Post-Quantum Cryptography: a Cryptanalysis Approach

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The security of many cryptographic protocols in use today relies on the computational hardness of mathematical problems such as integer factorization. These problems can be solved using quantum computers, and therefore most of our security infrastructures will become completely insecure once quantum computers are built. Post-quantum cryptography aims at developing security protocols that will remain secure even after quantum computers are built. The biggest security agencies in the world including GCHQ and the NSA (the American National Security Agency) have recommended a move towards post-quantum protocols, and the new generation of cryptographic standards will aim at post-quantum security.Driven by the need to upgrade our cybersecurity infrastructures, many cryptographic algorithms have recently been developed which are claimed to offer post-quantum security. These proposals are based on a few distinct mathematical problems which are hoped to remain difficult for quantum computers, including lattice problems, multivariate polynomial system solving, coding theory problems, isogeny problems, and the security of cryptographic hash functions. Unfortunately, many of these problems, and more importantly the cryptographic algorithms that are built on top of them, have not been subject to a thorough security analysis yet, therefore leaving us with a risk to oversee major weaknesses in algorithms to be deployed in security applications. In this fellowship, we will develop breakthrough cryptanalysis techniques to analyse the security of post-quantum cryptography candidate algorithms, and determine which algorithms may or may not be further considered for digital security applications. Using the insight gained through cryptanalysis, we will then develop new post-quantum cryptographic algorithms offering better security, efficiency and functionality properties in applications.