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**Unformatted text preview: **A Tutorial on Linear and Differential Cryptanalysis by Howard M. Heys Electrical and Computer Engineering Faculty of Engineering and Applied Science Memorial University of Newfoundland St. Johns, NF, Canada A1B 3X5 email: howard@engr.mun.ca Abstract: In this paper, we present a detailed tutorial on linear cryptanalysis and differential cryptanalysis, the two most significant attacks applicable to symmetric-key block ciphers. The intent of the paper is to present a lucid explanation of the attacks, detailing the practical application of the attacks to a cipher in a simple, conceptually revealing manner for the novice cryptanalyst. The tutorial is based on the analysis of a simple, yet realistically structured, basic Substitution-Permutation Network cipher. Understanding the attacks as they apply to this structure is useful, as the Rijndael cipher, recently selected for the Advanced Encryption Standard (AES), has been derived from the basic SPN architecture. As well, experimental data from the attacks is presented as confirmation of the applicability of the concepts as outlined. 2 1. Introduction 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 pre- eminence 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 two attacks....

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