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 ...
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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.
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...
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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.
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...
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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.
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...
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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.
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 ...
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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.
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 linea...
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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.
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...
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ISBN:
(纸本)9781479961917
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 given quasigroup of order 4 is used for coding. At the end, we will compare the considered special cases.
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 symmet...
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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.
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.
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.
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. In the letter...
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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. In the letter we propose an encryption scheme based on quadratic residue theory. In particular, we incorporate the encrypting procedure and error-detecting code into a complete communication system.
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