LIGA: A Cryptosystem Based on the Hardness of Rank-Metric List and Interleaved Decoding

We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. LIGA is an improved variant of the Faure-Loidreau (FL) system, which was broken in a structural attack by Gaborit, Otmani, and Tal\'e Kalachi (GOT, 2018). We keep the FL encryption and decryption algorithms, but modify the insecure key generation algorithm. Our crucial observation is that the GOT attack is equivalent to decoding an interleaved Gabidulin code. The new key generation algorithm constructs public keys for which all polynomial-time interleaved decoders fail---hence LIGA resists the GOT attack. We also prove that the public-key encryption version of LIGA is IND-CPA secure in the standard model and the KEM version is IND-CCA2 secure in the random oracle model, both under hardness assumptions of formally defined problems related to list decoding and interleaved decoding of Gabidulin codes. We propose and analyze various exponential-time attacks on these problems, calculate their work factors, and compare the resulting parameters to NIST proposals. The strengths of LIGA are short ciphertext sizes and (relatively) small key sizes. Further, LIGA guarantees correct decryption and has no decryption failure rate. It is not based on hiding the structure of a code. Since there are efficient and constant-time algorithms for encoding and decoding Gabidulin codes, timing attacks on the encryption and decryption algorithms can be easily prevented.Comment: Extended version of arXiv:1801.0368

Are there dedicated neural mechanisms for imitation? A study of grist and mills

Are there brain regions that are specialized for the execution of imitative actions? We compared two hypotheses of imitation: the mirror neuron system (MNS) hypothesis predicts frontal and parietal engagement which is specific to imitation, while the Grist-Mills hypothesis predicts no difference in brain activation between imitative and matched non-imitative actions. Our delayed imitation fMRI paradigm included two tasks, one where correct performance was defined by a spatial rule and another where it was defined by an item-based rule. For each task, participants could learn a sequence from a video of a human hand performing the task, from a matched “Ghost” condition, or from text instructions. When participants executed actions after seeing the Hand demonstration (compared to Ghost and Text demonstrations), no activation differences occurred in frontal or parietal regions; rather, activation was localized primarily to occipital cortex. This adds to a growing body of evidence which indicates that imitation-specific responses during action execution do not occur in canonical mirror regions, contradicting the mirror neuron system hypothesis. However, activation differences did occur between action execution in the Hand and Ghost conditions outside MNS regions, which runs counter to the Grist-Mills hypothesis. We conclude that researchers should look beyond these hypotheses as well as classical MNS regions to describe the ways in which imitative actions are implemented by the brain

Efficient Decoding of Gabidulin Codes over Galois Rings

This paper presents the first decoding algorithm for Gabidulin codes over Galois rings with provable quadratic complexity. The new method consists of two steps: (1) solving a syndrome-based key equation to obtain the annihilator polynomial of the error and therefore the column space of the error, (2) solving a key equation based on the received word in order to reconstruct the error vector. This two-step approach became necessary since standard solutions as the Euclidean algorithm do not properly work over rings

Neural responses when learning spatial and object sequencing tasks via imitation

Humans often learn new things via imitation. Here we draw on studies of imitation in children to characterise the brain system(s) involved in the imitation of different sequence types using functional magnetic resonance imaging. On each trial, healthy adult participants learned one of two rule types governing the sequencing of three pictures: a motor-spatial rule (in the spatial task) or an object-based rule (in the cognitive task). Sequences were learned via one of three demonstration types: a video of a hand selecting items in the sequence using a joystick (Hand condition), a computer display highlighting each item in order (Ghost condition), or a text-based demonstration of the sequence (Text condition). Participants then used a joystick to execute the learned sequence. Patterns of activation during demonstration observation suggest specialisation for object-based imitation in inferior frontal gyrus, specialisation for spatial sequences in anterior intraparietal sulcus (IPS), and a general preference for imitation in middle IPS. Adult behavioural performance contrasted with that of children in previous studies—indicating that they experienced more difficulty with the cognitive task—while neuroimaging results support the engagement of different neural regions when solving these tasks. Further study is needed on whether children’s differential performance is related to delayed IPS maturation

Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring $\mathbb{Z}_{p^r}$, where $p$ is a prime and $r$ is a positive integer. LRPC codes have originally been proposed by Gaborit et al.(2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank

Yakhot's model of strong turbulence: A generalization of scaling models of turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on the expression for the scaling exponents $\zeta_{n}$. We show that Yakhot's result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys. Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical justification for the method of extended self--similarity (ESS).Comment: 8 page