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In 2005, Philippe Guillot presented a new construction of Boolean functions using linear codes as an extension of the Maiorana–McFarland’s (MM) construction of bent functions. In this paper, we study a new family of Boolean functions with cryptographically strong properties, such as non-linearity, propagation criterion, resiliency, and balance. The construction of cryptographically strong Boolean functions is a daunting task, and there is currently a wide range of algebraic techniques and heuristics for constructing such functions, however, these methods can be complex, computationally difficult to implement, and not always produce a sufficient variety of functions. We present in this paper a construction of Boolean functions using algebraic codes following Guillot’s work.

In this chapter, we discuss results obtained on an application of the Hadamard transform to cryptanalysis, and in particular, we determine the probability to decipher different pseudo-random number generators used as components of stream ciphers.

We present an efficient endomorphism for the Jacobian of a curve $C$ of genus 2 (hyperelliptic) for divisors having a Non disjoint support. This extends the work of Costello and Lauter in [12] who calculated explicit formulae for divisor doubling and addition of divisors with disjoint support in $\mathbb{J}(C)$ using only base field operations. Explicit formulae is presented for this third case and a slightly different approach for divisor doubling., 3 figures, presented at CECC2014, Budapest Hungary

A parallel backtrack search is carried out to classify, up to isomorphism, all combinatorial (19 4 ) configurations. A total of 269 224 652 such configurations were found. We prove that two of the combinatorial (19 4 ) configurations are not geometrically realizable over any field. Also we confirmed the computation of the 971 171 combinatorial (18 4 ) configurations which lacked an independent verification.

In this work we discuss results obtained from an application of the Hadamard transform to cryptanalysis, and in particular, we determine the probability to decipher different pseudo-random number generators used as components of stream ciphers. Also, we found a relationship between entropy and Hadamard’s values.

A computer search over the words of weight 3 in the code of blocks of a classical Steiner triple system (STS) on 31 points is carried out to classify all STS(31) whose incidence matrix has 2-rank equal to 27, one more than the possible minimum of 26. There is a total of 1239 nonisomorphic STS(31) of 2-rank 27.