An Efficient Quasigroup Block Cipher

In earlier work the authors reported on methods they investigated to implement quasigroup block encryption in hardware, with an emphasis on low cost. The aim was to design and deliver a hardware design solution that was inexpensive but did not sacrifice encryption security; the desired target for the design is low-bandwidth, low-cost areas such as Supervisory Control And Data Acquisition (SCADA) systems. Here the authors report on further refinements of this design with the aim of making a singlechip solution.

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“…In Battey two quasigroup generation algorith [2] [3]. Both of these are however aimed at imp of generating quasigroups and minimizin requirement.…”

Section: Results Of Algorithm Cryptanalysismentioning

confidence: 99%

“…In previous work we developed a block cipher based on quasigroups [3]. This block cipher was implemented in a simulated Field Programmable Gate Array (FPGA) in [18].…”

Section: Introductionmentioning

confidence: 99%

Towards a New Quasigroup Block Cipher for a Single-Chip FPGA Implementation

Mahoney

Parakh

2015

2015 24th International Conference on Computer Communication and Networks (ICCCN)

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“…19,20 It is build around an order 2 8 quasigroup and designed with respect to the usually low processing power of sensor nodes. 19,20 It is build around an order 2 8 quasigroup and designed with respect to the usually low processing power of sensor nodes.…”

Section: Block Ciphersmentioning

confidence: 99%

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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“…The theory of quasigroup applications in cryptology goes through a period of rapid enough growth now. Quasigroup theory is widely used in the design of hash functions [2,3], secret sharing systems [4], authentication of a message [5,6], zero knowledge protocols [7], stream ciphers [8,9], and block ciphers [10,11], etc.…”

Section: Introductionmentioning

confidence: 99%

“…Battey and Parakh designed a quasigroup block cipher with a randomly chosen quasigroup of order 256 [10]. A quasigroup of order 256 maybe too big for low memory devices, and a random chosen quasigroup may not be optimal in linearity and differential uniformity.…”

Section: Introductionmentioning

confidence: 99%

A Lightweight block cipher based on quasigroups

2017

2017 6th International Conference on Advanced Materials and Computer Science (ICAMCS 2017)

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Abstract. The extensive deployment of tiny computing devices, such as sensors, tablets and smart phones, present a requirement for encryption systems fit for low-resource equipments. Despite implementation advances, Advanced Encryption Standard (AES) is not suitable for extremely constrained environments such as sensor networks and smart phones. In this paper, we give a new lightweight block cipher based on quasigroups. A quasigroup can be viewed as a series of S-boxes. All the S-boxes of the quasigroup used in this new cipher are optimal in linearity and differential uniformity, and all the components of these S-boxes have the highest algebraic degree. We compare the performance of this new cipher with AES by using the NIST-STS, the randomness of the new cipher is better than that of AES.

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An Efficient Quasigroup Block Cipher

Cited by 16 publications

References 11 publications

Towards a New Quasigroup Block Cipher for a Single-Chip FPGA Implementation

Towards a New Quasigroup Block Cipher for a Single-Chip FPGA Implementation

An acceleration of quasigroup operations by residue arithmetic

A Lightweight block cipher based on quasigroups

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