Yassir Nawaz

Towards a general RC4-Like keystream generator

RC4 was designed in 1987 when 8-bit and 16-bit processors were commercially available. Today, most processors use 32-bit or 64-bit words but using original RC4 with 32/64 bits is infeasible due to the large memory constraints and the number of operations in the key scheduling algorithm. In this paper we propose a new 32/64-bit RC4-like keystream generator. The proposed generator produces 32 or 64 bits in each iteration and can be implemented in software with reasonable memory requirements. It has a huge internal state and offers higher resistance to state recovery attacks than the original 8-bit RC4. Further, on a 32-bit processor the generator is 3.1 times faster than original RC4. We also show that it can resist attacks that are successful on the original RC4. The generator is suitable for high speed software encryption.

WG: A family of stream ciphers with designed randomness properties

In this paper we present a family of stream ciphers which generate a keystream with ideal two-level autocorrelation. The design also guarantees other randomness properties, i.e., balance, long period, ideal tuple distribution, and high and exact linear complexity. We discuss how these properties are achieved by the proposed design and show how to select various parameters to obtain an efficient stream cipher for the desired security level. We also show that the proposed generators are secure against time/memory/data tradeoff attacks, algebraic attacks and correlation attacks. Finally we present WG-128 as a concrete example of a WG stream cipher with a key size of 128bits.

Upper bounds on algebraic immunity of boolean power functions

Algebraic attacks have received a lot of attention in studying security of symmetric ciphers. The function used in a symmetric cipher should have high algebraic immunity (AI) to resist algebraic attacks. In this paper we are interested in finding AI of Boolean power functions. We give an upper bound on the AI of any Boolean power function and a formula to find its corresponding low degree multiples. We prove that the upper bound on the AI for Boolean power functions with Inverse, Kasami and Niho exponents are � √ n� + � n � √ n� �− 2, � √ n� + � n � √ n� � and � √ n� + � n � √ n� � respectively. We also generalize this idea to Boolean polynomial functions. All existing algorithms to determine AI and cor- responding low degree multiples become too complex if the function has more than 25 variables. In our approach no algorithm is required. The AI and low degree multiples can be obtained directly from the given formula.

Algebraic Immunity of S-Boxes Based on Power Mappings: Analysis and Construction

The algebraic immunity of an S-box depends on the number and type of linearly independent multivariate equations it satisfies. In this paper, techniques are developed to find the number of linearly independent, multivariate, bi-affine, and quadratic equations for S-boxes based on power mappings. These techniques can be used to prove the exact number of equations for any class of power mappings. Two algorithms to calculate the number of bi-affine and quadratic equations for any (n,n) S-box based on power mapping are also presented. The time complexity of both algorithms is only O(n 2) . To design algebraically immune S-boxes, four new classes of S-boxes that guarantee zero bi-affine equations and one class of S-boxes that guarantees zero quadratic equations are presented. The algebraic immunity of power mappings based on Kasami, Niho, Dobbertin, Gold, Welch, and inverse exponents are discussed along with other cryptographic properties and several cryptographically strong S-boxes are identified. It is conjectured that a known Kasami-like highly nonlinear power mapping is differentially 4 -uniform. Finally, an open problem to find an (n,n) bijective nonlinear S-box with more than 5n quadratic equations is solved.

Upper bound for algebraic immunity on a subclass of Maiorana McFarland class of bent functions

Studying algebraic immunity of Boolean functions is recently a very important research topic in cryptography. It is recently proved by Courtois and Meier that for any Boolean function of n-variable the maximum algebraic immunity is @?n2@?. We found a large subclass of Maiorana McFarland bent functions on n-variable with a proven low level of algebraic immunity =<@?n4@?+2. To the best of our knowledge we provide for the first time a new upper bound for algebraic immunity for a nontrivial class of Boolean functions. We also discuss that this result has some fascinating implications.

Distributing fixed time slices in heterogeneous networks of workstations (NOWs)

Heterogeneous Networks of Workstations (NOWs) offer a cost-effective solution for parallel processing. The completion time of a parallel task over NOWs depends on how the task is divided and distributed among the heterogeneous workstations. In this paper we present a distribution scheme which attempts to minimize the tasks completion time over a heterogeneous NOWs. The scheme is based on the idea of distributing fixed time slices of work as opposed to fixed work slices. Our simulations show that the proposed scheme outperforms both fixed and variable work distribution schemes commonly in use. The scheme is very simple and requires no active monitoring of the network. Furthermore it is adaptive and copes very well with the changes in background loads on workstations and network interference.