Quasigroup Representation of Some Feistel and Generalized Feistel Ciphers

Mileva, Aleksandra; Markovski, Smile

doi:10.1007/978-3-642-37169-1_16

Cited by 8 publications

(6 citation statements)

References 15 publications

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“…For case (ii), we need to show that there are 2 m solutions. Taking the 2 m power of the right side of equation (13),…”

Section: Mmentioning

confidence: 99%

“…Nonlinear orthomorphisms (or CPPs) are of cryptographic interest, and Mittenthal used them for the design of a nonlinear dynamic substitution device [7,8]. PPs have been applied in the Lay-Massey scheme, the block cipher SMS4, the stream cipher Loiss [1,9,10], the design of Hash functions, quasigroups, and also in the constructions of some cryptographically strong functions [2,[11][12][13][14]. In [15][16][17], the authors investigated the set stability of switched delayed logical networks (SDLNs), the optimal state estimation of finite-field networks (FFNs), and containment problem of finite-field networks (FFNs).…”

Section: Introductionmentioning

confidence: 99%

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Constructions and Necessities of Some Permutation Polynomials over Finite Fields

Liu

2021

Mathematical Problems in Engineering

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Let F q denote the finite field with q elements. Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, and combinatorial design. The study of permutation polynomials has a long history, and many results are obtained in recent years. In this paper, we obtain some further results about the permutation properties of permutation polynomials. Some new classes of permutation polynomials are constructed, and the necessities of some permutation polynomials are studied.

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“…For case (ii), we need to show that there are 2 m solutions. Taking the 2 m power of the right side of equation (13),…”

Section: Mmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constructions and Necessities of Some Permutation Polynomials over Finite Fields

Liu

2021

Mathematical Problems in Engineering

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“…That enables strong quasigroup cryptography for devices with stringent resource constraints such as active Radio‐frequency identification (RFID) tags. Quasigroup representation of block ciphers that use Feistel and generalized Feistel networks was defined in Mileva and Markovski . A quasigroup representation was developed for several block ciphers including 64‐bit Misty1, and 128‐bit Camellia, Four‐Cell, Four‐Cell + , and SMS4.…”

Section: Quasigroups In Computer Security and Cryptographymentioning

confidence: 99%

“…Quasigroups can be also used to model cryptosystems based on other cryptographic primitives. A quasigroup representation has been devised for block ciphers based on Feistel networks (ie, Feistel and generalized Feistel ciphers) …”

Section: Introductionmentioning

confidence: 99%

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An acceleration of quasigroup operations by residue arithmetic

Krömer

Platoš

Nowaková

et al. 2017

Concurrency and Computation

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Quasigroup operations are essential for a wide range of cryptographic procedures that includes cryptographic hash functions, electronic signatures, pseudorandom number generators, and stream and block ciphers. Quasigroup cryptography achieves high levels of security at low memory and computational costs by an iterative application of quasigroup operations to streams and blocks of data. The use of large quasigroups can further improve the strength of cryptographic operations. However, the order of used quasigroups is the main factor affecting the memory requirements of quasigroup cryptographic schemes. Alternative quasigroup representations that do not store their multiplication tables in computer memory yield increased computational costs.In any case, an efficient implementation of quasigroup operations is critical for practical applications of quasigroup cryptography. Residue number systems allow a fast, concurrent realization of addition and multiplication. In this work, residue arithmetic is used to accelerate quasigroup operations, and an efficient computational approach to their implementation, designed with respect to the extended instruction sets of modern processors, is proposed. KEYWORDSacceleration, quasigroup operations, residue arithmetic, residue number systems, security INTRODUCTIONQuasigroups are algebraic structures with a large number of applications in cryptography and computer security. 1-5 A quasigroup consists of a set of elements (carrier) and a binary operation (multiplication) that maps every 2 of its elements onto a third element. Mathematically, they are grupoids closely related to the combinatorial concept of latin squares 2,3,6,7 and the geometric notion of k−nets (3−nets). 2,8 Multiplication (Cayley) tables of finite quasigroups can be expressed as latin squares, and k−nets can be coordinatized by systems of orthogonal quasigroups.In general, quasigroups are noncommutative, nonassociative, nonidempotent, and noninvolutory and do not have neutral elements. 9 These properties make them suitable for applications in cryptography, and they have been used as fundamental elements of a wide range of cryptographic algorithms with success. Their applications in this area include novel high-performance stream 4-6,10-13 and block 4,5,14-22 ciphers, cryptographic hash 4,5,23-27 and trapdoor 4,14,23 functions, fast and secure electronic signatures (eg, message authentication codes), 4,14,23,28 pseudorandom number generators, 5,29-31 error-detecting 2 and error-correcting 2,9,32 codes, and simultaneous encryption and error-correction coding (cryptcoding). 4Quasigroups can be also used to model cryptosystems based on other cryptographic primitives. A quasigroup representation has been devised for block ciphers based on Feistel networks (ie, Feistel and generalized Feistel ciphers). 33The attractiveness of quasigroups for practical cryptographic applications consists in the combination of provably strong security and inexpensive realization of quasigroup-based cryptographic operations. They support la...

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Constructions of complete permutation polynomials

Zeng

et al. 2018

Des. Codes Cryptogr.

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Quasigroup Representation of Some Feistel and Generalized Feistel Ciphers

Cited by 8 publications

References 15 publications

Constructions and Necessities of Some Permutation Polynomials over Finite Fields

Constructions and Necessities of Some Permutation Polynomials over Finite Fields

An acceleration of quasigroup operations by residue arithmetic

Constructions of complete permutation polynomials

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