On the lower bound of cost of MDS matrices

Ever since lightweight cryptography emerged as one of the trending topics in symmetric key cryptography, optimizing the implementation cost of MDS matrices has been in the center of attention. In this direction, various metrics like d-XOR, s-XOR and g-XOR have been proposed to mimic the hardware cost. Consequently, efforts also have been made to search for the optimal MDS matrices for dimensions relevant to cryptographic applications according to these metrics. However, finding the optimal MDS matrix in terms of hardware cost still remains an unsolved problem. In this paper, we settle the question of the optimal 4 x 4 MDS matrices over GL(n, F2) under the recently proposed metric sequential XOR count based on words (sw-XOR). We prove that the sw-XOR of such matrices is at least 8n + 3, and the bound is tight as matrices with sw-XOR cost 35 and 67 for the values of n = 4 and 8, respectively, were already known. Moreover, the lower bound for these values of n matches with the known lower bounds according to s-XOR and g-XOR metrics

Development of Trust Based Access Control Models Using Fuzzy Logic in Cloud Computing

Cloud computing is the technology that provides the different types of services (Saas, Paas,and IaaS) as a useful resource on the Internet. So, computing in a cloud is the popular form of Internet applications and utilized by many users. The services and resources in the cloud environment are much vulnerable to attacks and threats. In the cloud environment, resource trust value will help the cloud users to select the services of a cloud provider for processing and storing their important information. Also, service providers can give access to the users on the basis of trust value, in order to secure the cloud resources from the malicious users. Although, over the time various control access models have been proposed for secure access to the cloud environment based on cryptography, identity, and trust. In this, trust models are proposed which comes under subjective trust model based on the behavior of user and service provider to calculate the value of trust. The trust is fuzzy in nature which motivated us to apply fuzzy logic for calculating the trust values of the cloud users and service providers in the cloud environment, this will make the more efficient environment. Parameters such as performance and elasticity are taken for trust evaluation of the resource. The attributes for calculating performance is workload and response time, for calculating elasticity we have taken scalability, availability, security, and usability. The fuzzy c-means clustering is applied on parameters for evaluating the trust value of users are bad requests, bogus requests, unauthorized requests and total requests. The proposed model is applied to a platform as a service in public cloud

On the Lower Bound of Cost of MDS Matrices

Ever since lightweight cryptography emerged as one of the trending topics in symmetric key cryptography, optimizing the implementation cost of MDS matrices has been in the center of attention. In this direction, various metrics like d-XOR, s-XOR and g-XOR have been proposed to mimic the hardware cost. Consequently, efforts also have been made to search for the optimal MDS matrices for dimensions relevant to cryptographic applications according to these metrics. However, finding the optimal MDS matrix in terms of hardware cost still remains an unsolved problem. In this paper, we settle the question of the optimal 4 x 4 MDS matrices over GL(n, F2) under the recently proposed metric sequential XOR count based on words (sw-XOR). We prove that the sw-XOR of such matrices is at least 8n + 3, and the bound is tight as matrices with sw-XOR cost 35 and 67 for the values of n = 4 and 8, respectively, were already known. Moreover, the lower bound for these values of n matches with the known lower bounds according to s-XOR and g-XOR metrics

Exhaustive Search for Various Types of MDS Matrices

MDS matrices are used in the design of diffusion layers in many block ciphers and hash functions due to their optimal branch number. But MDS matrices, in general, have costly implementations. So in search for efficiently implementable MDS matrices, there have been many proposals. In particular, circulant, Hadamard, and recursive MDS matrices from companion matrices have been widely studied. In a recent work, recursive MDS matrices from sparse DSI matrices are studied, which are of interest due to their low fixed cost in hardware implementation. In this paper, we present results on the exhaustive search for (recursive) MDS matrices over GL(4, F2). Specifically, circulant MDS matrices of order 4, 5, 6, 7, 8; Hadamard MDS matrices of order 4, 8; recursive MDS matrices from companion matrices of order 4; recursive MDS matrices from sparse DSI matrices of order 4, 5, 6, 7, 8 are considered. It is to be noted that the exhaustive search is impractical with a naive approach. We first use some linear algebra tools to restrict the search to a smaller domain and then apply some space-time trade-off techniques to get the solutions. From the set of solutions in the restricted domain, one can easily generate all the solutions in the full domain. From the experimental results, we can see the (non) existence of (involutory) MDS matrices for the choices mentioned above. In particular, over GL(4, F2), we provide companion matrices of order 4 that yield involutory MDS matrices, circulant MDS matrices of order 8, and establish the nonexistence of involutory circulant MDS matrices of order 6, 8, circulant MDS matrices of order 7, sparse DSI matrices of order 4 that yield involutory MDS matrices, and sparse DSI matrices of order 5, 6, 7, 8 that yield MDS matrices. To the best of our knowledge, these results were not known before. For the choices mentioned above, if such MDS matrices exist, we provide base sets of MDS matrices, from which all the MDS matrices with the least cost (with respect to d-XOR and s-XOR counts) can be obtained. We also take this opportunity to present some results on the search for sparse DSI matrices over finite fields that yield MDS matrices. We establish that there is no sparse DSI matrix S of order 8 over F28 such that S8 is MDS

Cherubism: Case Report with Review of Literature

Cherubism is a rare hereditary fibro-osseous lesion characterized by painless expansion of jaws in childhood and is known to regress without treatment after puberty. Wait and watch approach has been advocated by many authors. The disease starts early in life manifesting itself fully in the second decade of life and is almost regressed in the third decade. Here, we report two cases of cherubism with clinico-radiographic presentation of its classical features in their third and fourth decade of life respectively and review the literature