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The Exact Multi-user Security of 2-Key Triple DES

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Topics in Cryptology – CT-RSA 2024 (CT-RSA 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14643))

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Abstract

We study the tight multi-user (mu) security of 2-key triple encryption (2kTE) with its application to 2-key TDES. With an n-bit block and k-bit key primitive block cipher, our new mu lower bound regarding the number of primitive queries is \(2^{\min \{2k,k+n\}}/q\) with \(q\) construction queries, which matches the previous best attacks and is tight. The bound ensures \((112 - \log _2 q)\)-bit security with 2-key TDES, and this can be used to evaluate and predict the security of systems supporting 2-key TDES for legacy use. We finally show that the FX construction does not efficiently improve the mu security with 2kTE, unlike the previous result with 3-key triple encryption appeared in CCS 2022. We show a concrete key-recovery attack with \(O(2^{n+k}/q)\) primitive queries.

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Notes

  1. 1.

    The security of the single encryption is k bits by an exhaustive key search.

  2. 2.

    [9] is better with \(k<n\), e.g., DES, but it is out of the scope of [11] because \(q = 2^k\).

  3. 3.

    This is because in the ideal world, a random permutation and the underlying ideal cipher are independently defined.

  4. 4.

    Thus \(X^{(\alpha _1)} = M^{(\nu , \alpha )}\), \(W^{(\alpha _1)} = K_1^{(\nu )}\), and \(W^{(\alpha _2)} = K_2^{(\nu )}\).

  5. 5.

    This is because for each \(\nu \in [u]\), \(K_2^{(\nu )}\) is used at only the 2nd round.

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Authors and Affiliations

  1. Mitsubishi Electric Corporation, Kamakura, Kanagawa, Japan

    Yusuke Naito

  2. NTT Social Informatics Laboratories, Tokyo, Japan

    Yu Sasaki

  3. The University of Electro-Communications, Tokyo, Japan

    Takeshi Sugawara

Authors
  1. Yusuke Naito
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  2. Yu Sasaki
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  3. Takeshi Sugawara
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Correspondence to Yusuke Naito .

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  1. University of Klagenfurt, Klagenfurt, Austria

    Elisabeth Oswald

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Naito, Y., Sasaki, Y., Sugawara, T. (2024). The Exact Multi-user Security of 2-Key Triple DES. In: Oswald, E. (eds) Topics in Cryptology – CT-RSA 2024. CT-RSA 2024. Lecture Notes in Computer Science, vol 14643. Springer, Cham. https://doi.org/10.1007/978-3-031-58868-6_5

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  • DOI: https://doi.org/10.1007/978-3-031-58868-6_5

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