Lattice‐based cryptosystems in standardisation processes: A survey

Abstract

The current widely used public‐key cryptosystems are vulnerable to quantum attacks. To prepare for cybersecurity in the quantum era, some projects have been launched to call for post‐quantum alternatives. Due to solid security and desirable performance, lattice‐based cryptosystems are viewed as promising candidates in the upcoming standardisation of post‐quantum cryptography. This study surveys the lattice‐based cryptosystems in the post‐quantum standardisation processes including the NIST Post‐Quantum Cryptography Standardisation and the Chinese Cryptographic Algorithm Design Competition, from both design and security aspects. We present generic design paradigms of lattice‐based schemes and describe several representative proposals and recent progress. We also recap some main cryptanalytic results and methods for estimating the concrete security of lattice‐based schemes.

Lattice-Based Threshold Secret Sharing Scheme and Its Applications: A Survey

“…Lattice-based cryptography utilizes mathematical problems defined on lattices to design cryptographic schemes for encryption, signatures, and key exchange, among others. These schemes typically rely on challenging problems such as the shortest vector problem (SVP), closest vector problem (CVP), and learning with errors (LWE) [25][26][27][28]. These problems are generally computationally hard, which provides lattice-based cryptographic schemes with strong security given current computational capabilities.…”