R -LWE-Based Distributed Key Generation and Threshold Decryption

Ferran Alborch, Ramiro Martínez and Paz Morillo
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Ferran Alborch: Department of Mathematics, Campus Nord, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Ramiro Martínez: Department of Mathematics, Campus Nord, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Paz Morillo: Department of Mathematics, Campus Nord, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain

Mathematics, 2022, vol. 10, issue 5, 1-31

Abstract: Ever since the appearance of quantum computers, prime factoring and discrete logarithm-based cryptography have been questioned, giving birth to the so-called post-quantum cryptography. The most prominent field in post-quantum cryptography is lattice-based cryptography, protocols that are proved to be as difficult to break as certain hard lattice problems like Learning with Errors (LWE) or Ring Learning with Errors ( R -LWE). Furthermore, the application of cryptographic techniques to different areas, like electronic voting, has also nourished a great interest in distributed cryptography. In this work, we will give two original threshold protocols based in the lattice problem R -LWE: one for key generation and one for decryption. We will prove them both correct and secure under the assumption of hardness of some well-known lattice problems. Finally, we will give a rough implementation of the protocols in C to give some tentative results about their viability, in particular our model generates keys in the order of 10 3 ms and decrypts and encrypts in the order of 10 2 ms.

Keywords: post-quantum cryptography; threshold cryptography; lattices; Ring Learning with Errors (R-LWE); R-LWE encryption (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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