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Another look at XCB

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Abstract

XCB is a tweakable enciphering scheme (TES) which was first proposed in 2004. The scheme was modified in 2007. We call these two versions of XCB as XCBv1 and XCBv2 respectively. XCBv2 was later proposed as a standard for encryption of sector oriented storage media in IEEE-std 1619.2 2010. There is no known proof of security for XCBv1 but the authors provided a concrete security bound for XCBv2 and a “proof” justifying the bound. In this paper we show that XCBv2 is not secure as a TES by showing an easy distinguishing attack on it. For XCBv2 to be secure, the message space should contain only messages whose lengths are multiples of the block length of the block cipher. Even for such restricted message spaces, the bound that the authors claim is not justified. We show this by pointing out some errors in the proof. For XCBv2 on full block messages, we provide a new security analysis. The resulting bound that can be proved is much worse than what has been claimed by the authors. Further, we provide the first concrete security bound for XCBv1, which holds for all message lengths. In terms of known security bounds, both XCBv1 and XCBv2 are worse compared to existing alternative TESs.

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Notes

  1. While arguing about efficiency of XCB the authors stress on a software implementation of the multiplier which uses pre-computed tables, and in such a software implementation only XCB may have its efficiency comparable with constructions which only uses block ciphers. It is known that in hardware XCB performs worse than all known efficient TES [10].

  2. In [12], the authors use a non-standard terminology. They do not distinguish between a pseudorandom permutation (PRP) and a strong pseudorandom permutation (SPRP). According to their definitions a PRP is what is generally understood as a SPRP.

References

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Acknowledgments

The authors thanks the reviewers for their careful reading of the paper and providing useful comments. Debrup Chakraborty acknowledges the support from project 166763 funded by Consejo Nacional de Ciencia y Tecnología (CONACyT), Mexico.

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Authors and Affiliations

  1. Department of Computer Science, CINVESTAV-IPN, Av. IPN 2508 San Pedro Zacatenco, Mexico City, 07360, Mexico

    Debrup Chakraborty & Vicente Hernandez-Jimenez

  2. Applied Statistics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, 700108, India

    Palash Sarkar

Authors
  1. Debrup Chakraborty
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  2. Vicente Hernandez-Jimenez
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  3. Palash Sarkar
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Corresponding author

Correspondence to Debrup Chakraborty.

Appendix A: XCB in IEEE 1619.2

Appendix A: XCB in IEEE 1619.2

Here we describe XCB verbatim as described in IEEE-std 1619.2, 2010.

  1. 1.

    H ← AES-Enc(K, 0128)

  2. 2.

    K e ← msb k (AES-Enc(K, 0125|0012)|AES-Enc(K, 0125|0102))

  3. 3.

    K d ← msb k (AES-Enc(K, 0125|0112)|AES-Enc(K, 0125|1002))

  4. 4.

    K c ← msb k (AES-Enc(K, 0125|1012)|AES-Enc(K, 0125|1102))

  5. 5.

    A ← P[m − 128 : m − 1]

  6. 6.

    B ← P[0 : m − 127]

  7. 7.

    C ← AES-Enc(K e , A)

  8. 8.

    D ← C ⊕ h 1(H, Z, B)

  9. 9.

    E ← B ⊕ c(K c , D, # B)

  10. 10.

    F ← D ⊕ h 2(H, Z, E)

  11. 11.

    G ← AES-Dec(K d , F)

  12. 12.

    C T ← E|G

In the above description A|B denotes the concatenation of the strings A and B, and # B is the length of B in bits. Here the length of the plaintext P is m bits. Note that the length of B is m − 126 bits and this is also the length of E. The length of G is 128 bits and so the length of CT is m − 126+128=m+2 bits. So, applying the encryption function increases the length by 2 bits.

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Chakraborty, D., Hernandez-Jimenez, V. & Sarkar, P. Another look at XCB. Cryptogr. Commun. 7, 439–468 (2015). https://doi.org/10.1007/s12095-015-0127-8

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  • DOI: https://doi.org/10.1007/s12095-015-0127-8

Keywords

Mathematics Subject Classifications (2010)