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Generalizing cryptosystems based on the subset sum problem

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Abstract

We identify a generic construction of cryptosystems based on the subset sum problem and characterize the required homomorphic map. Using the homomorphism from the Damgård-Jurik cryptosystem, we then eliminate the need for a discrete logarithm oracle in the key generation step of the Okamoto et al. scheme to provide a practical cryptosystem based on the subset sum problem. We also analyze the security of our cryptosystem and show that with proper parameter choices, it is computationally secure against lattice-based attacks. Finally, we present a practical application of this system for RFID security and privacy.

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Authors and Affiliations

  1. Max Planck Institute for Software Systems (MPI-SWS), 66111, Saarbruecken, Germany

    Aniket Kate

  2. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Ian Goldberg

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  1. Aniket Kate
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  2. Ian Goldberg
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Correspondence to Ian Goldberg.

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Kate, A., Goldberg, I. Generalizing cryptosystems based on the subset sum problem. Int. J. Inf. Secur. 10, 189–199 (2011). https://doi.org/10.1007/s10207-011-0129-2

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