshop on Fault Diagnosis and Tolerance in Cryptography,Los Alamitos,USA. New York: IEEE, 2013:108-118.

[27] DOBRAUNIG C, EICHLSEDER M, KORAK T, et al. Statistical fault attacks on nonce-based authenticated encryption schemes[C]//International Conference on the Theory and Application of Cryptology and Information Security,Hanoi,Vietnam. Berlin: Springer, 2011:369-395.

[28] LI W, LIAO L F, GU D W, et al. Ciphertext-only fault analysis on the LED lightweight cryptosystem in the Internet of Things[J]. IEEE Transactions on Dependable and Secure Computing, 2019, 16(3):454-461.

[29] LI W, LI J Y, GU D W, et al. Statistical fault analysis of the Simeck lightweight cipher in the ubiquitous sensor networks[J]. IEEE Transactions on Information Forensics and Security, 2021,16:4224-4233.

[30] REED I. A class of multiple-error-correcting codes and the decoding scheme[J]. Transactions of the IRE Professional Group on Information Theory, 1954, 4(4):38-49.

[31] WILKS S S. The large-sample distribution of the likelihood ratio for testing composite hypotheses[J]. The Annals of Mathematical Statistics, 1938, 9(1):60-62.

Funding

National Natural Science Foundation of China(61772129)

National Natural Science Foundation of China(61932014)

National Cryptography Development Fund,China(MMJJ20180101)