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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.
KEYWORDS: Symmetric-key cryptography, block ciphers, substitution-permutation networks, linear cryptanalysis, differential cryptanalysis.
1 INTRODUCTION
In this paper, we present a tutorial on two powerful cryptanalysis techniques applied to symmetric-key block ciphers: linear cryptanalysis [16] and differential cryptanalysis [1]. Linear cryptanalysis was introduced by Matsui at EUROCRYPT '93 as a theoretical attack on the Data Encryption Standard (DES) [19] and later successfully used in the practical cryptanalysis of DES [17]; 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 [2]. 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 [20] were designed using techniques specifically targeted at thwarting linear and differential cryptanalysis. This is evident, for example, in the Rijndael cipher [6], 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...