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PositionBased Quantum Cryptography: Impossibility and Constructions
, 2010
"... In this work, we study positionbased 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, no secure positionverificati ..."
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In this work, we study positionbased 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, no secure positionverification is possible at all. That is, we show a generic attack that breaks any positionverification scheme of a very general form. On the positive side, we show that if adversaries do not share any entangled quantum state but can compute arbitrary quantum operations, secure positionverification is achievable. Jointly, these results suggest the interesting question whether secure positionverification is possible in case of a bounded amount of entanglement. Our positive result can be interpreted as resolving this question in the simplest case, where the bound is set to zero. In models where secure positioning is achievable, it has a number of interesting applications. For example, it enables secure communication over an insecure channel without having any preshared key, with the guarantee that only a party at a specific location can learn the content of the conversation. More generally, we show that in settings where secure positionverification is achievable, other positionbased cryptographic schemes are possible as well, such as secure positionbased authentication and positionbased
The GardenHose Model
"... Abstract. We define a new model of communication complexity, called the gardenhose model. Informally, the gardenhose complexity of a function f: {0, 1} n × {0, 1} n → {0, 1} is given by the minimal number of water pipes that need to be shared between two parties, Alice and Bob, in order for them t ..."
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Abstract. We define a new model of communication complexity, called the gardenhose model. Informally, the gardenhose complexity of a function f: {0, 1} n × {0, 1} n → {0, 1} is given by the minimal number of water pipes that need to be shared between two parties, Alice and Bob, in order for them to compute the function f as follows: Alice connects her ends of the pipes in a way that is determined solely by her input x ∈ {0, 1} n and, similarly, Bob connects his ends of the pipes in a way that is determined solely by his input y ∈ {0, 1} n. Alice turns on the water tap that she also connected to one of the pipes. Then, the water comes out on Alice’s or Bob’s side depending on the function value f(x, y). We prove almostlinear lower bounds on the gardenhose complexity for concrete functions like inner product, majority, and equality, and we show the existence of functions with exponential gardenhose complexity. Furthermore, we show a connection to classical complexity theory by proving that all functions computable in logspace have polynomial gardenhose complexity. We consider a randomized variant of the gardenhose complexity, where Alice and Bob hold preshared randomness, and a quantum variant, where Alice and Bob hold preshared quantum entanglement, and we show that the randomized gardenhose complexity is within a polynomial factor of the deterministic gardenhose complexity. Examples of (partial) functions are given where the quantum gardenhose complexity is logarithmic in n while the classical gardenhose complexity can be lower bounded by n c for constant c> 0. Finally, we show an interesting connection between the gardenhose model and the (in)security of a certain class of quantum positionverification schemes. 1