Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/142808
Title: Zero-knowledge arguments for matrix-vector relations and lattice-based group encryption
Authors: Libert, Benoǐt
Ling, San
Mouhartem, Fabrice
Nguyen, Khoa
Wang, Huaxiong
Keywords: Science::Mathematics
Issue Date: 2016
Source: Libert, B., Ling, S., Mouhartem, F., Nguyen, K., & Wang, H. (2016). Zero-knowledge arguments for matrix-vector relations and lattice-based group encryption. Proceedings of 22nd International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT 2016), 10032, 101-131. doi:10.1007/978-3-662-53890-6_4
Abstract: Group encryption (GE) is the natural encryption analogue of group signatures in that it allows verifiably encrypting messages for some anonymous member of a group while providing evidence that the receiver is a properly certified group member. Should the need arise, an opening authority is capable of identifying the receiver of any ciphertext. As introduced by Kiayias, Tsiounis and Yung (Asiacrypt’07), GE is motivated by applications in the context of oblivious retriever storage systems, anonymous third parties and hierarchical group signatures. This paper provides the first realization of group encryption under lattice assumptions. Our construction is proved secure in the standard model (assuming interaction in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions. As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hidden but certified public key, which incurs to prove quadratic statements about LWE relations. Specifically, our protocol allows arguing knowledge of witnesses consisting of X ∈ ℤqm×n, s ∈ ℤnq and a small-norm e ∈ ℤm which underlie a public vector b = X · s + e ∈ ℤmq while simultaneously proving that the matrix X ∈ ℤm×nq has been correctly certified. We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting.
URI: https://hdl.handle.net/10356/142808
ISBN: 978-3-662-53889-0
DOI: 10.1007/978-3-662-53890-6_4
Rights: © 2016 International Association for Cryptologic Research. All rights reserved. This paper was published by Springer in Proceedings of 22nd International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT 2016) and is made available with permission of International Association for Cryptologic Research.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Conference Papers

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