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Algebraic Techniques in Differential Cryptanalysis Revisited

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Information Security and Privacy (ACISP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6812))

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Abstract

At FSE 2009, Albrecht et al. proposed a new cryptanalytic method that combines algebraic and differential cryptanalysis. They introduced three new attacks, namely Attack A, Attack B and Attack C. For Attack A, they explain that the time complexity is difficult to determine. The goal of Attacks B and C is to filter out wrong pairs and then recover the key. In this paper, we show that Attack C does not provide an advantage over differential cryptanalysis for typical block ciphers, because it cannot be used to filter out any wrong pairs that satisfy the ciphertext differences. Furthermore, we explain why Attack B provides no advantage over differential cryptanalysis for PRESENT. We verify our results for PRESENT experimentally, using both PolyBoRi and MiniSat. Our work helps to understand which equations are important in the differential-algebraic attack. Based on our findings, we present two new differential-algebraic attacks. Using the first method, our attack on 15-round PRESENT-80 requires 259 chosen plaintexts and has a worst-case time complexity of 273.79 equivalent encryptions. Our new attack on 14-round PRESENT-128 requires 255 chosen plaintexts and has a worst-case time complexity of 2112.83 equivalent encryptions. Although these attacks have a higher time complexity than the differential attacks, their data complexity is lower.

This work was supported in part by the Research Council K.U.Leuven: GOA TENSE, the IAP Program P6/26 BCRYPT of the Belgian State (Belgian Science Policy), and in part by the European Commission through the ICT program under contract ICT-2007-216676 ECRYPT II.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Meiqin Wang & Yue Sun

  2. Department of Electrical Engineering ESAT/SCD-COSIC, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001, Heverlee, Belgium

    Meiqin Wang, Nicky Mouha & Bart Preneel

  3. Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium

    Meiqin Wang, Nicky Mouha & Bart Preneel

Authors
  1. Meiqin Wang
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  2. Yue Sun
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  3. Nicky Mouha
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  4. Bart Preneel
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Editors and Affiliations

  1. Department of Computer Science and Software Engineering, The University of Melbourne, 3010, Victoria, Australia

    Udaya Parampalli

  2. Qualcomm Incorporated, Suite 301, Level 3, 77 King Street, NSW 2000, Sydney, Australia

    Philip Hawkes

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Wang, M., Sun, Y., Mouha, N., Preneel, B. (2011). Algebraic Techniques in Differential Cryptanalysis Revisited. In: Parampalli, U., Hawkes, P. (eds) Information Security and Privacy. ACISP 2011. Lecture Notes in Computer Science, vol 6812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22497-3_9

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  • DOI: https://doi.org/10.1007/978-3-642-22497-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22496-6

  • Online ISBN: 978-3-642-22497-3

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