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Lecture notes in computer science

Dual-Mode Cryptosystem Based on the Learning with Errors Problem

Jingnan He, Wenpan Jing, Bao Li, Xianhui Lu, Dingding Jia

Published Jan 1, 2017• 2 citations
Publisher
DOI
10.1007/978-3-319-59870-3_29

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Cloud computing is a promising paradigm to provide flexible and reliable services. Nevertheless, concern and anxiety about data security and tenants’ privacy are still a major barrier for the popularity of cloud computing. Oblivious transfer (OT) is a cryptographic primitive that enables a client to selectively retrieve data in a privacy-preserving manner. It can be used to construct high-level protocols enabling applications in the cloud-computing paradigm. Technically, it has been proven that OT protocols can be constructed using a CPA-secure public-key encryption scheme. Along these lines, Peikert et al. formulated a dual-mode cryptosystem on which they constructed a single-bit OT scheme. Obviously, it has deficiencies in performance, which makes it unqualified for use in cloud-computing scenarios. This paper aims at providing an efficient multi-bit OT scheme for secure cloud applications. We first propose a multi-bit dual-mode cryptosystem based on the learning with errors (LWE) problem. Based on this multi-bit dual-mode cryptosystem, we construct a multi-bit OT. We present details of the OT construction together with security analysis of our scheme, and finally provide an example of how it can be used in specific application scenarios.

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Dual‐Mode Encryption for UC‐Secure String OT from Learning with Errors

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Universal composability (UC) is a primary security flavor for designing oblivious transfer (OT) due to its advantage of arbitrary composition. However, the study of UC‐secure OT over lattices is still far behind compared with constructions over prequantum assumptions. Relying on the learning with errors (LWE) assumption, Quach proposes a dual‐mode encryption scheme (SCN’20) for deriving a two‐round OT whose security is provably UC‐secure in the common reference string (CRS) model. Due to its use of a randomized rounding function proposed by Benhamouda et al. (PKC’18), this OT can only be limited to transmitting single‐bit messages. Therefore, conducting trivial repetitions of Quach’s OT when transmitting multibit strings would be very costly. In this work, we put forward a modified dual‐mode encryption cryptosystem under the decisional LWE assumption, from which we can derive a UC‐secure string OT with both full‐fledged dual‐mode security and better efficiency on transmitting strings. The key technique we adopt is a key reconciliation scheme proposed by Jiang et al. (PKC’20), which is utilized to extend the single‐bit symmetric encryption key (produced by the aforementioned rounding function) to a multibit case. Through a comprehensive performance analysis, we demonstrate that our proposal can indeed strike a balance between security and efficiency.

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Cloud computing is a promising paradigm to provide flexible and reliable services. Nevertheless, concern and anxiety about data security and tenants’ privacy are still a major barrier for the popularity of cloud computing. Oblivious transfer (OT) is a cryptographic primitive that enables a client to selectively retrieve data in a privacy-preserving manner. It can be used to construct high-level protocols enabling applications in the cloud-computing paradigm. Technically, it has been proven that OT protocols can be constructed using a CPA-secure public-key encryption scheme. Along these lines, Peikert et al. formulated a dual-mode cryptosystem on which they constructed a single-bit OT scheme. Obviously, it has deficiencies in performance, which makes it unqualified for use in cloud-computing scenarios. This paper aims at providing an efficient multi-bit OT scheme for secure cloud applications. We first propose a multi-bit dual-mode cryptosystem based on the learning with errors (LWE) problem. Based on this multi-bit dual-mode cryptosystem, we construct a multi-bit OT. We present details of the OT construction together with security analysis of our scheme, and finally provide an example of how it can be used in specific application scenarios.
Due to the advantages such as the worst-case hardness assumption, lattice-based cryptography is believed to the most promising research direction in post-quantum cryptography. As one of the two main hard problems commonly used in lattice-based cryptography, Learning With Errors (LWE) problem is widely used in constructing numerous cryptosystems. In order to improve the efficiency of lattice-based cryptosystems, Zhang et al. (2019) introduced the Asymmetric LWE (ALWE) problem. In this paper, the relation between the ALWE problem and the standard LWE problem is studied, and it shows that for certain error distributions the two problems are polynomially equivent, which paves the way for constructing secure lattice-based cryptosystems from the ALWE problem.
Universal composability (UC) is a primary security flavor for designing oblivious transfer (OT) due to its advantage of arbitrary composition. However, the study of UC‐secure OT over lattices is still far behind compared with constructions over prequantum assumptions. Relying on the learning with errors (LWE) assumption, Quach proposes a dual‐mode encryption scheme (SCN’20) for deriving a two‐round OT whose security is provably UC‐secure in the common reference string (CRS) model. Due to its use of a randomized rounding function proposed by Benhamouda et al. (PKC’18), this OT can only be limited to transmitting single‐bit messages. Therefore, conducting trivial repetitions of Quach’s OT when transmitting multibit strings would be very costly. In this work, we put forward a modified dual‐mode encryption cryptosystem under the decisional LWE assumption, from which we can derive a UC‐secure string OT with both full‐fledged dual‐mode security and better efficiency on transmitting strings. The key technique we adopt is a key reconciliation scheme proposed by Jiang et al. (PKC’20), which is utilized to extend the single‐bit symmetric encryption key (produced by the aforementioned rounding function) to a multibit case. Through a comprehensive performance analysis, we demonstrate that our proposal can indeed strike a balance between security and efficiency.