Paper 2023/933

More Efficient Lattice-Based Electronic Voting from NTRU

Abstract

In recent years, there has been much focus on developing core cryptographic primitives based on lattice assumptions, driven by the NIST call for post-quantum key encapsulation and digital signature algorithms. However, more work must be conducted on efficient privacy-preserving protocols based on quantum-safe assumptions. Electronic voting is one such privacy-preserving protocol whose adoption is increasing across the democratic world. E-voting offers both a fast and convenient alternative to postal voting whilst further ensuring cryptographic privacy of votes and offering full verifiability of the process. Owing to the sensitivity of voting and its infrastructure challenges, it is crucial to ensure security against quantum computers is baked into e-voting solutions. We present an e-voting scheme from quantum-safe assumptions based on the hardness of the RLWE and NTRU lattice problems, providing concrete parameters and an efficient implementation. Our design achieves a factor $5.3 \times$ reduction in ciphertext size, $2.5 \times$ reduction in total communication cost, and $2 \times$ reduction in total computation time compared to the state-of-the-art lattice-based voting scheme by Aranha et al. (ACM CCS 2023). We argue that the efficiency of this scheme makes it suitable for real-world elections. Our scheme makes use of non-ternary NTRU secrets to achieve optimal parameters. In order to compute the security of our design, we extend the ternary-NTRU work of Ducas and van Woerden (ASIACRYPT 2021) by determining the concrete fatigue point (for general secrets) of NTRU to be $q = 0.0058 \cdot \sigma^2 \cdot d^{2.484}$ (above which parameters become overstretched) for modulus $q$, ring dimension $d$, and secrets drawn from a Gaussian of parameter $\sigma$. We consider this relation to be of independent interest and demonstrate its significance by improving the efficiency of the (partially) blind signature scheme by del Pino and Katsumata (CRYPTO 2022).