2,265 research outputs found

    Large substitution boxes with efficient combinational implementations

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    At a fundamental level, the security of symmetric key cryptosystems ties back to Claude Shannon\u27s properties of confusion and diffusion. Confusion can be defined as the complexity of the relationship between the secret key and ciphertext, and diffusion can be defined as the degree to which the influence of a single input plaintext bit is spread throughout the resulting ciphertext. In constructions of symmetric key cryptographic primitives, confusion and diffusion are commonly realized with the application of nonlinear and linear operations, respectively. The Substitution-Permutation Network design is one such popular construction adopted by the Advanced Encryption Standard, among other block ciphers, which employs substitution boxes, or S-boxes, for nonlinear behavior. As a result, much research has been devoted to improving the cryptographic strength and implementation efficiency of S-boxes so as to prohibit cryptanalysis attacks that exploit weak constructions and enable fast and area-efficient hardware implementations on a variety of platforms. To date, most published and standardized S-boxes are bijective functions on elements of 4 or 8 bits. In this work, we explore the cryptographic properties and implementations of 8 and 16 bit S-boxes. We study the strength of these S-boxes in the context of Boolean functions and investigate area-optimized combinational hardware implementations. We then present a variety of new 8 and 16 bit S-boxes that have ideal cryptographic properties and enable low-area combinational implementations

    SPACE EGGS - Satellite Coverage Model for Low Earth Orbit Constellations

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    The effectiveness calculations of global, regional, and area coverage for proliferated small satellite constellations in low altitude orbits stress the capability of conventional analytical techniques. A new approach that combines the Mollweide (equal area) projection with an on-screen color manipulation of the picture elements (or pixels) has been developed and utilized over the past decade. This technique enables the optimization of large satellite constellations with multiple communication or sensor viewing configurations, with a minimum number of calculations. Complex viewing geometries are well adapted with this analytical approach, along with exclusion requirements such as the sun, moon or earth avoidance. This technique has proven useful in minimizing the number of low altitude communication satellites (for any planet) and optimizing the sensor suite for specific missions

    Optimizing S-box Implementations for Several Criteria using SAT Solvers

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    We explore the feasibility of applying SAT solvers to optimizing implementations of small functions such as S-boxes for multiple optimization criteria, e.g., the number of nonlinear gates and the number of gates. We provide optimized implementations for the S-boxes used in Ascon, ICEPOLE, Joltik/Piccolo, Keccak/Ketje/Keyak, LAC, Minalpher, PRIMATEs, Pr\o st, and RECTANGLE, most of which are candidates in the secound round of the CAESAR competition. We then suggest a new method to optimize for circuit depth and we make tooling publicly available to find efficient implementations for several criteria. Furthermore, we illustrate with the 5-bit S-box of PRIMATEs how multiple optimization criteria can be combined

    Solving Circuit Optimisation Problems in Cryptography and Cryptanalysis

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    One of the hardest problems in computer science is the problem of gate-eficient implementation. Such optimizations are particularly important in industrial hardware implementations of standard cryptographic algorithms. In this paper we focus on optimizing some small circuits such as S-boxes in cryptographic algorithms. We consider the notion of Multiplicative Complexity studied in 2008 by Boyar and Peralta and applied to find interesting optimizations for the S-box of the AES cipher. We applied this methodology to produce a compact implementation of several ciphers. In this short paper we report our results on PRESENT and GOST, two block ciphers known for their exceptionally low hardware cost. This kind of representation seems to be very promising in implementations aiming at preventing side channel attacks on cryptographic chips such as DPA. More importantly, we postulate that this kind of minimality is also an important and interesting tool in cryptanalysis

    Minimization of Bitsliced Representation of 4×4 S-Boxes based on Ternary Logic Instruction

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    The article is devoted to methods and tools for generating software-oriented bit-sliced descriptions of bijective 4×4 S-Boxes with a reduced number of instructions based on a ternary logical instruction. Bitsliced descriptions generated by the proposed method make it possible to improve the performance and security of software implementations of crypto-algorithms using 4×4 S-Boxes on various processor architectures. The paper develops a heuristic minimization method that uses a ternary logical instruction, which is available in ×86–64 processors with AVX-512 support and some GPU processors. Thanks to the combination of various heuristic techniques (preliminary calculations, exhaustive search to a certain depth, refinement search) in the method, it was possible to reduce the number of gates in bit-sliced descriptions of S-Boxes compared to other known methods. The corresponding software in the form of a utility in the Python language was developed and its operation was tested on 225 S-Boxes of various crypto-algorithms. It was established that the developed method generates a bit-sliced description with a smaller number of ternary instructions in 90.2% of cases, compared to the best-known method implemented in the sboxgates utility

    Optimizing visual properties of game content through neuroevolution

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    This paper presents a search-based approach to generating game content that satisfies both gameplay requirements and user-expressed aesthetic criteria. Using evolutionary constraint satisfaction, we search for spaceships (for a space combat game) represented as compositional patternproducing networks. While the gameplay requirements are satisfied by ad-hoc defined constraints, the aesthetic evaluation function can also be informed by human aesthetic judgement. This is achieved using indirect interactive evolution, where an evaluation function re-weights an array of aesthetic criteria based on the choices of a human player. Early results show that we can create aesthetically diverse and interesting spaceships while retaining in-game functionality.peer-reviewe

    Optimizing Implementations of Lightweight Building Blocks

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    We study the synthesis of small functions used as building blocks in lightweight cryptographic designs in terms of hardware implementations. This phase most notably appears during the ASIC implementation of cryptographic primitives. The quality of this step directly affects the output circuit, and while general tools exist to carry out this task, most of them belong to proprietary software suites and apply heuristics to any size of functions. In this work, we focus on small functions (4- and 8-bit mappings) and look for their optimal implementations on a specific weighted instructions set which allows fine tuning of the technology. We propose a tool named LIGHTER, based on two related algorithms, that produces optimized implementations of small functions. To demonstrate the validity and usefulness of our tool, we applied it to two practical cases: first, linear permutations that define diffusion in most of SPN ciphers; second, non-linear 4-bit permutations that are used in many lightweight block ciphers. For linear permutations, we exhibit several new MDS diffusion matrices lighter than the state-of-the-art, and we also decrease the implementation cost of several already known MDS matrices. As for non-linear permutations, LIGHTER outperforms the area-optimized synthesis of the state-of-the-art academic tool ABC. Smaller circuits can also be reached when ABC and LIGHTER are used jointly

    Shorter Linear Straight-Line Programs for MDS Matrices

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    Recently a lot of attention is paid to the search for efficiently implementable MDS matrices for lightweight symmetric primitives. Previous work concentrated on locally optimizing the multiplication with single matrix elements. Separate from this line of work, several heuristics were developed to find shortest linear straight-line programs. Solving this problem actually corresponds to globally optimizing multiplications by matrices. In this work we combine those, so far largely independent line of works. As a result, we achieve implementations of known, locally optimized, and new MDS matrices that significantly outperform all implementations from the literature. Interestingly, almost all previous locally optimized constructions behave very similar with respect to the globally optimized implementation. As a side effect, our work reveals the so far best implementation of the AES MixColumns operation with respect to the number of XOR operations needed
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