The quantum solace and spectre

Quantum computing is a rapidly advancing field with significant implications for cryptography and secure connections. Unlike classical computers, which use bits (0 or 1), quantum computers utilize qubits that can exist in multiple states simultaneously due to superposition. This allows quantum computers to perform certain calculations much faster than their classical counterparts. However, they cannot solve undecidable problems nor disprove the Church-Turing thesis. Quantum computing has the potential to break most of today's cryptographic algorithms, posing a threat to privacy and security in digital communications. Fortunately, researchers are developing post-quantum cryptography algorithms that can resist quantum attacks. These new algorithms rely on mathematical problems such as lattice-based schemes, isogenies, multivariate cryptography, and code-based cryptography. The National Institute of Standards and Technology (NIST) has been running a post-quantum process since 2016 to standardize these new cryptographic algorithms. The current finalists include lattice-based schemes like Classic McEliece, CRYSTALS-KYBER, NTRU, and SABER, as well as multivariate cryptography scheme Rainbow and digital signature schemes CRYSTALS-DILITHIUM and FALCON. As quantum computing continues to advance, it is crucial for the development of secure post-quantum cryptographic algorithms to protect our communications and data from potential threats posed by quantum computers.