12,753 research outputs found
Doubly Perfect Nonlinear Boolean Permutations
Due to implementation constraints the XOR operation is widely used in order
to combine plaintext and key bit-strings in secret-key block ciphers. This
choice directly induces the classical version of the differential attack by the
use of XOR-kind differences. While very natural, there are many alternatives to
the XOR. Each of them inducing a new form for its corresponding differential
attack (using the appropriate notion of difference) and therefore block-ciphers
need to use S-boxes that are resistant against these nonstandard differential
cryptanalysis. In this contribution we study the functions that offer the best
resistance against a differential attack based on a finite field
multiplication. We also show that in some particular cases, there are robust
permutations which offers the best resistant against both multiplication and
exponentiation base differential attacks. We call them doubly perfect nonlinear
permutations
Further Results of the Cryptographic Properties on the Butterfly Structures
Recently, a new structure called butterfly introduced by Perrin et at. is
attractive for that it has very good cryptographic properties: the differential
uniformity is at most equal to 4 and algebraic degree is also very high when
exponent . It is conjecture that the nonlinearity is also optimal for
every odd , which was proposed as a open problem. In this paper, we further
study the butterfly structures and show that these structure with exponent
have also very good cryptographic properties. More importantly, we
prove in theory the nonlinearity is optimal for every odd , which completely
solve the open problem. Finally, we study the butter structures with trivial
coefficient and show these butterflies have also optimal nonlinearity.
Furthermore, we show that the closed butterflies with trivial coefficient are
bijective as well, which also can be used to serve as a cryptographic
primitive.Comment: 20 page
Cryptographic properties of Boolean functions defining elementary cellular automata
In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time
QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments
QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments
Algorithm 959: VBF: A Library of C plus plus Classes for Vector Boolean Functions in Cryptography
VBF is a collection of C++ classes designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This implementation uses the NTL library from Victor Shoup, adding new modules that call NTL functions and complement the existing ones, making it better suited to cryptography. The class representing a vector Boolean function can be initialized by several alternative types of data structures such as Truth Table, Trace Representation, and Algebraic Normal Form (ANF), among others. The most relevant cryptographic criteria for both block and stream ciphers as well as for hash functions can be evaluated with VBF: it obtains the nonlinearity, linearity distance, algebraic degree, linear structures, and frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions are presented. Finally, three real applications of the library are described: the first one analyzes the KASUMI block cipher, the second one analyzes the Mini-AES cipher, and the third one finds Boolean functions with very high nonlinearity, a key property for robustness against linear attacks
C-DIFFERENTIALS AND GENERALIZED CRYPTOGRAPHIC PROPERTIES OF VECTORIAL BOOLEAN AND P-ARY FUNCTIONS
This dissertation investigates a newly defined cryptographic differential, called a c-differential, and its relevance to the nonlinear substitution boxes of modern symmetric block ciphers. We generalize the notions of perfect nonlinearity, bentness, and avalanche characteristics of vectorial Boolean and p-ary functions using the c-derivative and a new autocorrelation function, while capturing the original definitions as special cases (i.e., when c=1). We investigate the c-differential uniformity property of the inverse function over finite fields under several extended affine transformations. We demonstrate that c-differential properties do not hold in general across equivalence classes typically used in Boolean function analysis, and in some cases change significantly under slight perturbations. Thus, choosing certain affine equivalent functions that are easy to implement in hardware or software without checking their c-differential properties could potentially expose an encryption scheme to risk if a c-differential attack method is ever realized. We also extend the c-derivative and c-differential uniformity into higher order, investigate some of their properties, and analyze the behavior of the inverse function's second order c-differential uniformity. Finally, we analyze the substitution boxes of some recognizable ciphers along with certain extended affine equivalent variations and document their performance under c-differential uniformity.Commander, United States NavyApproved for public release. Distribution is unlimited
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