Tag - Cryptography
I overview recent extensions of state-of-the-art discrete-variable (DV) tomographic, error-correction, and cryptographic protocols to continuous-variable (CV) systems, including: (1) a theory of appropriately defined CV state designs, and their applications to design-based CV shadow tomography; (2) a cryptographic protocol utilizing squeezed states whose proof of security is based on a CV extension of DV monogamy-of-entanglement games; (3) sample efficiency of homodyne and photon-number-resolving tomography obtained via recasting said protocols in terms of shadow tomography; and (4) a new class of quantum spherical codes inspired by classical spherical codes.
Polynomial completeness of a universal algebra A means that any operation on A is a composition of basic operations with a specialization of some variables. In the talk we consider algebraic properties of finite polynomially complete quasigroups, the problem of recognition of its completeness in terms of its Latin square. Basing on this approach we can construct polynomially complete quasigroups of any order greater than 32 which is a power of 2. As an application we consider cryptosystems based on quasigroups.
What do internet commerce, online banking, and updates to your phone apps have in common? All of them depend on modern public key cryptography for security. For example, there is the RSA cryptosystem that is used by many internet browsers, and there is the elliptic curve based ECDSA digital signature scheme that is used in many applications, including Bitcoin. All of these cryptographic construction are doomed if/when someone (NSA? Russia? China?) builds a full-scale operational quantum computer. It hasn't happened yet, as far as we know, but there are vast resources being thrown at the problem, and slow-but-steady progress is being made. So the search is on for cryptographic algorithms that are secure against quantum computers. The first part of my talk will be a mix of math and history and prognostication centred around the themes of quantum computers and public key cryptography. The second part will discuss cryptographic constructions based on hard lattice problems, which is one of the approaches being proposed to build a post-quantum cryptographic infrastructure.
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