Partial duality is a of ribbon graphs relative to subset their edges generalizing the classical Euler–Poincaré duality. This operation often changes genus. Recently J.L. Gross, T. Mansour, and T.W. Tucker formulated conjecture that for any graph different from plane trees partial duals, there which does change A family counterexamples was found by Qi Yan Xian’an Jin. In this note we prove essen...

We prove the related-key security of the Iterated Even-Mansour cipher under broad classes of related key derivation (RKD) functions. Our result extends the classes of RKD functions considered by Farshim and Procter (FSE, 15). Moreover, we present a far simpler proof which uses techniques similar to those used by Cogliati and Seurin (EUROCRYPT, 15) in their proof that the four-round Even-Mansour...

We analyze the security of the iterated Even-Mansour cipher (a.k.a. key-alternating cipher), a very simple and natural construction of a blockcipher in the random permutation model. This construction, first considered by Even and Mansour (J. Cryptology, 1997) with a single permutation, was recently generalized to use t permutations in the work of Bogdanov et al. (EUROCRYPT 2012). They proved th...

Generalized additive models are a powerful generalization of linear and logistic regression models. In this paper we show that a natural regression graph learning algorithm efficiently learns generalized additive models. Efficiency is proven in two senses: the estimator’s future prediction accuracy approaches optimality at rate inverse polynomial in the size of the training data, and its runtim...

We count the number of permutations with k occurrences of the pattern 2–13 in permutations by lattice path enumeration. We give closed forms for k ≤ 8, extending results of Claesson and Mansour.

The r-round (iterated) Even-Mansour cipher (also known as key-alternating cipher) defines a block cipher from r fixed public n-bit permutations P1, . . . , Pr as follows: given a sequence of n-bit round keys k0, . . . , kr, an n-bit plaintext x is encrypted by xoring round key k0, applying permutation P1, xoring round key k1, etc. The (strong) pseudorandomness of this construction in the random...

We propose new key recovery attacks on the two minimal two-round n-bit Even-Mansour ciphers that are secure up to 2 queries against distinguishing attacks proved by Chen et al. Our attacks are based on the meet-in-the-middle technique which can significantly reduce the data complexity. In particular, we introduce novel matching techniques which enable us to compute one of the two permutations w...

The tweakable Even-Mansour construction generalizes the conventional Even-Mansour scheme through replacing round keys by strings derived from a master key and a tweak. Besides providing plenty of inherent variability, such a design builds a tweakable block cipher from some lower level primitive. In the present paper, we evaluate the multi-key security of TEM-1, one of the most commonly used one...