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We provide an efficient multi-node, multi-GPU implementation of the Block Wiedemann Algorithm (BWA)to find the solution of a large sparse system of linear equations over GF(2). One of the important applications ofsolving such systems arises in most integer factorization algorithms like Number Field Sieve. In this paper, wedescribe how hybrid parallelization can be adapted to speed up the most time-consuming sequence generation stage of BWA. This stage involves generating a sequence of matrix-matrix products and matrix transpose-matrix products where the matrices are very large, highly sparse, and have entries over GF(2). We describe a GPU-accelerated parallel method for the computation of these matrix-matrix products using techniques like row-wise parallel distribution of the first matrix over multi-node multi-GPU platform using MPI and CUDA and word-wise XORing of rows of the second matrix. We also describe the hybrid parallelization of matrix transpose-matrix product computation, where we divide both the matrices row-wise into equal-sized blocks using MPI. Then after a GPU-accelerated matrix transpose-matrix product generation, we combine all those blocks using MPI_BXOR operation in MPI_Reduce to obtain the result. The performance of hybrid parallelization of the sequence generation step on a hybrid cluster using multiple GPUs has been compared with parallelization on only multiple MPI processors. We have used this hybrid parallel sequence generation tool for the benchmarking of an HPC cluster. Detailed timings of the complete solution of number field sieve matrices of RSA-130, RSA-140, and RSA-170 are also compared in this paper using up to 4 NVidia V100 GPUs of a DGX station. We got a speedup of 2.8 after parallelization on 4 V100 GPUs compared to that over 1 GPU.

<p>In the present cyber age, public services are getting more and more dependent on use of Information and communication technologies (ICT) day by day. A number of applications viz., Internet of Things, PDF, cloud computing and virtualization and machine to machine (M2M) system usage are sneaking deeply into our everyday life. The more we depend on ICT, the more deepens our concern about IT security or cyber security. Cyber security protects the data and integrity of assets that belong to or connect to a network. It is meant to defend those assets against all sorts of threat actors throughout the life cycle of a cyber attack. It is quite unsurprising that cyber security industry is growing at the same pace as ICT is doing.</p>

Group Key Distribution (GKD) protocols are designed to distribute a group key to several users for establishing a secure communication over a public network. The central trusted authority, called the key distribution center (KDC) is in charge of distributing the group keys. For securing the communication, all the users share a common secret key in advance with KDC. In this paper, we propose a secure and efficient Group Authenticated Key Distribution (GAKD) protocol based on the simple idea of encryption in matrix rings. In this protocol, each user registers in private with the KDC, while all the other information can be transferred publicly. The scheme also supports authentication of group keys without assuming computational hard problems such as Integer Factorization Problem (IFP).The analysis of our GAKD protocol shows that the proposed protocol is resistant to reply, passive and impersonation attacks. Our construction leads to a secure, cost and computation- effective GAKD protocol.

Here, we assume the construction of cyclic codes over ℜ={F}_{2}[u,v]/ < u^2, v^2 - v, uv - vu >. In particular, dual cyclic codes over ℜ= {F}_{2}[u]/ <u^2> with respect to Euclidean inner product are discussed. The cyclic dual codes over ℜ are studied with respect to DNA codes (reverse and reverse complement). Many interesting results are obtained. Some examples are also provided, which explain the main results. The GC-Content and DNA codes over ℜ are discussed. We summarise the article by giving a special DNA table.

Conventional cryptanalysis techniques necessitate an extensive analysis of non-linear functions defining the relationship of plain data, key, and corresponding cipher data. These functions have very high degree terms and make cryptanalysis work extremely difficult. The advent of deep learning algorithms along with the better and efficient computing resources has brought new opportunities to analyze cipher data in its raw form. The basic principle of designing a cipher is to introduce randomness into it, which means the absence of any patterns in cipher data. Due to this fact, the analysis of cipher data in its raw form becomes essential. Deep learning algorithms are different from conventional machine learning algorithms as the former directly work on raw data without any formal requirement of feature selection or feature extraction steps. With these facts and the assumption of the suitability of employing deep learning algorithms for cipher data, authors introduced a deep learning based method for finding biases in stream ciphers in the black-box analysis model. The proposed method has the objective to predict the occurrence of an output bit/byte at a specific location in the stream cipher generated keystream. The authors validate their method on stream cipher RC4 and its improved variant RC4A and discuss the results in detail. Further, the authors apply the method on two more stream ciphers namely Trivium and TRIAD. The proposed method can find bias in RC4 and shows the absence of this bias in its improved variant and other two ciphers. Focusing on RC4, the authors present a comparative analysis with some existing methods in terms of approach and observations and showed that their process is more straightforward and less complicated than the existing ones.