In this paper, we present a tutorial on two powerful cryptanalysis techniques applied to symmetric-key block ciphers: linear cryptanalysis [1] and differential cryptanalysis [2]. Linear cryptanalysis was introduced by Matsui at EUROCRYPT ’93 as a theoretical attack on the Data Encryption Standard (DES) [3] and later successfully used in the practical cryptanalysis of DES [4]; differential cryptanalysis was first presented by Biham and Shamir at CRYPTO ’90 to attack DES and eventually the details of the attack were packaged as a book [5]. Although the early target of both attacks was DES, the wide applicability of both attacks to numerous other block ciphers has solidified the preeminence of both cryptanalysis techniques in the consideration of the security of all block ciphers. For example, many of the candidates submitted for the recent Advanced Encryption Standard process undertaken by the National Institute of Standards and Technology [6] were designed using techniques specifically targeted at thwarting linear and differential cryptanalysis. This is evident, for example, in the Rijndael cipher [7], the encryption algorithm selected to be the new standard. The concepts discussed in this paper could be used to form an initial understanding required to comprehend the design principles and security analysis of the Rijndael cipher, as well as many other ciphers proposed in recent years. The paper is structured as a tutorial and, as such, is intended to not be rigorously mathematical. It introduces the basic concepts of linear and differential cryptanalysis but is by no means a definitive source for understanding all the many refinements and improvements of the attacks over the years. The basic purpose of the paper is to use a simple (yet somewhat realistic) cipher structure to study the most basic concepts of the two attacks. Other more formal discussions exist on the topic. For example, overviews of the attacks as applied to Substitution-Permutation Networks (the cipher structured to be considered in this paper) are presented in [8] and [9]. For a general introduction to block ciphers and their analysis, see [10]. The need for a tutorial on the attacks arises from the very difficult nature of both attacks and the lack of simplified , yet detailed, reference material describing the attacks. Conventional cryptographic references and texts [11][12][13][14] generally present material on block ciphers in a very descriptive manner, with little detail illustrating the concepts of the attacks. Consequently, most published material detailing the attacks has a research focus and gives little intuition and explanation for the non-expert. When the basic concepts of the attack are described in the literature (as in Matsui’s and Biham and Sh amir’s original papers) , they are typically presented in reference to DES which is, in nature, somewhat convoluted in a manner which interferes with the understanding the cryptanalytic concepts…

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