Leveraging kleptography to strengthen post-quantum cryptography

<title>Abstract</title> Quantum computing poses a significant threat to the security of many current cryptographic algorithms. This imminent risk has accelerated the development and standardization of new cryptosystems, known as post-quantum cryptosystems and designed to protect digital information in the quantum era using classical computing resources. CRYSTALS-Kyber is a lattice-based post-quantum encryption scheme that has been selected as a standard by the National Institute of Standards and Technology. This work presents a novel kleptographic attack against the CRYSTALS-Kyber scheme, providing both theoretical insights and practical results that demonstrate its feasibility. One of the conclusions is that this post-quantum cryptosystem may be vulnerable to kleptographic backdoors. As a result, this study offers a mathematical analysis along with software implementations and practical methodologies to detect such backdoors, thereby contributing to the development of more transparent and verifiable cryptographic standards.