Recent years have witnessed an exceptional research interest in cryptographic hash functions, especially after the popular attacks against MD5 and SHA-1 in 2005. In 2007, the U.S. National Institute of Standards and Technology (NIST) has also significantly boosted this interest by announcing a public competition to select the next hash function standard, to be named SHA-3. Not surprisingly, the...

Following Gennaro, Gentry, and Parno (Cryptology ePrint Archive 2009/547), we use fully homomorphic encryption to design improved schemes for delegating computation. In such schemes, a delegator outsources the computation of a function F on many, dynamically chosen inputs xi to a worker in such a way that it is infeasible for the worker to make the delegator accept a result other than F (xi). T...

And now you ask: What is the running time of the main program in terms of n? Given the above, this is difficult to answer. f(a) makes a2 multiplications. How much time does a multiplication take? That depends strongly on the multiplication algorithm, let’s call the time needed for a multiplication of length-a integers m(a). So the time spent by f(a) is at most “a2m(a) + additional stuff”. For a...

In this paper, we introduce a way of constructing a rough set via grill ordered topological spaces. Increasing and decreasing sets are defined based on grill and comparisons between current approximations and previous approximations by Shafei and Kandil are carried out. Also it is shown that the chances of getting better approximation by our method of approximations are greater than any of the ...

Cryptology consists of two complementary fields of research. One is cryptography where the development of new schemes or algorithms are concerned with its security analysis. The other one is cryptanalysis where attacks for the cryptographic algorithms are being studied. Hash function, message authentication code (or MAC), encryption and authenticated encryption are widely used objects in crypto...

This paper provides an overview of current cryptographic techniques, targeting management and focussing on applicability of cryptographic tools and on the level of their security. The paper shows real-life examples and latest developments in the area. It also brings recommendations that should help managers to understand the necessary basics, what is really important and how to manage cryptology.

Project co-funded by the European Commission within the 6th Framework Programme Dissemination Level PU Public X PP Restricted to other programme participants (including the Commission services) RE Restricted to a group specified by the consortium (including the Commission services) CO Confidential, only for members of the consortium (including the Commission services)

A probability is an indicator how likely something is to happen. For example, if we roll probability a die, we may ask what the probability is that we roll a six. In other words, there is a certain event A := “we roll a six”, and we ask for the probability Pr[A] that this event event occurs. In our example, for a fair die, Pr[A] = 16 because there are six equally likely numbers we can roll. So,...