Factorable M{dimensional lters are interesting because they can be implemented e ciently: their computational complexity is O(Mn) instead of O(n ) (as in the case of generic non{factorable lters). Unfortunately, the pass{band support of a factorable lter can assume only very simple shapes (parallelepipeds with edges pairwise parallel to the axes), which are not adequate for most applications. I...

We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods across a cut of a graph. For many graph problems this number is the runtime bottleneck when using a divide-and-conquer approach. Boolean-width is similar to rank-width, which is related to the number of GF [2]-sums (1+1=0) of neighborhoods instead of the Boolean-sums (1+1=1) used for boole...

The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, k-error linear complexity, the minimum error and the k-error linear complexity profile, the notion of m-tight error linear complexity is presented. An efficient algorithm for computing m-tight error linear complexity is derived from the algo...

The security of pairing-based cryptosystems depends on the difficulty of the discrete logarithm problem (DLP) over certain types of finite fields. One of the most efficient algorithms for computing a pairing is the ηT pairing over supersingular curves on finite fields whose characteristic is 3. Indeed many high-speed implementations of this pairing have been reported, and it is an attractive ca...

In this work, the performance of probabilistic algebraic attacks is compared to classical (fast) algebraic attacks in the context of their application to certain linear beedback shift register (LFSR)-based stream ciphers. Using some results from coding theory it is shown that in terms of time complexity classical deterministic algebraic attacks are in general a more efficient cryptanalytic tool...

!he incidence matrix If of points and d-flats in PG(t, q) is a (O,l)-matrix which may be considered a _trAx with entries from the field GF (q) , where q is a prime power, q'" p. Let r d (t, 9.) denote thr rank of If over (JF (q). In this paper, & fonml.a for r t 1 (t, q) and an upper bound for r (t,q), 1 S d S t-l, are given. In the case q =p, the 'bound on rd(t,p) is attained. Similar results ...

The “Gluing Algorithm” of Semaev [Des. Codes Cryptogr. 49 (2008), 47–60] — that finds all solutions of a sparse system of linear equations over the Galois field GF (q) — has average running time O(mq| k 1Xj |), where m is the total number of equations, and ∪k1Xj is the set of all unknowns actively occurring in the first k equations. Our goal here is to minimize the exponent of q in the case whe...

Condensation is a critical technique for the Modular Atlas project, which analyzes modular matrix representations for finite groups. For large simple groups, these representations are more efficient computationally than the next alternative: permutation representations. A new approach to direct condensation is presented that uses parallel disk as primary storage. This approach offers a running ...

We consider the complexity of the equivalence and containment problems for regular expressions and context-free grammars, concentrating on the relationship between complexity and various language properties. Finiteness and boundedness of languages are shown to play important roles in the complexity of these problems. An encoding into grammars of Tur ing machine computations exponential in the s...