The q-ary image of some qm-ary cyclic codes: permutation group and soft-decision decoding

Using a particular construction of generator matrices of the q-ary image of qm-ary cyclic codes, it is proved that some of these codes are invariant under the action of particular permutation groups. The equivalence of such codes with some two-dimensional (2-D) Abelian codes and cyclic codes is deduced from this property. These permutations are also used in the area of the soft-decision decoding of some expanded Reed–Solomon (RS) codes to improve the performance of generalized minimum-distance decoding

Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding

Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators (PCG) can be used to generate large amounts of useful forms of correlated (pseudo)randomness, using minimal interactions followed solely by local computations, yielding silent secure two-party computation protocols (protocols where the preprocessing phase requires almost no communication). An additional property called programmability allows to extend this to build N-party protocols. However, known constructions for programmable PCG's can only produce OLE's over large fields, and use rather new splittable Ring-LPN assumption. In this work, we overcome both limitations. To this end, we introduce the quasi-abelian syndrome decoding problem (QA-SD), a family of assumptions which generalises the well-established quasi-cyclic syndrome decoding assumption. Building upon QA-SD, we construct new programmable PCG's for OLE's over any field $\mathbb{F}_q$ with $q>2$. Our analysis also sheds light on the security of the ring-LPN assumption used in Boyle $\textit{et al.}$ (Crypto 2020). Using our new PCG's, we obtain the first efficient N-party silent secure computation protocols for computing general arithmetic circuit over $\mathbb{F}_q$ for any $q>2$.Comment: This is a long version of a paper accepted at CRYPTO'2

In search of mathematical primitives for deriving universal projective hash families

We provide some guidelines for deriving new projective hash families of cryptographic interest. Our main building blocks are so called group action systems; we explore what properties of this mathematical primitives may lead to the construction of cryptographically useful projective hash families. We point out different directions towards new constructions, deviating from known proposals arising from Cramer and Shoup's seminal work

Exponential Quantum Speed-ups are Generic

A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any sufficiently long quantum circuit one can construct a black-box problem which is solved by the circuit with a constant number of quantum queries, but which requires exponentially many classical queries, even if the classical machine has the ability to postselect. We prove the result in two steps. In the first, we show that almost any element of an approximate unitary 3-design is useful to solve a certain black-box problem efficiently. The problem is based on a recent oracle construction of Aaronson and gives an exponential separation between quantum and classical bounded-error with postselection query complexities. In the second step, which may be of independent interest, we prove that linear-sized random quantum circuits give an approximate unitary 3-design. The key ingredient in the proof is a technique from quantum many-body theory to lower bound the spectral gap of local quantum Hamiltonians.Comment: 24 pages. v2 minor correction

Agonistic behavior of captive saltwater crocodile, crocodylus porosus in Kota Tinggi, Johor

Agonistic behavior in Crocodylus porosus is well known in the wild, but the available data regarding this behavior among the captive individuals especially in a farm setting is rather limited. Studying the aggressive behavior of C. porosus in captivity is important because the data obtained may contribute for conservation and the safety for handlers and visitors. Thus, this study focuses on C. porosus in captivity to describe systematically the agonistic behaviour of C. porosus in relation to feeding time, daytime or night and density per pool. This study was carried out for 35 days in two different ponds. The data was analysed using Pearson’s chi-square analysis to see the relationship between categorical factors. The study shows that C. porosus was more aggressive during daylight, feeding time and non-feeding time in breeding enclosure (Pond C, stock density =0.0369 crocodiles/m2) as compared to non-breeding pond (Pond B, stock density =0.3317 crocodiles/m2) where it is only aggressive during the nighttime. Pond C shows the higher domination in the value of aggression in feeding and non-feeding time where it is related to its function as breeding ground. Chi-square analysis shows that there is no significant difference between ponds (p=0.47, χ2= 2.541, df= 3), thus, there is no relationship between categorical factors. The aggressive behaviour of C. porosus is important for the farm management to evaluate the risk in future for the translocation process and conservation of C. porosus generally

On the Communication Complexity of High-Dimensional Permutations

We study the multiparty communication complexity of high dimensional permutations in the Number On the Forehead (NOF) model. This model is due to Chandra, Furst and Lipton (CFL) who also gave a nontrivial protocol for the Exactly-n problem where three players receive integer inputs and need to decide if their inputs sum to a given integer n. There is a considerable body of literature dealing with the same problem, where (N,+) is replaced by some other abelian group. Our work can be viewed as a far-reaching extension of this line of research. We show that the known lower bounds for that group-theoretic problem apply to all high dimensional permutations. We introduce new proof techniques that reveal new and unexpected connections between NOF communication complexity of permutations and a variety of well-known problems in combinatorics. We also give a direct algorithmic protocol for Exactly-n. In contrast, all previous constructions relied on large sets of integers without a 3-term arithmetic progression