Abstract
Impossible-differential cryptanalysis finds the correct round-key of a block cipher by eliminating wrong guesses which do not satisfy some impossible path(s). In this paper, we report our parallel implementation of the impossible-differential cryptanalysis of five-round AES-128, originally proposed by Biham and Keller [4]. In this attack, the time complexity is \(2^{31}\) and the data complexity is \(2^{29.5}\). But the primary memory requirement is very high, about 4 TB, making the attack somewhat impractical to implement. The first practical implementation of this attack appears in Kakarla et al. [11], where the primary memory requirement is reduced to 128.5 GB, and the running time achieved is 48 h. Here, we propose an improvement of the attack by exploiting data and task parallelism. We use a nine-node cluster (one master node and eight worker nodes) to implement the attack. In our attack, the time complexity and the data complexity remain the same as [11], but the primary memory requirement is reduced to 96.5 GB per node. This parallelism helps us retrieve the full key in only 6.5 mins.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bahrak, B., Aref, M.R.: Impossible differential attack on seven-round AES-128. IET Inf. Secur. 2(2), 28–32 (2008). https://doi.org/10.1049/iet-ifs:20070078
Bar-On, A., Dunkelman, O., Keller, N., Ronen, E., Shamir, A.: Improved key recovery attacks on reduced-round AES with practical data and memory complexities. In: Advances in Cryptology - CRYPTO 2018–38th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19–23, 2018, Proceedings, Part II, pp. 185–212 (2018). https://doi.org/10.1007/978-3-319-96881-0_7
Biham, Eli, Biryukov, Alex, Shamir, Adi: Cryptanalysis of skipjack reduced to 31 rounds using impossible differentials. In: Stern, Jacques (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 12–23. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_2
Biham, E., Keller, N.: Cryptanalysis of reduced variants of rijndael. In: 3rd AES Conference, vol. 230 (2000)
Biham, E., Shamir, A.: Differential Cryptanalysis of the Data Encryption Standard. Springer-Verlag, Berlin (1993)
Bogdanov, A., Khovratovich, D., Rechberger, C.: Biclique cryptanalysis of the full AES. In: Advances in Cryptology - ASIACRYPT 2011–17th International Conference on the Theory and Application of Cryptology and Information Security, Seoul, South Korea, December 4–8, 2011. Proceedings, pp. 344–371 (2011). https://doi.org/10.1007/978-3-642-25385-0_19
Cheon, Jung Hee, Kim, MunJu, Kim, Kwangjo, Jung-Yeun, Lee, Kang, SungWoo: Improved impossible differential cryptanalysis of rijndael and crypton. In: Kim, Kwangjo (ed.) ICISC 2001. LNCS, vol. 2288, pp. 39–49. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45861-1_4
Daemen, J., Rijmen, V.: The Design of Rijndael: AES - The Advanced Encryption Standard. Information Security and Cryptography, Springer, Berlin (2002). https://doi.org/10.1007/978-3-662-04722-4
Ferguson, Niels, Kelsey, John, Lucks, Stefan, Schneier, Bruce, Stay, Mike, Wagner, David, Whiting, Doug: Improved cryptanalysis of rijndael. In: Goos, Gerhard, Hartmanis, Juris, van Leeuwen, Jan, Schneier, Bruce (eds.) FSE 2000. LNCS, vol. 1978, pp. 213–230. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44706-7_15
Grassi, L.: Mixture differential cryptanalysis: a new approach to distinguishers and attacks on round-reduced AES. IACR Trans. Symmetric Cryptol. 2018(2), 133–160 (2018). https://doi.org/10.13154/tosc.v2018.i2.133-160
Kakarla, S., Mandava, S., Saha, D., Roy Chowdhury, D.: On the practical implementation of impossible differential cryptanalysis on reduced-round AES. In: Applications and Techniques in Information Security - 8th International Conference, ATIS 2017, Auckland, New Zealand, July 6–7, 2017, Proceedings, pp. 58–72 (2017). https://doi.org/10.1007/978-981-10-5421-1_6
Mala, H., Dakhilalian, M., Rijmen, V., Modarres-Hashemi, M.: Improved impossible differential cryptanalysis of 7-round AES-128. In: Progress in Cryptology - INDOCRYPT 2010–11th International Conference on Cryptology in India, Hyderabad, India, December 12–15 2010, Proceedings, pp. 282–291 (2010). https://doi.org/10.1007/978-3-642-17401-8_20
Phan, R.C.: Impossible differential cryptanalysis of 7-round advanced encryption standard (AES). Inf. Process. Lett. 91(1), 33–38 (2004). https://doi.org/10.1016/j.ipl.2004.02.018
Tunstall, M.: Improved “partial sums”-based square attack on AES. IACR Cryptology ePrint Archive 2012, 280 (2012). http://eprint.iacr.org/2012/280
Zhang, W., Wu, W., Feng, D.: New results on impossible differential cryptanalysis of reduced AES. In: Information Security and Cryptology - ICISC 2007, 10th International Conference, Seoul, Korea, November 29–30, 2007, Proceedings, pp. 239–250 (2007). https://doi.org/10.1007/978-3-540-76788-6_19
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Pal, D., Agrawal, D., Das, A., Chowdhury, D.R. (2019). An Efficient Parallel Implementation of Impossible-Differential Cryptanalysis for Five-Round AES-128. In: Bhasin, S., Mendelson, A., Nandi, M. (eds) Security, Privacy, and Applied Cryptography Engineering. SPACE 2019. Lecture Notes in Computer Science(), vol 11947. Springer, Cham. https://doi.org/10.1007/978-3-030-35869-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-35869-3_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35868-6
Online ISBN: 978-3-030-35869-3
eBook Packages: Computer ScienceComputer Science (R0)