Nonlinearity Properties of the Mixing Operations of the Block Cipher IDEA

Yıldırım, Hamdi Murat

doi:10.1007/978-3-540-24582-7_5

Cited by 2 publications

(5 citation statements)

References 5 publications

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“…In order to derive each of these linear relation, at least one of those key subblocks were restricted to take 0 and 1 (see Example 1 and Table 1). Additional key values, 2, 2 n − 1, 2 n−1 and 2 n−1 + 1, making the nonlinearity of the vector valued function g z of zero were discovered in [12]. Similar to the work in paper [2], we take into account 0, 1 or these key values as round multiplicative keys to derive extra 39 linear relations, which are not marked by (*) in Table 1.…”

Section: A New List Of Linear Relationsmentioning

confidence: 96%

“…However, the nonlinearity N (g Z ) of the vector function g Z is not zero for every Z ∈ Z 2 n . The following theorem, which is proved in [12], gives a list of Z values such that N (g Z ) is zero.…”

Section: Nonlinearity Of Multiplication Operationmentioning

confidence: 99%

“…On the other hand, we consider the widely known and accepted measurement for nonlinearity based on the Hamming distance presented in [10] to study the nonlinearity of the multiplication operation. It is proved that this type of nonlinearity of is zero for six cases for n ≥ 2 [12].…”

Section: Introductionmentioning

confidence: 97%

“…The addition modulo 2 n ( ) and exclusive-OR (XOR) (⊕, bitwise addition on modulo 2) are operations and have been widely used as building blocks in many cryptosystems: in RC6, Twofish, MARS, FEAL, SAFER as block ciphers and in ChaCha, Phelix, Snow as stream ciphers. The design of both the International Data Encryption Algorithm (IDEA) [4], the MESH block ciphers [9], WIDEA [3] cipher and RIDEA cipher [12] are based on the successive use of these operations and the multiplication modulo 2 16 + 1 ( ) operation. Extensive survey of such block ciphers whose design following the Lai-Massey design paradigm and their analyses are provided by Nakahara [8].…”

Section: Introductionmentioning

confidence: 99%

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Exploiting Linearity of Modular Multiplication

Yıldırım

2020

Mathematical Aspects of Computer and Information Sciences

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The XOR ⊕ and the addition operations have been widely used as building blocks for many cryptographic primitives. These operations and the multiplication operation are successively used in the design of IDEA and the MESH block ciphers. This work presents several interesting algebraic properties of the multiplication operation. By fixing one operand, we obtain vector valued function g Z on Z n 2 , associated with . In this paper we show that the nonlinearity of g Z remains the same under some transformations of Z and moreover we give an upper bound for the nonlinearity of g Z when Z is a power of 2. Under weak-key assumptions, we furthermore present a list of new linear relations for 1round IDEA cipher, some of directly derived and others algorithmically generated using these relations and known ones. We extend the largest linear weak key class for IDEA cipher with size 2 23 to derive such a class with sizes 2 24 . Under the independent key subblocks (subkeys) and weak-key assumptions we derive many linear relations for IDEA cipher using linear relations for 1-round IDEA cipher.

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Section: A New List Of Linear Relationsmentioning

confidence: 96%

Section: Nonlinearity Of Multiplication Operationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Exploiting Linearity of Modular Multiplication

Yıldırım

2020

Mathematical Aspects of Computer and Information Sciences

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“…• One could attack other ciphers based on IDEA, such as MESH [24] and RIDEA [25]. • We have consistently worked with differences based on xor and subtraction as difference operators.…”

Section: Future Work and Open Problemsmentioning

confidence: 99%

Differential entropy analysis of the IDEA block cipher

Biryukov

Nakahara

Yıldırım

2014

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper describes a new cryptanalytic technique that combines differential cryptanalysis with Shannon entropy. We call it differential entropy (DE). The objective is to exploit the non-uniform distribution of output differences from a given mapping as a distinguishing tool in cryptanalysis. Our preferred target is the IDEA block cipher, since we detected significantly low entropy at the output of its multiplication operation. We looked to further extend this entropy analysis to larger components and for a number of rounds. We present key-recovery attacks on up to 2.5-round IDEA in the single-key model and without weakkey assumptions.

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Nonlinearity Properties of the Mixing Operations of the Block Cipher IDEA

Cited by 2 publications

References 5 publications

Exploiting Linearity of Modular Multiplication

Exploiting Linearity of Modular Multiplication

Differential entropy analysis of the IDEA block cipher

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