Number-Theoretic Cryptographic Framework for Securing Generative Artificial Intelligence Against Adversarial Attacks

Abstract

The rapid adoption of Generative Artificial Intelligence (GenAI) has intensified concerns regarding security, privacy, and robustness against adversarial attacks. Most existing defense mechanisms rely on adversarial training, differential privacy, or cryptographic techniques applied as external protection layers, which often lack formal mathematical guarantees and are weakly coupled with the internal generative process.This study proposes a novel Number-Theoretic Cryptographic Framework that embeds cryptographic primitives directly into the GenAI lifecycle, including latent-space representations and model parameter handling. Unlike prior approaches, the proposed framework integrates number-theoretic hardness assumptions specifically lattice-based and elliptic-curve cryptography into the core generative mechanism, enabling mathematically grounded and provably secure protection against adversarial exploitation.A comprehensive synthetic dataset is constructed by jointly modeling cryptographic parameters, generative model specifications, and adversarial attack scenarios to systematically evaluate the framework. Experimental results demonstrate that number-theoretic cryptographic integration significantly reduces privacy leakage and model extraction vulnerability while preserving generative utility. Lattice-based schemes provide the strongest privacy protection, while elliptic-curve cryptography achieves a balanced trade-off between security and computational efficiency. This work introduces a new paradigm for securing GenAI by unifying generative modeling with formal number-theoretic cryptographic security, offering a robust and future-proof solution against both classical and post-quantum adversarial threats.