69 research outputs found
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 , where is a prime and 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 . 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
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