# A Survey on Cybersecurity in IoT
## 3 Data Integrity and Privacy
### Advanced Cryptographic Techniques for Data Integrity
#### 3.1.2 Quantum Computing and IoT Security  
Quantum computing represents a transformative technological development, offering unparalleled computational capabilities while simultaneously posing significant threats to the security of classical cryptographic systems. In the context of IoT security, the emergence of quantum computing necessitates a reevaluation of cryptographic protocols to ensure long-term resilience against quantum attacks [98].  
Classical cryptographic systems, such as RSA and elliptic curve cryptography, rely on the computational difficulty of problems like integer factorization and the discrete logarithm problem. Quantum algorithms, such as [PERSON]'s algorithm, efficiently solve these problems, rendering these cryptosystems vulnerable. For example, RSA encryption relies on the hardness of factoring a large composite modulus \(N\), where \(N=p\cdot q\) for two large primes \(p\) and \(q\). [PERSON]'s algorithm can factor \(N\) in polynomial time, undermining the security of RSA-encrypted communications. To mitigate these risks, the field of post-quantum cryptography focuses on developing cryptographic protocols resistant to quantum attacks. These protocols are based on mathematical problems believed to remain intractable even for quantum computers, such as lattice-based cryptography, code-based cryptography, hash-based signatures, and multivariate polynomial problems [99].  
Lattice-based cryptography is particularly promising due to its versatility and efficiency. One example is the learning-with-errors problem, which serves as the foundation for many lattice-based schemes. The learning-with-errors problem can be stated as follows. Given a matrix \(\mathbf{A}\in\mathbb{Z}_{q}^{m\times n}\), a secret vector \(\mathbf{s}\in\mathbb{Z}_{q}^{n}\), and a noise vector \(\mathbf{e}\in\mathbb{Z}_{q}^{m}\), compute the vector \(\mathbf{b}=\mathbf{A}\mathbf{s}+\mathbf{e}\mod q\). The task of recovering \(\mathbf{s}\) from \((\mathbf{A},\mathbf{b})\) is computationally hard, even with quantum resources. This hardness forms the basis of several cryptographic primitives, including encryption schemes, key exchanges, and digital signatures [100].  
Code-based cryptography leverages the hardness of decoding random linear codes. One notable example is the McEliece cryptosystem, which uses error-correcting codes to provide secure communication. Similarly, hash-based signatures, such as those based on Merkle trees, offer quantum-resistant authentication mechanisms by relying on the one-way nature of cryptographic hash functions [101].  
Multivariate polynomial cryptography is another approach where the security relies on the difficulty of solving systems of multivariate quadratic equations over finite fields. Protocols based on this approach are efficient and suitable for resource-constrained environments, such as IoT devices. The adoption of post-quantum cryptographic protocols presents unique challenges for IoT systems. Many IoT devices are resource-constrained, with limited computational power, memory, and energy availability. Implementing quantum-resistant algorithms in such environments requires careful optimization to balance security and performance. Additionally, the transition to post-quantum cryptography involves ensuring compatibility with existing systems and standards, which adds complexity to the integration process [102].