Algebraic analysis of Trivium-like ciphers

Trivium is a bit-based stream cipher in the final portfolio of the eSTREAM project. In this paper, we apply the approach of Berbain et al. to Trivium-like ciphers and perform new algebraic analyses on them, namely Trivium and its reduced versions: Trivium-N, Bivium-A and Bivium-B. In doing so, we answer an open question in the literature. We demonstrate a new algebraic attack on Bivium-A. This attack requires less time and memory than previous techniques which use the F4 algorithm to recover Bivium-A's initial state. Though our attacks on Bivium-B, Trivium and Trivium-N are worse than exhaustive keysearch, the systems of equations which are constructed are smaller and less complex compared to previous algebraic analysis. Factors which can affect the complexity of our attack on Trivium-like ciphers are discussed in detail

Algebraic analysis of Trivium-like ciphers

Trivium is a bit-based stream cipher in the final portfolio of the eSTREAM project. In this paper, we apply the approach of Berbain et al. to Trivium-like ciphers and perform new algebraic analyses on them, namely Trivium and its reduced versions: Trivium-N, Bivium-A and Bivium-B. In doing so, we answer an open question in the literature. We demonstrate a new algebraic attack on Bivium-A. This attack requires less time and memory than previous techniques which use the F4 algorithm to recover Bivium-A\u27s initial state. Though our attacks on Bivium-B, Trivium and Trivium-N are worse than exhaustive keysearch, the systems of equations which are constructed are smaller and less complex compared to previous algebraic analysis. Factors which can affect the complexity of our attack on Trivium-like ciphers are discussed in detail

Применение SAT-решателей для построения булевых функций с заданными криптографическими свойствами

Представлен подход к решению некоторых криптографических задач, основанный на их сведении к классической задаче о выполнимости и последующем использовании SAT-решателей. Построены формулы, определяющие условия взаимной однозначности и дифференциальной равномерности векторной булевой функции

Trivial Transciphering With Trivium and TFHE

We examine the use of Trivium and Kreyvium as transciphering mechanisms for use with the TFHE FHE scheme. Originally these two ciphers were investigated for FHE transciphering only in the context of the BGV/BFV FHE schemes; this is despite Trivium and Kreyvium being particarly suited to TFHE. Recent work by Dobraunig et al. gave some initial experimental results using TFHE. We show that these two symmetric ciphers have excellent performance when homomorphically evaluated using TFHE. Indeed we improve upon the results of Dobraunig et al. by at least two orders of magnitude in terms of latency. This shows that, for TFHE at least, one can transcipher using a standardized symmetric cipher (Trivium), without the need for special FHE-friendly ciphers being employed. For applications wanting extra security, but without the benefit of relying on a standardized cipher, our work shows that Kreyvium is a good candidate

A multistep strategy for polynomial system solving over finite fields and a new algebraic attack on the stream cipher Trivium

In this paper we introduce a multistep generalization of the guess-and-determine or hybrid strategy for solving a system of multivariate polynomial equations over a finite field. In particular, we propose performing the exhaustive evaluation of a subset of variables stepwise, that is, by incrementing the size of such subset each time that an evaluation leads to a polynomial system which is possibly unfeasible to solve. The decision about which evaluation to extend is based on a preprocessing consisting in computing an incomplete Grobner basis after the current evaluation, which possibly generates linear polynomials that are used to eliminate further variables. If the number of remaining variables in the system is deemed still too high, the evaluation is extended and the preprocessing is iterated. Otherwise, we solve the system by a Grobner basis computation. Having in mind cryptanalytic applications, we present an implementation of this strategy in an algorithm called MultiSolve which is designed for polynomial systems having at most one solution. We prove explicit formulas for its complexity which are based on probability distributions that can be easily estimated by performing the proposed preprocessing on a testset of evaluations for different subsets of variables. We prove that an optimal complexity of MultiSolve is achieved by using a full multistep strategy with a maximum number of steps and in turn the classical guess-and-determine strategy, which essentially is a strategy consisting of a single step, is the worst choice. Finally, we extensively study the behaviour of MultiSolve when performing an algebraic attack on the well-known stream cipher Trivium

Automated Microstructure Analysis of Large Regions

The mechanical and physical properties of materials are often related to grain size. To accurately measure grain size over a large region, it is imperative to acquire high-resolution image data for each of the grains and detect all of them. Although there is an existing technique, Electron Backscatter Diffraction (EBSD), that can achieve the objective, it is an expensive technique which requires a Scanning Electron Microscope (SEM). Therefore, it is beneficial to develop a less expensive technique that can use traditional and cheap equipment, such as an optical microscope. This thesis is dedicated to making an optical microscope automatically scan over a large region of a specimen and offer microstructural quantification including grain boundary identification, grain size number and grain size distribution. In addition, the maps of grain size and grain aspect ratio will be created to give users a better visualization. The feature of multiple zoom levels for the microstructure is also added for users to navigate through the large regions easily. Finally, software has been developed to help users identify “rare events” in microstructure, such as abnormal grains, and flag those rare events in the map for visual inspection