Topic
Boolean function
About: Boolean function is a research topic. Over the lifetime, 10089 publications have been published within this topic receiving 201604 citations. The topic is also known as: Boolean operation.
Papers published on a yearly basis
1 / 2
Papers
9 Sep 2012
TL;DR: It is shown that the differential fault attack can indeed be efficiently mounted for the Boolean function used in Grain v1 and the exact design criteria for Boolean functions to be used in grain like structure is provided.
Abstract: In this paper we study a differential fault attack against the Grain family of stream ciphers. The attack works due to certain properties of the Boolean functions and corresponding choices of the taps from the LFSR. The existing works, by Berzati et al. (2009) and Karmakar et al. (2011), are applicable only on Grain-128 exploiting certain properties of the combining Boolean function h. That idea could not easily be extended to the corresponding Boolean function used in Grain v1. Here we show that the differential fault attack can indeed be efficiently mounted for the Boolean function used in Grain v1. In this case we exploit the idea that there exists certain suitable α such that $h(\mathbf{x}) + h({\mathbf x} + \mathbf{\alpha})$ is linear. In our technique, we present methods to identify the fault locations and then construct set of linear equations to obtain the contents of the LFSR and the NFSR. As a countermeasure to such fault attack, we provide exact design criteria for Boolean functions to be used in Grain like structure.
100 citations
TL;DR: In this paper, a framework for the formal specification and verification of quantum circuits based on the Feynman path integral is introduced, which provides a structured and natural way of specifying quantum operations, particularly for quantum implementations of classical functions.
Abstract: We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of specifying quantum operations, particularly for quantum implementations of classical functions. Verification of circuits over all levels of the Clifford hierarchy with respect to either a specification or reference circuit is enabled by a novel rewrite system for exponential sums with free variables. Our algorithm is further shown to give a polynomial-time decision procedure for checking the equivalence of Clifford group circuits. We evaluate our methods by performing automated verification of optimized Clifford+T circuits with up to 100 qubits and thousands of T gates, as well as the functional verification of quantum algorithms using hundreds of qubits. Our experiments culminate in the automated verification of the Hidden Shift algorithm for a class of Boolean functions in a fraction of the time it has taken recent algorithms to simulate.
99 citations
TL;DR: Different from traditional methods, this work converts the construction of n × n S-box into a process of putting n Boolean functions one by one into a container and proposes a novel genetic algorithm to construct bijective S-boxes with high nonlinearity.
98 citations
1 Jan 2004
TL;DR: A general secondary construction of Boolean functions, permitting to obtain resilient functions achieving the best possible trade-offs between resiliency order, algebraic degree and nonlinearity and applied to design more numerous functions achieving optimum trade-off between the three characteristics.
Abstract: We first give a survey of the known secondary constructions of Boolean functions, permitting to obtain resilient functions achieving the best possible trade-offs between resiliency order, algebraic degree and nonlinearity (that is, achieving Siegenthaler’s bound and Sarkar et al.’s bound). We introduce then, and we study, a general secondary construction of Boolean functions. This construction includes as particular cases the known secondary constructions previously recalled. We apply this construction to design more numerous functions achieving optimum trade-offs between the three characteristics (and additionally having no linear structure). We conclude the paper by indicating generalizations of our construction to Boolean and vectorial functions, and by relating it to a known secondary construction of bent functions.
98 citations
28 Oct 1981
TL;DR: This work provides an intimate link between PDL as defined by the Segerberg axioms and the mu-calculi of de Bakker and Park and shows that its satisfiability problem is decidable in exponential time.
Abstract: We describe a mu-calculus which amounts to modal logic plus a minimization operator, and show that its satisfiability problem is decidable in exponential time. This result subsumes corresponding results for propositional dynamic logic with test and converse, thus supplying a better setting for those results. It also encompasses similar results for a logic of flowgraphs. This work provides an intimate link between PDL as defined by the Segerberg axioms and the mu-calculi of de Bakker and Park.
98 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 3 |
| 2025 | 85 |
| 2024 | 130 |
| 2023 | 258 |
| 2022 | 454 |
| 2021 | 278 |