Ran Gelles

Semiquantum key distribution

Secure key distribution among two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? Recently, a semi-quantum key distribution protocol was presented (Boyer, Kenigsberg and Mor, Physical Review Letters, 2007), in which one of the parties (Bob) is classical, and yet, the protocol is proven to be completely robust against an eavesdropping attempt. Here we extend that result much further. We present two protocols with this constraint, and prove their robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate parties could notice. One protocol presented here is identical to the one referred to above, however, its robustness is proven here in a much more general scenario. The other protocol is very different as it is based on randomization.

Efficient and Explicit Coding for Interactive Communication

We revisit the problem of reliable interactive communication over a noisy channel, and obtain the first fully explicit (randomized) efficient constant-rate emulation procedure for reliable interactive communication. Our protocol works for any discrete memory less noisy channel with constant capacity, and fails with exponentially small probability in the total length of the protocol. Following a work by Schulman [Schulman 1993] our simulation uses a tree-code, yet as opposed to the non-constructive absolute tree-code used by Schulman, we introduce a relaxation in the notion of goodness for a tree code and define a potent tree code. This relaxation allows us to construct an explicit emulation procedure for any two-party protocol. Our results also extend to the case of interactive multiparty communication. We show that a randomly generated tree code (with suitable constant alphabet size) is an efficiently decodable potent tree code with overwhelming probability. Furthermore we are able to partially derandomize this result by means of epsilon-biased distributions using only O(N) random bits, where N is the depth of the tree.

Security and Composability of Randomness Expansion from Bell Inequalities

The nonlocal behavior of quantum mechanics can be used to generate guaranteed fresh randomness from an untrusted device that consists of two nonsignalling components; since the generation process requires some initial fresh randomness to act as a catalyst, one also speaks of randomness expansion. R. Colbeck and A. Kent [J. Phys. A 44, 095305 (2011)] proposed the first method for generating randomness from untrusted devices, but without providing a rigorous analysis. This was addressed subsequently by S. Pironio et al. [Nature (London) 464, 1021 (2010)], who aimed at deriving a lower bound on the min-entropy of the data extracted from an untrusted device based only on the observed nonlocal behavior of the device. Although that article succeeded in developing important tools for reaching the stated goal, the proof itself contained a bug, and the given formal claim on the guaranteed amount of min-entropy needs to be revisited. In this paper we build on the tools provided by Pironio et al. and obtain a meaningful lower bound on the min-entropy of the data produced by an untrusted device based on the observed nonlocal behavior of the device. Our main result confirms the essence of the (improperly formulated) claims of Pironio et al. and puts them on solid ground. We also address the question of composability and show that different untrusted devices can be composed in an alternating manner under the assumption that they are not entangled. This enables superpolynomial randomness expansion based on two untrusted yet unentangled devices.

Position-based quantum cryptography: Impossibility and constructions

In this work, we study position-based cryptography in the quantum setting. The aim is to use the geographical position of a party as its only credential. On the negative side, we show that if adversaries are allowed to share an arbitrarily large entangled quantum state, the task of secure position-verification is impossible. To this end, we prove the following very general result. Assume that Alice and Bob hold respectively subsystems

Optimal Coding for Streaming Authentication and Interactive Communication

A

Efficient Coding for Interactive Communication

and

Adaptive protocols for interactive communication

B

Maximal Noise in Interactive Communication over Erasure Channels and Channels with Feedback

of a (possibly) unknown quantum state

Capacity of Interactive Communication over Erasure Channels and Channels with Feedback

|\psi\rangle \in {\cal H}_A \otimes {\cal H}_B

How to Catch L 2 -Heavy-Hitters on Sliding Windows

. Their goal is to calculate and share a new state