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Lecture notes in computer science

Error-Free Lattice-Based Key Encapsulation Mechanism Based on Ring-LWE

Chik How Tan, Theo Fanuela Prabowo

Published Jan 1, 2021• 1 citation
Publisher
DOI
10.1007/978-3-030-70881-8_11

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In order to resist the security risks caused by quantum computing, post-quantum cryptography (PQC) has been a research focus. Constructing a key encapsulation mechanism (KEM) based on lattices is one of the promising PQC routines. The algebraically structured learning with errors (LWE) problem over power-of-two cyclotomics has been one of the most widely used hardness assumptions for lattice-based cryptographic schemes. However, power-of-two cyclotomic rings may be exploited in the inflexibility of selecting parameters. Recently, trinomial cyclotomic rings of the form Zq[x]/(xn−xn/2+1), where n=2k3l, k≥1,l≥0, have received widespread attention due to their flexible parameter selection. In this paper, we propose Tyber, a variant scheme of the NIST-standardized KEM candidate Kyber over trinomial cyclotomic rings. We provide three parameter sets, aiming at the quantum security of 128, 192, and 256 bits (actually achieving 129, 197, and 276 bits) with matching and negligible error probabilities. When compared to Kyber, our Tyber exhibits stronger quantum security, by 22, 31, and 44 bits, than Kyber for three security levels.
Post Quantum Key Encapsulation Mechanism (PKEM) is used to securely exchange symmetric keys over an insecure channel. It allows two parties to establish a shared secret key, which can then be used for symmetric encryption, ensuring confidentiality against quantum attacks. By encapsulating the key, it reduces the need to directly encrypt large amounts of data with the public key, which is computationally expensive. Traditional cryptographic tools, while effective, are complex and susceptible to quantum attacks. This paper contains a robust and lightweight post-quantum security solution, and their performance analysis. The authentication scheme, based on Ring-Learning with Errors (Ring-LWE), uses Bernstein reconstruction in polynomial multiplication to significantly lower computational costs, enabling even resource-limited mobile devices to achieve secure mutual authentication. This paper also contains an analysis of post-quantum key encapsulation mechanism (PKEM), and it also covers design, security, and real-world implementation issues and provides a prospective outlook on PKEM, taking into account current investigations, possible innovations, and the changing field of quantum computing. The proposed work also offers a thorough investigation of the security features of post-quantum KEMs, together with theoretical and practical concerns.
There are cryptographic systems that are secure against attacks by both classical and quantum computers. One of these systems is the NewHope key encapsulation mechanism (KEM) based on the Ring-learning with error problem (Ring-LWE problem). The Ring-LWE problem is presumed to be hard to solve even on a quantum computer. A KEM scheme allows sharing of a common key between two parts (Alice & Bob). This thesis presents original contributions to the security and analysis of key mismatch and information leakage attacks on NewHope KEM and some vulnerabilities on (small)-Ring-LWE problem (a variant of Ring-LWE problem). The first contribution contains some improvements on key mismatch attacks proposed by Bauer et al. and Qin et al. (Bauer et al., 2019; Qin et al., 2019). These key mismatch attacks retrieve Alices secret key. And, we propose two new methods named Fast Qin and Double Qin. The methods Fast Qin and Double Qin require around 240k and 34k oracle queries, respectively; instead of 840k queries of the Qin et al.s method. Moreover, these two new methods are adapted to retrieve Alices secret key on NewHope-512 (a variant of NewHope). The second contribution analyzes the information leakage of Bobs secret key on NewHope when it is reused. Our result corroborates that Bobs secret key must not be reused since with two communications to Bob, his secret key is leaked. In Ring-LWE problem, a polynomial a is selected randomly and a polynomial b is calculated as b = a.s+e where s is the secret polynomial (selected randomly) and the e is a noise polynomial. Our third contribution shows that in small-Ring-LWE, a variant where polynomials s and e are small, there are values of the public parameter a that leak a large percentage of the coefficients of the secret s. And, the last contribution shows that the secret s can be retrieved successfully if at least 50% of the random known coefficients of s and e are known.