Analysis of the trusted-device scenario in continuous-variable quantum key distribution

The assumption that detection and/or state-preparation devices used for continuous-variable quantum key distribution (CV-QKD) are beyond influence of potential eavesdroppers leads to a significant performance enhancement in terms of achievable key rate and transmission distance. We provide a detailed and comprehensible derivation of the Holevo bound in this so-called trusted-device scenario. Modelling an entangling-cloner attack and using some basic algebraic matrix transformations, we show that the computation of the Holevo bound can be reduced to the solution of a quadratic equation. As an advantage of our derivation, the mathematical complexity of our solution does not increase with the number of trusted-noise sources. Finally, we provide a numerical evaluation of our results, illustrating the counter-intuitive fact that an appropriate amount of trusted receiver loss and noise can even be beneficial for the key rate.Comment: 14 pages, 6 figure

Open-closed duality and Double Scaling

Nonperturbative terms in the free energy of Chern-Simons gauge theory play a key role in its duality to the closed topological string. We show that these terms are reproduced by performing a double scaling limit near the point where the perturbation expansion diverges. This leads to a derivation of closed string theory from this large-N gauge theory along the lines of noncritical string theories. We comment on the possible relevance of this observation to the derivation of superpotentials of asymptotically free gauge theories and its relation to infrared renormalons.Comment: 10 pages, LaTe

Efficient non-malleable codes and key derivation for poly-size tampering circuits

Non-malleable codes, defined by Dziembowski, Pietrzak, and Wichs (ICS '10), provide roughly the following guarantee: if a codeword c encoding some message x is tampered to c' = f(c) such that c' ≠ c , then the tampered message x' contained in c' reveals no information about x. The non-malleable codes have applications to immunizing cryptosystems against tampering attacks and related-key attacks. One cannot have an efficient non-malleable code that protects against all efficient tampering functions f. However, in this paper we show 'the next best thing': for any polynomial bound s given a-priori, there is an efficient non-malleable code that protects against all tampering functions f computable by a circuit of size s. More generally, for any family of tampering functions F of size F ≤ 2s , there is an efficient non-malleable code that protects against all f in F . The rate of our codes, defined as the ratio of message to codeword size, approaches 1. Our results are information-theoretic and our main proof technique relies on a careful probabilistic method argument using limited independence. As a result, we get an efficiently samplable family of efficient codes, such that a random member of the family is non-malleable with overwhelming probability. Alternatively, we can view the result as providing an efficient non-malleable code in the 'common reference string' model. We also introduce a new notion of non-malleable key derivation, which uses randomness x to derive a secret key y = h(x) in such a way that, even if x is tampered to a different value x' = f(x) , the derived key y' = h(x') does not reveal any information about y. Our results for non-malleable key derivation are analogous to those for non-malleable codes. As a useful tool in our analysis, we rely on the notion of 'leakage-resilient storage' of Davì, Dziembowski, and Venturi (SCN '10), and, as a result of independent interest, we also significantly improve on the parameters of such schemes

Gauge theory of Finance?

Some problems with the recent stimulating proposal of a ``Gauge Theory of Finance'' by Ilinski and collaborators are outlined. First, the derivation of the log-normal distribution is shown equivalent both in information and mathematical content to the simpler and well-known derivation, dating back from Bachelier and Samuelson. Similarly, the re-derivation of Black-Scholes equation is shown equivalent to the standard one because the limit of no uncertainty is equivalent to the standard risk-free replication argument. Both re-derivations of the log-normality and Black-Scholes result do not provide a test of the theory because it is degenerate in the limits where these results apply. Third, the choice of the exponential form a la Boltzmann, of the weight of a given market configuration, is a key postulate that requires justification. In addition, the ``Gauge Theory of Finance'' seems to lead to ``virtual'' arbitrage opportunities for pure Markov random walk market when there should be none. These remarks are offered in the hope to improve the formulation of the ``Gauge Theory of Finance'' into a coherent and useful framework.Comment: 4 page