### Browsing by Author "Hermelin, Miia"

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Item Cryptographic properties of the Bluetooth combination generator(2000) Hermelin, Miia; Teknillisen fysiikan ja matematiikan osasto; Teknillinen korkeakoulu; Helsinki University of Technology; Nevanlinna, OlaviItem Deformation of a thin shell under a concentrated load(2005) Hermelin, Miia; Pitkäranta, Juhani; Teknillisen fysiikan ja matematiikan osasto; Teknillinen korkeakoulu; Helsinki University of Technology; Pitkäranta, JuhaniItem Multidimensional linear cryptanalysis(Aalto-yliopiston teknillinen korkeakoulu, 2010) Hermelin, Miia; Tietojenkäsittelytieteen laitos; Department of Information and Computer Science; Aalto-yliopiston teknillinen korkeakoulu; Nyberg, Kaisa, Prof.Linear cryptanalysis is an important tool for studying the security of symmetric ciphers. In 1993 Matsui proposed two algorithms, called Algorithm 1 and Algorithm 2, for recovering information about the secret key of a block cipher. The algorithms exploit a biased probabilistic relation between the input and output of the cipher. This relation is called the (one-dimensional) linear approximation of the cipher. Mathematically, the problem of key recovery is a binary hypothesis testing problem that can be solved with appropriate statistical tools. The same mathematical tools can be used for realising a distinguishing attack against a stream cipher. The distinguisher outputs whether the given sequence of keystream bits is derived from a cipher or a random source. Sometimes, it is even possible to recover a part of the initial state of the LFSR used in a key stream generator. Several authors considered using many one-dimensional linear approximations simultaneously in a key recovery attack and various solutions have been proposed. In this thesis a unified methodology for using multiple linear approximations in distinguishing and key recovery attacks is presented. This methodology, which we call multidimensional linear cryptanalysis, allows removing unnecessary and restrictive assumptions. We model the key recovery problems mathematically as hypothesis testing problems and show how to use standard statistical tools for solving them. We also show how the data complexity of linear cryptanalysis on stream ciphers and block ciphers can be reduced by using multiple approximations. We use well-known mathematical theory for comparing different statistical methods for solving the key recovery problems. We also test the theory in practice with reduced round Serpent. Based on our results, we give recommendations on how multidimensional linear cryptanalysis should be used.Item Multidimensional Linear Cryptanalysis(2018-11-12) Hermelin, Miia; Cho, Joo Yeon; Nyberg, Kaisa; Department of Computer Science; ADVA Optical Networking; Defense Forces Technical Research CentreLinear cryptanalysis introduced by Matsui is a statistical attack which exploits a binary linear relation between plaintext, ciphertext and key, either in Algorithm 1 for recovering one bit of information of the secret key of a block cipher, or in Algorithm 2 for ranking candidate values for a part of the key. The statistical model is based on the expected and observed bias of a single binary value. Multiple linear approximations have been used with the goal to make the linear attack more efficient. More bits of information of the key can potentially be recovered possibly using less data. But then also more elaborated statistical models are needed to capture the joint behaviour of several not necessarily independent binary variables. Also more options are available for generalising the statistics of a single variable to several variables. The multidimensional extension of linear cryptanalysis to be introduced in this paper considers using multiple linear approximations that form a linear subspace. Different extensions of Algorithm 1 and Algorithm 2 will be presented and studied. The methods will be based on known statistical tools such as goodness-of-fit test and log-likelihood ratio. The efficiency of the different methods will be measured and compared in theory and experiments using the concept of advantage introduced by Selçuk. The block cipher Serpent with a reduced number of rounds will be used as test bed. The multidimensional linear cryptanalysis will also be compared with previous methods that use biasedness of multiple linear approximations. It will be shown in the simulations that the multidimensional method is potentially more powerful. Its main theoretical advantage is that the statistical model can be given without the assumption about statistical independence of the linear approximations.