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Faster Cryptographic Hash Function from Supersingular Isogeny Graphs

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Selected Areas in Cryptography (SAC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13742))

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Abstract

We propose a variant of the CGL hash algorithm [5] that is significantly faster than the original algorithm, and prove that it is preimage and collision resistant. For \(n = \log p\) where p is the characteristic of the finite field, the performance ratio between CGL and the new proposal is \((5.7n + 110) / (13.5\log n + 46.4)\). This gives an exponential speed up as the size of p increases. Assuming the best quantum preimage attack on the hash algorithm has complexity \(O(p^{\frac{1}{4}})\), we attain a concrete speed-up for a 256-bit quantum preimage security level by a factor 33.5. For a 384-bit quantum preimage security level, the speed-up is by a factor 47.8.

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Author information

Authors and Affiliations

  1. Ryerson University, Toronto, Canada

    Javad Doliskani

  2. Institute for Quantum Computing, University of Waterloo, Waterloo, Canada

    Geovandro C. C. F. Pereira

  3. University of Washington Tacoma, Tacoma, USA

    Paulo S. L. M. Barreto

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  1. Javad Doliskani
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  2. Geovandro C. C. F. Pereira
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  3. Paulo S. L. M. Barreto
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Correspondence to Javad Doliskani .

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Editors and Affiliations

  1. Inria and École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France

    Benjamin Smith

  2. Electrical and Computer Engineering, University of Windsor, Windsor, ON, Canada

    Huapeng Wu

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Doliskani, J., Pereira, G.C.C.F., Barreto, P.S.L.M. (2024). Faster Cryptographic Hash Function from Supersingular Isogeny Graphs. In: Smith, B., Wu, H. (eds) Selected Areas in Cryptography. SAC 2022. Lecture Notes in Computer Science, vol 13742. Springer, Cham. https://doi.org/10.1007/978-3-031-58411-4_18

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  • DOI: https://doi.org/10.1007/978-3-031-58411-4_18

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