Quantum-safe cryptography for the Internet

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Public key cryptography is essential in securing all Internet communications. For example, the Transport Layer Security (TLS) protocol uses public key cryptography to protect every "https" web page for entering passwords or credit card numbers. However, all public key algorithms used in practice are based on mathematical problemssuch as factoring, discrete logarithms, or elliptic curveswhich could be broken by a quantum computer. The field of quantum-safe cryptography, also called post-quantum or quantum-resistant cryptography, aims to construct public key cryptosystems that are believed to be secure even against quantum computers. Ongoing advancements in physics point toward the eventual construction of large-scale quantum computers. Such future devices would still be able to decrypt present-day communications, allowing anyone to decrypt data transmitted today. Thus, it is important to start developing and deploying quantum-safe cryptography now, even before quantum computers are built.***Several mathematical techniques have been proposed for constructing quantum-safe cryptosystems, including lattices (and the learning-with-errors problem), error-correcting codes, multivariate equations, and hash functions. These have been used to construct public key encryption and digital signature schemes, as well as complex functionality like fully homomorphic encryption.***Unfortunately, all current quantum-safe algorithms have drawbacks that make them unsuitable for practical use. Some require larger key sizes or ciphertexts, increasing communication costs; others have slow implementations. Existing research in quantum-safe cryptography has focused on public key encryption and digital signatures, whereas most real-world protocols need authenticated key exchange. There is little research on how to efficiently and securely integrate them in applications, and their performance characteristics.***The overall aim of this research program is to design cryptographic systems that are secure against attacks by quantum computers and are practical for use on the Internet, with a specific focus on authenticated key exchange protocols. We will achieve this by designing new and improved algorithms for a variety of cryptographic tasks and analysing and testing these algorithms in the context of deployed protocols to identify techniques that are suitable for long-term use.***The results of this research will support the creation of Internet technologies that protect communication from quantum computers. The anticipated outcomes are practical new encryption algorithms, open source software, and recommendations for the use of quantum-safe cryptography in Internet protocols, ready for use by Internet standards bodies. Canadian Internet users will benefit from enhanced security. This research supports Canada's strategic investment in becoming a leader in quantum technologies.**