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41st International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO)

作者： Ilievska, Natasha Ss Cyril & Methodius Univ Fac Comp Sci & Engn Skopje North Macedonia

ISBN: (纸本)9789532330953

Using simulations, we analyze an error-detecting code from the aspect of the number of errors that the code surely detects. In order to conclude whether and how the order of the quasigroup used for coding affects the number of errors that the code surely detects, we use quasigroups of different orders for coding. Also, we code input blocks of different lengths in order to conclude whether the number of errors that the code surely detects depends on the length of the input block, i.e., the length of the code word.

关键词： error-detecting code linear quasigroup noise channel binary symmetric channel code word

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On the error-Detection Properties of the error-detecting code 26

On the Error-Detection Properties of the Error-Detecting Cod...

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26th Telecommunications Forum (TELFOR)

作者： Ilievska, Natasha Ss Cyril & Methodius Univ Fac Comp Sci & Engn Rudzer Boshkovikj 16PO 393 Skopje 1000 Macedonia

ISBN: (纸本)9781538671719

In this paper we consider an error-detecting code. The code is defined using linear quasigroups. In the focus of the paper is the number of errors that the code surely detects. Using simulations, we obtain this number in the case when linear quasigroups of order 4 that give smallest probability of undetected errors are used for coding.

关键词： linear quasigroup error-detecting code binary symmetric channel code word

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Number of errors that the error-detecting code Surely Detects 1

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9th International Conference on ICT Innovations - Data-Driven Innovation

作者： Ilievska, Natasa Ss Cyril & Methodius Univ Fac Comp Sci & Engn Skopje North Macedonia

ISBN: (数字)9783319675978

ISBN: (纸本)9783319675978;9783319675961

In this paper we consider an error-detecting code based on linear quasigroups. We give a proof that the code is linear. Also, we obtain the generator and the parity-check matrices of the code, from where we obtain the Hamming distance of the code when a linear quasigroup of order 4 from the best class of quasigroups of order 4 for coding, i.e., the class of quasigroups of order 4 that gives smallest probability of undetected errors is used for coding. With this we determine the number of errors that the code will detect for sure.

关键词： Linear code Hamming distance Generator matrix Parity-check matrix error-detecting code Linear quasigroup Probability of undetected errors

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On the error-detecting capability of the linear quasigroup code

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2021年第6期32卷 723-753页

作者： Ilievska, Natasha Ss Cyril & Methodius Univ Fac Comp Sci & Engn Skopje North Macedonia

In this paper we consider an error-detecting code based on linear quasigroups. Namely, each input block a0a1 horizontal ellipsis an-1 is extended into a block a0a1 horizontal ellipsis an-1d0d1 horizontal ellipsis dn-1, where the redundant characters d0,d1, horizontal ellipsis ,dn-1 are defined with di=ai*ai+1*ai+2, where * is a linear quasigroup operation and the operations in the indexes are modulo n. We give a proof that under some conditions the code is linear. Using this fact, we contribute to the determination of the error-detecting capability of the code. Namely, we determine the Hamming distance of the code and from there we obtain the number of errors that the code will detect for sure when linear quasigroups of order 4 from the best class of quasigroups of order 4 for which the constant term in the linear representation is zero matrix are used for coding. All results in the paper are derived for arbitrary length of the input blocks. With the obtained results we showed that when a small linear quasigroup of order 4 from the best class of quasigroups of order 4 is used for coding, the number of errors that the code surely detects is upper bounded with 4.

关键词： error-detecting code Linear quasigroup Linear code Hamming distance Generator matrix Parity-check matrix

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Sufficient conditions for good and proper error-detecting codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第6期43卷 2023-2026页

作者： Dodunekova, R Dodunekov, SM GOTHENBURG UNIV S-41296 GOTHENBURGSWEDEN BULGARIAN ACAD SCI INST MATH & INFORMATBU-1113 SOFIABULGARIA

The performance of linear block codes over a finite field is investigated when they are used for pure error detection. Sufficient conditions for a code to be good or proper for error detection are derived.

关键词： error-detecting code probability of undetected error

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Simulation of Some New Models of error-detecting codes 22

Simulation of Some New Models of Error-Detecting Codes

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22nd Telecommunications Forum Telfor (TELFOR)

作者： Ilievska, Natasha Gligoroski, Danilo Ss Cyril & Methodius Univ Skopje Fac Comp Sci & Engn Rugjer Boshkovikj 16POB 393 Skopje 1000 Macedonia Norwegian Univ Sci & Technol Dept Telemat Trondheim Norway

We will define two models of error-detecting codes based on quasigroups of arbitrary order. For some special cases of these two models we provide experimental results for the probability of undetected errors if a give... 详细信息

ISBN: (纸本)9781479961917

关键词： binary symmetric channel error-detecting code probability of undetected errors quasigroup

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An operation-centered approach to fault detection in symmetric cryptography ciphers

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IEEE TRANSACTIONS ON COMPUTERS 2007年第5期56卷 635-649页

作者： Breveglieri, Luca Koren, Israel Maistri, Paolo Politecn Milan Dept Elect & Informat Technol I-20133 Milan Italy Univ Massachusetts Dept Elect & Comp Engn Amherst MA 01003 USA TIMA Lab Grenoble France

One of the most effective ways of attacking a cryptographic device is by deliberate fault injection during computation, which allows retrieving the secret key with a small number of attempts. Several attacks on symmetric and public-key cryptosystems have been described in the literature and some dedicated error-detection techniques have been proposed to foil them. The proposed techniques are ad hoc ones and exploit specific properties of the cryptographic algorithms. In this paper, we propose a general framework for error detection in symmetric ciphers based on an operation-centered approach. We first enumerate the arithmetic and logic operations included in the cipher and analyze the efficacy and hardware complexity of several error-detecting codes for each such operation. We then recommend an error-detecting code for the cipher as a whole based on the operations it employs. We also deal with the trade-off between the frequency of checking for errors and the error coverage. We demonstrate our framework on a representative group of 11 symmetric ciphers. Our conclusions are supported by both analytical proofs and extensive simulation experiments.

关键词： cryptography symmetric cipher error-detecting code parity code residue code fault attacks fault detection

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PUBLIC-KEY ENCRYPTION ALGORITHM INCORPORATING error-DETECTION

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ELECTRONICS LETTERS 1989年第6期25卷 389-390页

作者： HARN, L KIESLER, T Missouri Univ. Kansas City MO USA

Owing to their mathematical properties, quadratic residues have been used successfully in designing a number of cryptographic applications, such as oblivious transfer protocol and coin flipping protocol. The authors propose an encryption scheme based on quadratic residue theory. In particular, they incorporate the encrypting procedure and error-detecting code into a complete communication system.

关键词： authentication complete communication system cryptography encrypting procedure encryption scheme error detection error detection codes error-detecting code public key cryptography quadratic residue theory

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Towards the Fixed Length Redundancy code 27

Towards the Fixed Length Redundancy Code

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27th Telecommunications Forum (TELFOR)

作者： Ilievska, Natasha Ss Cyril & Methodius Univ Fac Comp Sci & Engn Rudzer Boshkovikj 16PO 393 Skopje 1000 North Macedonia

ISBN: (纸本)9781728147895

In our previous work we have defined an error-detecting code with a fixed length of the redundancy. The analysed code is defined using the algebraic structure quasigroup. In this paper we analyse the case when a linear quasigroup of order 4 is used for coding. We obtain the number of errors that the code surely detects when the length of the redundancy is 8, 12 and 16 bits. At the end, we give some properties and conclusions for the number of errors that the code surely detects.

关键词： Binary-symmetric channel coded block error-detecting code Linear quasigroup

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Tailoring Fault-Tolerance to Trotter Circuits 5

Tailoring Fault-Tolerance to Trotter Circuits

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2024 International Conference on Quantum Computing and Engineering

作者： Chen, Zhuangzhuang Rengaswamy, Narayanan Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

ISBN: (纸本)9798331541378

The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known [[n, n - 2, 2]] error-detecting code family. Our analysis shows that this family implements Trotter circuits with optimal depth, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. The solve-and-stitch algorithm has the potential to scale beyond this specific example and hence provide a principled approach to tailored fault-tolerance in quantum computing.

关键词： Quantum error correction fault-tolerance Trotter circuits quantum simulation error-detecting code Clifford gates flag gadgets logical Clifford synthesis (LCS)

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