35 research outputs found
Exhaustive Generation of Linear Orthogonal Cellular Automata
We consider the problem of exhaustively visiting all pairs of linear cellular
automata which give rise to orthogonal Latin squares, i.e., linear Orthogonal
Cellular Automata (OCA). The problem is equivalent to enumerating all pairs of
coprime polynomials over a finite field having the same degree and a nonzero
constant term. While previous research showed how to count all such pairs for a
given degree and order of the finite field, no practical enumeration algorithms
have been proposed so far. Here, we start closing this gap by addressing the
case of polynomials defined over the field \F_2, which corresponds to binary
CA. In particular, we exploit Benjamin and Bennett's bijection between coprime
and non-coprime pairs of polynomials, which enables us to organize our study
along three subproblems, namely the enumeration and count of: (1) sequences of
constant terms, (2) sequences of degrees, and (3) sequences of intermediate
terms. In the course of this investigation, we unveil interesting connections
with algebraic language theory and combinatorics, obtaining an enumeration
algorithm and an alternative derivation of the counting formula for this
problem.Comment: 9 pages, 1 figure. Submitted to the exploratory track of AUTOMATA
2023. arXiv admin note: text overlap with arXiv:2207.0040
Balanced crossover operators in Genetic Algorithms
In several combinatorial optimization problems arising in cryptography and design theory, the admissible solutions must often satisfy a balancedness constraint, such as being represented by bitstrings with a fixed number of ones. For this reason, several works in the literature tackling these optimization problems with Genetic Algorithms (GA) introduced new balanced crossover operators which ensure that the offspring has the same balancedness characteristics of the parents. However, the use of such operators has never been thoroughly motivated, except for some generic considerations about search space reduction. In this paper, we undertake a rigorous statistical investigation on the effect of balanced and unbalanced crossover operators against three optimization problems from the area of cryptography and coding theory: nonlinear balanced Boolean functions, binary Orthogonal Arrays (OA) and bent functions. In particular, we consider three different balanced crossover operators (each with two variants: \u201cleft-to-right\u201d and \u201cshuffled\u201d), two of which have never been published before, and compare their performances with classic one-point crossover. We are able to confirm that the balanced crossover operators perform better than one-point crossover. Furthermore, in two out of three crossovers, the \u201cleft-to-right\u201d version performs better than the \u201cshuffled\u201d version
Evolutionary Strategies for the Design of Binary Linear Codes
The design of binary error-correcting codes is a challenging optimization
problem with several applications in telecommunications and storage, which has
also been addressed with metaheuristic techniques and evolutionary algorithms.
Still, all these efforts focused on optimizing the minimum distance of
unrestricted binary codes, i.e., with no constraints on their linearity, which
is a desirable property for efficient implementations. In this paper, we
present an Evolutionary Strategy (ES) algorithm that explores only the subset
of linear codes of a fixed length and dimension. To that end, we represent the
candidate solutions as binary matrices and devise variation operators that
preserve their ranks. Our experiments show that up to length , our ES
always converges to an optimal solution with a full success rate, and the
evolved codes are all inequivalent to the Best-Known Linear Code (BKLC) given
by MAGMA. On the other hand, for larger lengths, both the success rate of the
ES as well as the diversity of the evolved codes start to drop, with the
extreme case of codes which all turn out to be equivalent to MAGMA's
BKLC.Comment: 15 pages, 3 figures, 3 table
NASCTY: Neuroevolution to Attack Side-channel Leakages Yielding Convolutional Neural Networks
Side-channel analysis (SCA) can obtain information related to the secret key
by exploiting leakages produced by the device. Researchers recently found that
neural networks (NNs) can execute a powerful profiling SCA, even on targets
protected with countermeasures. This paper explores the effectiveness of
Neuroevolution to Attack Side-channel Traces Yielding Convolutional Neural
Networks (NASCTY-CNNs), a novel genetic algorithm approach that applies genetic
operators on architectures' hyperparameters to produce CNNs for side-channel
analysis automatically. The results indicate that we can achieve performance
close to state-of-the-art approaches on desynchronized leakages with mask
protection, demonstrating that similar neuroevolution methods provide a solid
venue for further research. Finally, the commonalities among the constructed
NNs provide information on how NASCTY builds effective architectures and deals
with the applied countermeasures.Comment: 19 pages, 6 figures, 4 table
Bent functions in the partial spread class generated by linear recurring sequences
We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if their feedback polynomials are relatively prime. Then, we characterize the appropriate parameters for a family of pairwise coprime polynomials to generate a partial spread required for the support of a bent function, showing that such families exist if and only if the degrees of the underlying polynomials are either 1 or 2. We then count the resulting sets of polynomials and prove that, for degree 1, our LRS construction coincides with the Desarguesian partial spread. Finally, we perform a computer search of all PS− and PS+ bent functions of n=8 variables generated by our construction and compute their 2-ranks. The results show that many of these functions defined by polynomials of degree d=2 are not EA-equivalent to any Maiorana–McFarland or Desarguesian partial spread function
Smooth Number Message Authentication Code in the IoT Landscape
This paper presents the Smooth Number Message Authentication Code (SNMAC) for
the context of lightweight IoT devices. The proposal is based on the use of
smooth numbers in the field of cryptography, and investigates how one can use
them to improve the security and performance of various algorithms or security
constructs. The literature findings suggest that current IoT solutions are
viable and promising, yet they should explore the potential usage of smooth
numbers. The methodology involves several processes, including the design,
implementation, and results evaluation. After introducing the algorithm,
provides a detailed account of the experimental performance analysis of the
SNMAC solution, showcasing its efficiency in real-world scenarios. Furthermore,
the paper also explores the security aspects of the proposed SNMAC algorithm,
offering valuable insights into its robustness and applicability for ensuring
secure communication within IoT environments.Comment: 19 pages, 7 figure