317 research outputs found
Heuristic search of (semi-)bent functions based on cellular automata
An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter
Artificial Intelligence for the design of symmetric cryptographic primitives
Algorithms and the Foundations of Software technolog
On the Evolution of Boomerang Uniformity in Cryptographic S-boxes
S-boxes are an important primitive that help cryptographic algorithms to be
resilient against various attacks. The resilience against specific attacks can
be connected with a certain property of an S-box, and the better the property
value, the more secure the algorithm. One example of such a property is called
boomerang uniformity, which helps to be resilient against boomerang attacks.
How to construct S-boxes with good boomerang uniformity is not always clear.
There are algebraic techniques that can result in good boomerang uniformity,
but the results are still rare. In this work, we explore the evolution of
S-boxes with good values of boomerang uniformity. We consider three different
encodings and five S-box sizes. For sizes and , we
manage to obtain optimal solutions. For , we obtain optimal
boomerang uniformity for the non-APN function. For larger sizes, the results
indicate the problem to be very difficult (even more difficult than evolving
differential uniformity, which can be considered a well-researched problem).Comment: 15 pages, 3 figures, 4 table
On applications of simulated annealing to cryptology
Boolean functions are critical building blocks of symmetric-key ciphers. In most cases, the security of a cipher against a particular kind of attacks can be explained by the existence of certain properties of its underpinning Boolean functions. Therefore, the design of appropriate functions has received significant attention from researchers for several decades. Heuristic methods have become very powerful tools for designing such functions. In this thesis, we apply simulated annealing methods to construct Boolean functions with particular properties. Our results meet or exceed the best results of available theoretical constructions and/or heuristic searches in the literature, including a 10-variable balanced Boolean function with resiliency degree 2, algebraic degree 7, and nonlinearity 488 for the first time. This construction affirmatively answers the open problem about the existence of such functions. This thesis also includes results of cryptanalysis for symmetric ciphers, such as Geffe cipher and TREYFER cipher
A NOVEL ALGORITHM ENUMERATING BENT FUNCTIONS
By the relationship between the Walsh spectra at partial points
and the Walsh spectra of its sub-functions, by the action of
general linear group on the set of Boolean functions, and by the
Reed-Muller transform, a novel method is developed, which can
theoretically construct all bent functions. With this method, we
enumerate all bent functions in 6 variables; in 8-variable case,
our method is more efficient than the method presented by Clark
though we still can not enumerate all bent functions; enumeration
of all homogeneous bent functions of degree 3 in eight variables
can be done in one minute by a P4 1.7G HZ computer; construction
of homogenous bent function of degree 3 in 10 variables is
efficient too; the nonexistence of homogeneous bent
functions in 10 variables of degree 4 is prove
Ongoing Research Areas in Symmetric Cryptography
This report is a deliverable for the ECRYPT European network of excellence in cryptology. It gives a brief summary of some of the research trends in symmetric cryptography at the time of writing. The following aspects of symmetric cryptography are investigated in this report: • the status of work with regards to different types of symmetric algorithms, including block ciphers, stream ciphers, hash functions and MAC algorithms (Section 1); • the recently proposed algebraic attacks on symmetric primitives (Section 2); • the design criteria for symmetric ciphers (Section 3); • the provable properties of symmetric primitives (Section 4); • the major industrial needs in the area of symmetric cryptography (Section 5)
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