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International Conference on Information Security and Cryptology

ICISC 2013: Information Security and Cryptology -- ICISC 2013 pp 144–157Cite as

Optimal Storage for Rainbow Tables

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8565))

Abstract

Cryptanalytic time-memory trade-offs were introduced by Martin Hellman in 1980, and they have since had a major impact on practical cryptanalysis. Hellman’s technique has been studied as well as improved significantly, most notably by Philippe Oechslin who introduced the rainbow tables. As it has been highlighted in various papers, the way the memory is handled is extremely important. In this paper, we analytically describe how rainbow tables are currently stored, and we introduce a new structure that considerably reduces the memory requirement. We mathematically analyze these techniques, provide optimal parameterization, and show that our structure is extremely close to the theoretical lower bound. Using our optimized storage for rainbow tables realizes the equivalent of a speedup of three with respect to the naive approach.

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Notes

  1. 1.

    The technique works for inverting any one-way function, but we use the vocabulary of hash functions liberally.

  2. 2.

    We actually need to build several tables this way. The reason for this is that the coverage quickly saturates in Hellman tables. See [7]. Also note that with rainbow tables, although 3 or 4 tables are generally required for a good probability of success, the number of Hellman tables required is usually much bigger.

  3. 3.

    Since the endpoints are sorted, this lookup is inexpensive.

  4. 4.

    Although the word “perfect” is usually attributed to tables without merges in the literature, we find this terminology more intuitive and more adapted.

  5. 5.

    As said above, the constant factor greatly favors rainbow tables [11].

  6. 6.

    Note that endpoints are unique meaning that a zero difference is not possible. One can therefore also decrease the differences by one.

  7. 7.

    This experiment has been done on a laptop with an i5 Intel Processor, with the encoded differences in RAM. We used SHA-1 as a point of comparison for a hash function.

References

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Author information

Authors and Affiliations

  1. Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    Gildas Avoine & Xavier Carpent

  2. INSA de Rennes, IRISA UMR 6074, 35043, Rennes, France

    Gildas Avoine

Authors
  1. Gildas Avoine
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  2. Xavier Carpent
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Corresponding author

Correspondence to Xavier Carpent .

Editor information

Editors and Affiliations

  1. EWHA Womans University, Seoul, Korea, Republic of (South Korea)

    Hyang-Sook Lee

  2. Kookmin University, Seoul, Korea, Republic of (South Korea)

    Dong-Guk Han

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Avoine, G., Carpent, X. (2014). Optimal Storage for Rainbow Tables. In: Lee, HS., Han, DG. (eds) Information Security and Cryptology -- ICISC 2013. ICISC 2013. Lecture Notes in Computer Science(), vol 8565. Springer, Cham. https://doi.org/10.1007/978-3-319-12160-4_9

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  • DOI: https://doi.org/10.1007/978-3-319-12160-4_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12159-8

  • Online ISBN: 978-3-319-12160-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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