Zero-Sum Partitions of PHOTON Permutations

We describe an approach to zero-sum partitions using Todo’s division property at EUROCRYPT 2015. It follows the inside-out methodology, and includes MILP-assisted search for the forward and backward trails, and subspace approach to connect those two trails that is less restrictive than commonly done. As an application we choose PHOTON, a family of sponge-like hash function proposals that was recently standardized by ISO. With respect to the security claims made by the designers, we for the first time show zero-sum partitions for almost all of those full 12-round permutation variants that use a 4-bit S-Box. As with essentially any other zero-sum property in the literature, also here the gap between a generic attack and the shortcut is small

Strings from Feynman Graph counting : without large N

A well-known connection between n strings winding around a circle and permutations of n objects plays a fundamental role in the string theory of large N two dimensional Yang Mills theory and elsewhere in topological and physical string theories. Basic questions in the enumeration of Feynman graphs can be expressed elegantly in terms of permutation groups. We show that these permutation techniques for Feynman graph enumeration, along with the Burnside counting lemma, lead to equalities between counting problems of Feynman graphs in scalar field theories and Quantum Electrodynamics with the counting of amplitudes in a string theory with torus or cylinder target space. This string theory arises in the large N expansion of two dimensional Yang Mills and is closely related to lattice gauge theory with S_n gauge group. We collect and extend results on generating functions for Feynman graph counting, which connect directly with the string picture. We propose that the connection between string combinatorics and permutations has implications for QFT-string dualities, beyond the framework of large N gauge theory.Comment: 55 pages + 10 pages Appendices, 23 figures ; version 2 - typos correcte

Generation of N00N-like interferences with two thermal light sources

Measuring the $M$th-order intensity correlation function of light emitted by two statistically independent thermal light sources may display N00N-like interferences of arbitrary order $N = M/2$. We show that via a particular choice of detector positions one can isolate $M$-photon quantum paths where either all $M$ photons are emitted from the same source or $M/2$ photons are collectively emitted by both sources. The latter superposition displays N00N-like oscillations with $N = M/2$ which may serve, e.g., in astronomy, for imaging two distant thermal sources with $M/2$-fold increased resolution. We also discuss slightly modified detection schemes improving the visibility of the N00N-like interference pattern and present measurements verifying the theoretical predictions.Comment: 9 pages, 6 figure

Color-dressed recursive relations for multi-parton amplitudes

Remarkable progress inspired by twistors has lead to very simple analytic expressions and to new recursive relations for multi-parton color-ordered amplitudes. We show how such relations can be extended to include color and present the corresponding color-dressed formulation for the Berends-Giele, BCF and a new kind of CSW recursive relations. A detailed comparison of the numerical efficiency of the different approaches to the calculation of multi-parton cross sections is performed.Comment: 31 pages, 4 figures, 6 table

SU(3) Quantum Interferometry with single-photon input pulses

We develop a framework for solving the action of a three-channel passive optical interferometer on single-photon pulse inputs to each channel using SU(3) group-theoretic methods, which can be readily generalized to higher-order photon-coincidence experiments. We show that features of the coincidence plots vs relative time delays of photons yield information about permanents, immanants, and determinants of the interferometer SU(3) matrix