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2021 | OriginalPaper | Chapter

Password Protected Secret Sharing from Lattices

Authors : Partha Sarathi Roy, Sabyasachi Dutta, Willy Susilo, Reihaneh Safavi-Naini

Published in: Applied Cryptography and Network Security

Publisher: Springer International Publishing

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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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previous chapter Access Control Encryption from Group Encryption

next chapter Efficient Homomorphic Conversion Between (Ring) LWE Ciphertexts

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

It is worth mentioning that the secret key

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-78372-3_17/509977_1_En_17_IEq82_HTML.gif

does not play any role at any point during the execution of \(\mathsf {Rec}\). Thus user neither requires

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-78372-3_17/509977_1_En_17_IEq84_HTML.gif

to be shared and stored among the servers nor to keep it with her - she can delete

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-78372-3_17/509977_1_En_17_IEq85_HTML.gif

after executing the \(\mathsf {Init}\).

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Title: Password Protected Secret Sharing from Lattices
Authors: Partha Sarathi Roy
Sabyasachi Dutta
Willy Susilo
Reihaneh Safavi-Naini
Publisher: Springer International Publishing
Book: Applied Cryptography and Network Security
Print ISBN: 978-3-030-78371-6

Electronic ISBN: 978-3-030-78372-3

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-78372-3_17

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