Fixing the Sorting Algorithm for Android, Java and Python

Tim Peters developed the Timsort hybrid sorting algorithm in 2002. TimSort was first developed for Python, a popular programming language, but later ported to Java (where it appears as java.util.Collections.sort and java.util.Arrays.sort). TimSort is today used as the default sorting algorithm in Java, in Android (a widely used platform by Google for mobile devices), in Python and many other programming languages and frameworks. Given the popularity of these platforms this means that the number of computers, cloud services and mobile phones that use TimSort for sorting is well into the billions. After we had successfully verified Counting and Radix sort implementations in Java [1] with a formal verification tool called KeY, we were looking for a new challenge. TimSort seemed to fit the bill, as it is rather complex and widely used. Unfortunately, we weren’t able to prove its correctness. A closer analysis showed that this was, quite simply, because

A Generic Approach to Searching for Jacobians

We consider the problem of finding cryptographically suitable Jacobians. By applying a probabilistic generic algorithm to compute the zeta functions of low genus curves drawn from an arbitrary family, we can search for Jacobians containing a large subgroup of prime order. For a suitable distribution of curves, the complexity is subexponential in genus 2, and O(N^{1/12}) in genus 3. We give examples of genus 2 and genus 3 hyperelliptic curves over prime fields with group orders over 180 bits in size, improving previous results. Our approach is particularly effective over low-degree extension fields, where in genus 2 we find Jacobians over F_{p^2) and trace zero varieties over F_{p^3} with near-prime orders up to 372 bits in size. For p = 2^{61}-1, the average time to find a group with 244-bit near-prime order is under an hour on a PC.Comment: 22 pages, to appear in Mathematics of Computatio

Copy-move forgery detection: a survey on time complexity issues and solutions

As the image processing especially image editing software evolve, more image manipulations were possible to be done, thus authentication of image become a very crucial task. Copy-move forgery detection (CMFD), a popular research focus in digital image forensic, is used to authenticate an image by detecting malicious copy-move tampering in an image. Copy-move forgery occurs when a region in an image is copied and paste into the same image. There were many survey and review papers discussed about CMFD robustness and accuracy yet less attention was given to performance and time complexity. In this paper, we attempts to highlight the key factors contribute to the time complexity issue. Before that, the CMFD processes were first explained for better understanding. The trends of tackling those issues are then explored. Finally, numbers of proposed solutions will be outlined to conclude this paper