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Password Protected Secret Sharing from Lattices

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Applied Cryptography and Network Security (ACNS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12726))

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Abstract

A password protected secret sharing (\(\mathsf {PPSS}\)) allows a user to store shares of a secret on a set of L servers, and use a single password to authenticate itself to any subset of k servers at a later time to access the shares and reconstruct the secret. Security of \(\mathsf {PPSS}\) ensures that a coalition of up to \(k-1\) servers cannot reveal any information about the secret message or the password. A related primitive is threshold password authenticated key exchange protocol (\(\mathsf {TPAKE}\)) that allows a user to establish individual authenticated shared secret keys with members of a subset of k out of L servers, using a single password. These primitives are well motivated, with applications such as secure storage of secret keys, and secure group communication using passwords for authentication. In this paper, we give the first construction of these primitives that provide post-quantum security. We prove security of our constructions in concurrent setting, and in the standard model, reducing security to the decisional LWE problem.

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Notes

  1. 1.

    Throughout the paper, we will denote FHE of [11] by \(\mathsf {GSW}\) scheme. The acronym is the authors’ initials.

  2. 2.

    It is worth mentioning that the secret key does not play any role at any point during the execution of \(\mathsf {Rec}\). Thus user neither requires to be shared and stored among the servers nor to keep it with her - she can delete after executing the \(\mathsf {Init}\).

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Authors and Affiliations

  1. Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Northfields Avenue, Wollongong, NSW, 2522, Australia

    Partha Sarathi Roy & Willy Susilo

  2. Department of Computer Science, University of Calgary, 2500 University Drive, Calgary, NW, T2N 1N4, Canada

    Sabyasachi Dutta & Reihaneh Safavi-Naini

Authors
  1. Partha Sarathi Roy
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  2. Sabyasachi Dutta
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  3. Willy Susilo
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  4. Reihaneh Safavi-Naini
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Correspondence to Partha Sarathi Roy .

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Editors and Affiliations

  1. Waseda University, Tokyo, Japan

    Kazue Sako

  2. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Nils Ole Tippenhauer

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Roy, P.S., Dutta, S., Susilo, W., Safavi-Naini, R. (2021). Password Protected Secret Sharing from Lattices. In: Sako, K., Tippenhauer, N.O. (eds) Applied Cryptography and Network Security. ACNS 2021. Lecture Notes in Computer Science(), vol 12726. Springer, Cham. https://doi.org/10.1007/978-3-030-78372-3_17

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  • DOI: https://doi.org/10.1007/978-3-030-78372-3_17

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