In secret quantum communications the best eavesdropping attacks on quantum cryptography are based on imperfect cloning machines. The incoherent attack, based on quantum cloning, is the most common eavesdropping strategy. Using a probe, the eavesdropper imperfectly clones the sender’s quantum state which keeps one copy and sends the other. The physically allowed transformations of Eve’s quantum ...

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Public key cryptography is widely used for signing contracts, electronic voting, encryption, and to secure transactions over the Internet. The discovery by Peter Shor, in 1994, of an efficient algorithm based on quantum mechanics for factoring large integers and computing discrete logarithms undermined the security assumptions upon which currently used public key cryptographic algorithms are ba...

We call quantum security the area of IT security dealing with scenarios where one or more parties have access to quantum hardware. This encompasses both the fields of post-quantum cryptography (that is, traditional cryptography engineered to be resistant against quantum adversaries), and quantum cryptography (that is, security protocols designed to be natively run on a quantum infrastructure, s...

Among the many exciting new applications of quantum physics in the realm of computation and information theory, I am particularly fond of quantum cryptography, quantum computing and quantum teleportation [5]. Quantum cryptography allows for the confidential transmission of classical information under the nose of an eavesdropper, regardless of her computing power or technological sophistication ...

In this chapter we describe some of the recent progress in lattice-based cryptography. Lattice-based cryptographic constructions hold a great promise for post-quantum cryptography, as they enjoy very strong security proofs based on worst-case hardness, relatively efficient implementations, as well as great simplicity. In addition, lattice-based cryptography is believed to be secure against quan...