In cryptography, post-quantum cryptography (PQC) (sometimes referred to as quantum-proof, quantum-safe or quantum-resistant) refers to cryptographic algorithms (usually public-key algorithms) that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with currently popular algorithms is that their security relies on one of three hard mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem. All of these problems could be easily solved on a sufficiently powerful quantum computer running Shor's algorithm.
Even though current quantum computers lack processing power to break any real cryptographic algorithm, many cryptographers are designing new algorithms to prepare for a time when quantum computing becomes a threat. This work has gained greater attention from academics and industry through the PQCrypto conference series since 2006 and more recently by several workshops on Quantum Safe Cryptography hosted by the European Telecommunications Standards Institute (ETSI) and the Institute for Quantum Computing. The rumoured existence of widespread harvest now, decrypt later programs has also been seen as a motivation for the early introduction of post-quantum algorithms, as data recorded now may still remain sensitive many years into the future.
In contrast to the threat quantum computing poses to current public-key algorithms, most current symmetric cryptographic algorithms and hash functions are considered to be relatively secure against attacks by quantum computers. While the quantum Grover's algorithm does speed up attacks against symmetric ciphers, doubling the key size can effectively block these attacks. Thus post-quantum symmetric cryptography does not need to differ significantly from current symmetric cryptography.
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This course introduces the basics of cryptography. We review several types of cryptographic primitives, when it is safe to use them and how to select the appropriate security parameters. We detail how
Information is processed in physical devices. In the quantum regime the concept of classical bit is replaced by the quantum bit. We introduce quantum principles, and then quantum communications, key d
This advanced course will provide students with the knowledge to tackle the design of privacy-preserving ICT systems. Students will learn about existing technologies to prect privacy, and how to evalu
Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions are currently important candidates for post-quantum cryptography. Unlike more widely used and known public-key schemes such as the RSA, Diffie-Hellman or elliptic-curve cryptosystems — which could, theoretically, be defeated using Shor's algorithm on a quantum computer — some lattice-based constructions appear to be resistant to attack by both classical and quantum computers.
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: Lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic algorithms. In addition, some lattice problems which are worst-case hard can be used as a basis for extremely secure cryptographic schemes.
In cryptography, Learning with errors (LWE) is a mathematical problem that is widely used in cryptography to create secure encryption algorithms. It is based on the idea of representing secret information as a set of equations with errors. In other words, LWE is a way to hide the value of a secret by introducing noise to it. In more technical terms, it refers to the computational problem of inferring a linear -ary function over a finite ring from given samples some of which may be erroneous.
Explores topological waves for robust signal processing applications, focusing on resistance to perturbations and the design paradigm of topological systems.
Since the advent of internet and mass communication, two public-key cryptographic algorithms have shared the monopoly of data encryption and authentication: Diffie-Hellman and RSA. However, in the last few years, progress made in quantum physics -- and mor ...
Current cryptographic solutions will become obsolete with the arrival of large-scale universal quantum computers. As a result, the National Institute of Standards and Technology supervises a post-quantum standardization process which involves evaluating ca ...
Isogeny-based cryptography is an instance of post-quantum cryptography whose fundamental problem consists of finding an isogeny between two (isogenous) elliptic curves E and E′. This problem is closely related to that of computing the endomorphism ring of ...