Language：English   Publishing type：Research paper (scientific journal)   Publisher：Academic Press Inc.  

We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum distance of the involved codes. Supported in the previous results, we show algebraic constructions of good quantum codes and determine their parameters.

DOI： 10.1016/j.ffa.2018.04.010

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

Universal security over a network with linear network coding has been intensively studied. However, previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network, which restricts the possible packet lengths of optimal universal secure codes, does not allow to apply known list-decodable rank-metric codes and requires performing operations over a large field. In this paper, we introduce new parameters (relative generalized matrix weights and relative dimension/rank support profile) for code pairs that are linear over the field used in the network, and show that they measure the universal security performance of these code pairs. For one code and non-square matrices, generalized matrix weights coincide with the existing Delsarte generalized weights, hence we prove the connection between these latter weights and secure network coding, which was left open. As main applications, the proposed new parameters enable us to: 1) obtain optimal universal secure linear codes on noiseless networks for all possible packet lengths, in particular for packet lengths not considered before, 2) obtain the first universal secure list-decodable rank-metric code pairs with polynomial-sized lists, based on a recent construction by Guruswami et al
and 3) obtain new characterizations of security equivalences of linear codes. Finally, we show that our parameters extend relative generalized Hamming weights and relative dimension/length profile, respectively, and relative generalized rank weights and relative dimension/intersection profile, respectively.

DOI： 10.1109/TIT.2017.2766292

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1587/comex.2018XBL0109

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electronics, Information and Communication, Engineers, IEICE  

We show a simple example of a secret sharing scheme encoding classical secret to quantum shares that can realize an access structure impossible by classical information processing with limitation on the size of each share. The example is based on quantum stabilizer codes.

DOI： 10.1587/transfun.E100.A.2738

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electronics, Information and Communication, Engineers, IEICE  

Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes [4]-[8], [10]. In those works the focus is on full privacy and full reconstruction. In this paper we analyze additional parameters describing the asymptotic behavior of partial information leakage and possibly also partial reconstruction giving a more complete picture of the access structure for sequences of linear ramp secret sharing schemes. Our study involves a detailed treatment of the (relative) generalized Hamming weights of the considered codes.

DOI： 10.1587/transfun.E100.A.2699

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

In this note, we report two versions of Gilbert-Varshamov-type existential bounds for asymmetric quantum error-correcting codes.

DOI： 10.1007/s11128-017-1748-y

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

We propose a unitary procedure to reconstruct quantum secret for a quantum secret sharing scheme constructed from stabilizer quantum error-correcting codes. Erasure correcting procedures for stabilizer codes need to add missing shares for reconstruction of quantum secret, while unitary reconstruction procedures for certain class of quantum secret sharing are known to work without adding missing shares. The proposed procedure also works without adding missing shares.

DOI： 10.1007/s11128-017-1656-1

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Physics Publishing  

We have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.

DOI： 10.1088/2058-9565/aa7230

Scopus

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

We consider the random linear precoder at the source node as a secure network coding. We prove that it is strongly secure in the sense of Harada and Yamamoto and universal secure in the sense of Silva and Kschischang, while allowing arbitrary small but nonzero mutual information to the eavesdropper. Our security proof allows statistically dependent and non-uniform multiple secret messages, while all previous constructions of weakly or strongly secure network coding assumed independent and uniform messages, which are difficult to be ensured in practice.

DOI： 10.1109/TIT.2017.2694012

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee et al. (2012) to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, prove equality between its error correcting capability and half the minimum distance lower bound by Andersen and Geil (2008) that has not been done in the original proposal except for one-point Hermitian codes, remove the unnecessary computational steps so that it can run faster, and analyze its computational complexity in terms of multiplications and divisions in the finite field. As a unique decoding algorithm, the proposed one is empirically and theoretically as fast as the BMS algorithm for one-point Hermitian codes. As a list decoding algorithm, extensive experiments suggest that it can be much faster for many moderate size/usual inputs than the algorithm by Beelen and Brander (2010). It should be noted that as a list decoding algorithm the proposed method seems to have exponential worst-case computational complexity while the previous proposals (Beelen and Brander, 2010; Guruswami and Sudan, 1999) have polynomial ones, and that the proposed method is expected to be slower than the previous proposals for very large/special inputs. (C) 2016 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.jsc.2016.02.015

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1587/transfun.E100.A.726

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

The secure multiplex coding (SMC) is a technique to remove rate loss in the coding for wire-tap channels and broadcast channels with confidential messages caused by the inclusion of random bits into transmitted signals. SMC replaces the random bits by other meaningful secret messages, and a collection of secret messages serves as the random bits to hide the rest of messages. In the previous studies, multiple secret messages were assumed to have independent and uniform distributions, which is difficult to be ensured in practice. We remove this restrictive assumption by a generalization of the channel resolvability technique. We also give practical construction techniques for SMC by using an arbitrary given error-correcting code as an ingredient, and channel-universal coding of SMC. By using the same principle as the channel-universal SMC, we give coding for the broadcast channel with confidential messages universal to both channel and source distributions.

DOI： 10.1109/TIT.2016.2530088

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Maruzen Co., Ltd.  

We introduce a coding theoretic criterion for Yamamoto's strong security of the ramp secret sharing scheme. After that, by using it, we show the strong security of the strongly multiplicative ramp secret sharing proposed by Chen et al. in 2008.

DOI： 10.1587/transfun.E98.A.1576

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

Quantum secret sharing is a scheme for encoding a quantum state (the secret) into multiple shares and distributing them among several participants. If a sufficient number of shares are put together, then the secret can be fully reconstructed. If an insufficient number of shares are put together however, no information about the secret can be revealed. In quantum ramp secret sharing, partial information about the secret is allowed to leak to a set of participants, called an unqualified set, that cannot fully reconstruct the secret. By allowing this, the size of a share can be drastically reduced. This paper introduces a quantum analog of classical strong security in ramp secret sharing schemes. While the ramp secret sharing scheme still leaks partial information about the secret to unqualified sets of participants, the strong security condition ensures that qudits with critical information can no longer be leaked.

DOI： 10.1007/s11128-014-0863-2

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper, we elaborate on the implication of these parameters and devise a method to estimate their value for general one-point algebraic geometric codes. As it is demonstrated, for Hermitian codes, our bound is often tight. Furthermore, for these codes, the relative generalized Hamming weights are often much larger than the corresponding generalized Hamming weights.

DOI： 10.1109/TIT.2014.2345375

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

We show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil (2008) [1] for primary codes are consequences of each other. This implies that the Feng-Rao decoding algorithm can be applied to decode primary codes up to half their designed minimum distance. The technique applies to any linear code for which information on well-behaving pairs is available. Consequently we are able to decode efficiently a large class of codes for which no non-trivial decoding algorithm was previously known. Among those are important families of multivariate polynomial codes. Matsumoto and Miura (2000) [30] (see also Beelen and Hoholdt, 2008 [3]) derived from the Feng-Rao bound a bound for primary one-point algebraic geometric codes and showed how to decode up to what is guaranteed by their bound. The exposition in Matsumoto and Miura (2000) [30] requires the use of differentials which was not needed in Andersen and Geil (2008) [1]. Nevertheless we demonstrate a very strong connection between Matsumoto and Miura's bound and Andersen and Geil's bound when applied to primary one-point algebraic geometric codes. (c) 2013 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.ffa.2013.03.005

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan (2009) based on Grobner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander (2010). Our generalization enables us to apply the fast algorithm to compute a Grobner basis of a module proposed by Lee and O'Sullivan (2009), which was not possible in another generalization by Lax (2012). (C) 2013 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.jsc.2013.03.001

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Language：English   Publishing type：Research paper (scientific journal)  

By extending the notion of minimum rank distance, this paper introduces two
new relative code parameters of a linear code C_1 of length n over a field
extension and its subcode C_2. One is called the relative
dimension/intersection profile (RDIP), and the other is called the relative
generalized rank weight (RGRW). We clarify their basic properties and the
relation between the RGRW and the minimum rank distance. As applications of the
RDIP and the RGRW, the security performance and the error correction capability
of secure network coding, guaranteed independently of the underlying network
code, are analyzed and clarified. We propose a construction of secure network
coding scheme, and analyze its security performance and error correction
capability as an example of applications of the RDIP and the RGRW. Silva and
Kschischang showed the existence of a secure network coding in which no part of
the secret message is revealed to the adversary even if any dim C_1-1 links are
wiretapped, which is guaranteed over any underlying network code. However, the
explicit construction of such a scheme remained an open problem. Our new
construction is just one instance of secure network coding that solves this
open problem.

DOI： 10.1109/TIT.2015.2429713

arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Source coding with a helper is one of the most fundamental fixed-length source coding problem for correlated sources. For this source coding, Wyner and Ahlswede-Korner showed the achievable rate region which is the set of rate pairs of encoders such that the probability of error can be made arbitrarily small for sufficiently large block length. However, their expression of the achievable rate region consists of the sum of indefinitely many sets. Thus, their expression is not useful for computing the achievable rate region. This paper deals with correlated sources whose conditional distribution is related by a binary-input output-symmetric channel, and gives a parametric form of the achievable rate region in order to compute the region easily.

DOI： 10.1587/transfun.E95.A.2493

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Language：English   Publishing type：Research paper (international conference proceedings)  

DOI： 10.1109/ISIT.2012.6283510

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DOI： 10.1109/Allerton.2012.6483264

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DOI： 10.1587/transfun.E95.A.2067

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Other Link： https://www.wikidata.org/entity/Q57735066

Language：English   Publishing type：Research paper (international conference proceedings)  

We propose a new method for constructing small-bias spaces through a combination of Hermitian codes. For a class of parameters our multisets are much faster to construct than what can be achieved by use of the traditional algebraic geometric code construction. So, if speed is important, our construction is competitive with all other known constructions in that region. And if speed is not a matter of interest the small-bias spaces of the present paper still perform better than the ones related to norm-trace codes reported in [12]. © 2012 Springer-Verlag.

DOI： 10.1007/978-3-642-31662-3_3

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1155/2010/605421

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DOI： 10.1109/ISIT.2010.5513653

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DOI： 10.1109/ISIT.2010.5513253

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DOI： 10.1109/ISIT.2010.5513794

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DOI： 10.1109/ISIT.2010.5513791

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE COMPUTER SOC  

Rate-compatible asymmetric Slepian-Wolf coding with non-binary LDPC codes of moderate code length is presented. The proposed encoder and decoder use only one single mother code. With the proposed scheme, better compressed rate and lower error rate than those of conventional scheme are achieved with even smaller source length.

DOI： 10.1109/DCC.2010.96

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Language：English   Publishing type：Research paper (international conference proceedings)  

We study the information reconciliation (IR) scheme for quantum key distribution (QKD) protocols. The IR for the QKD can be seen as the asymmetric Slepian-Wolf problem, which low-density parity-check (LDPC) codes can solve with efficient algorithms, i.e., the belief propagation. However, the LDPC codes are needed to be chosen properly from a collection of codes optimized for multiple key rates, which leads to complex decoder devices and performance degradation for unoptimized key rates. Therefore, it is desired that establish an IR scheme with a single LDPC code which supports multiple rates. To this end, in this paper, we propose an IR scheme with a rate-compatible non-binary LDPC code. Numerical results show the proposed scheme achieves IR efficiency comparable to the best know conventional IR scheme with lower decoding error rates. © 2010 IEEE.

DOI： 10.1109/ISITA.2010.5649550

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Language：English   Publishing type：Research paper (other academic)  

DOI： 10.1109/ISIT.2009.5205945

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

We show the sufficient conditions for coding by nodes such that every sink can decode all information multicasted by the single source when there exists time-varying delay of information transmission at links in the network coding.

DOI： 10.1587/transfun.E92.A.2141

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

We consider the problem of secret key agreement in Gaussian Maurer's Model. In Gaussian Maurer's model, legitimate receivers, Alice and Bob, and a wire-tapper, Eve, receive signals randomly generated by a satellite through three independent memoryless Gaussian channels respectively. Then Alice and Bob generate a common secret key from their received signals. In this model, we propose a protocol for generating a common secret key by using the result of soft-decision of Alice and Bob's received signals. Then, we calculate a lower bound on the secret key rate in our proposed protocol. As a result of comparison with the protocol that only uses hard-decision, we found that the higher rate is obtained by using our protocol.

DOI： 10.1587/transfun.E92.A.525

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Language：English   Publishing type：Part of collection (book)   Publisher：Springer Berlin Heidelberg  

In applications to coding theory and cryptography, the characteristic of the coefficient field is often small or 2. We will briefly review an algorithm computing the radical of a polynomial ideal specialized for small characteristics. © 2009 Springer-Verlag Berlin Heidelberg.

DOI： 10.1007/978-3-540-93806-4_33

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We construct a practically implementable classical processing for the Bennett-Brassard 1984 (BB84) protocol and the six-state protocol that fully utilizes the accurate channel estimation method, which is also known as the quantum tomography. Our proposed processing yields at least as high a key rate as the standard processing by Shor and Preskill. We show two examples of quantum channels over which the key rate of our proposed processing is strictly higher than the standard processing. In the second example, the BB84 protocol with our proposed processing yields a positive key rate even though the so-called error rate is higher than the 25% limit.

DOI： 10.1103/PhysRevA.78.042316

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

We consider the mismatched measurements in the BB84 quantum key distribution protocol, in which measuring bases are different from transmitting bases. We give a lower bound on the amount of a secret key that can be extracted from the mismatched measurements. Our lower bound shows that we can extract a secret key from the mismatched measurements with certain quantum channels, such as the channel over which the Hadamard matrix is applied to each qubit with high probability. Moreover, the entropic uncertainty principle implies that one cannot extract the secret key from both matched measurements and mismatched ones simultaneously, when we use the standard information reconciliation and privacy amplification procedure.

DOI： 10.1093/ietfec/e91-a.10.2870

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DOI： 10.1109/ISIT.2008.4595082

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DOI： 10.1109/ISIT.2008.4595344

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DOI： 10.1007/978-3-540-69499-1_14

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DOI： 10.1109/ISIT.2007.4557180

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose a quantum-key-distribution protocol that enables three parties to agree at once on a shared common random bit string in the presence of an eavesdropper without use of entanglement. We prove its unconditional security and analyze the key rate.

DOI： 10.1103/PhysRevA.76.062316

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give estimates on the time complexity and the required symbol size of the proposed algorithm. We also estimate the probability of a random choice of local encoding vectors by all intermediate nodes giving a network error-correcting codes attaining the Singleton bound. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors.

DOI： 10.1093/ietfec/e90-a.9.1729

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DOI： 10.1103/PhysRevA.76.032312

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DOI： 10.1093/ietfec/E88-A.1.322

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DOI： 10.1103/PhysRevA.64.022314

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：Institute of Electronics, Information and Communication, Engineers, IEICE  

Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes [4]-[8], [10]. In those works the focus is on full privacy and full reconstruction. In this paper we analyze additional parameters describing the asymptotic behavior of partial information leakage and possibly also partial reconstruction giving a more complete picture of the access structure for sequences of linear ramp secret sharing schemes. Our study involves a detailed treatment of the (relative) generalized Hamming weights of the considered codes.

DOI： 10.1587/transfun.E100.A.2699

Scopus

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

DOI： 10.1587/transfun.E100.A.2738

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

DOI： 10.1007/s11128-017-1656-1

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：Institute of Physics Publishing  

We have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.

DOI： 10.1088/2058-9565/aa7230

Scopus

researchmap

Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

We consider the random linear precoder at the source node as a secure network coding. We prove that it is strongly secure in the sense of Harada and Yamamoto and universal secure in the sense of Silva and Kschischang, while allowing arbitrary small but nonzero mutual information to the eavesdropper. Our security proof allows statistically dependent and non-uniform multiple secret messages, while all previous constructions of weakly or strongly secure network coding assumed independent and uniform messages, which are difficult to be ensured in practice.

DOI： 10.1109/TIT.2017.2694012

Web of Science

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee et al. (2012) to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, prove equality between its error correcting capability and half the minimum distance lower bound by Andersen and Geil (2008) that has not been done in the original proposal except for one-point Hermitian codes, remove the unnecessary computational steps so that it can run faster, and analyze its computational complexity in terms of multiplications and divisions in the finite field. As a unique decoding algorithm, the proposed one is empirically and theoretically as fast as the BMS algorithm for one-point Hermitian codes. As a list decoding algorithm, extensive experiments suggest that it can be much faster for many moderate size/usual inputs than the algorithm by Beelen and Brander (2010). It should be noted that as a list decoding algorithm the proposed method seems to have exponential worst-case computational complexity while the previous proposals (Beelen and Brander, 2010; Guruswami and Sudan, 1999) have polynomial ones, and that the proposed method is expected to be slower than the previous proposals for very large/special inputs. (C) 2016 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.jsc.2016.02.015

Web of Science

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

DOI： 10.1587/transfun.E100.A.726

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

The secure multiplex coding (SMC) is a technique to remove rate loss in the coding for wire-tap channels and broadcast channels with confidential messages caused by the inclusion of random bits into transmitted signals. SMC replaces the random bits by other meaningful secret messages, and a collection of secret messages serves as the random bits to hide the rest of messages. In the previous studies, multiple secret messages were assumed to have independent and uniform distributions, which is difficult to be ensured in practice. We remove this restrictive assumption by a generalization of the channel resolvability technique. We also give practical construction techniques for SMC by using an arbitrary given error-correcting code as an ingredient, and channel-universal coding of SMC. By using the same principle as the channel-universal SMC, we give coding for the broadcast channel with confidential messages universal to both channel and source distributions.

DOI： 10.1109/TIT.2016.2530088

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

DOI： 10.1587/transfun.E98.A.1576

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：SPRINGER  

Quantum secret sharing is a scheme for encoding a quantum state (the secret) into multiple shares and distributing them among several participants. If a sufficient number of shares are put together, then the secret can be fully reconstructed. If an insufficient number of shares are put together however, no information about the secret can be revealed. In quantum ramp secret sharing, partial information about the secret is allowed to leak to a set of participants, called an unqualified set, that cannot fully reconstruct the secret. By allowing this, the size of a share can be drastically reduced. This paper introduces a quantum analog of classical strong security in ramp secret sharing schemes. While the ramp secret sharing scheme still leaks partial information about the secret to unqualified sets of participants, the strong security condition ensures that qudits with critical information can no longer be leaked.

DOI： 10.1007/s11128-014-0863-2

Web of Science

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

DOI： 10.1109/TIT.2015.2429713

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper, we elaborate on the implication of these parameters and devise a method to estimate their value for general one-point algebraic geometric codes. As it is demonstrated, for Hermitian codes, our bound is often tight. Furthermore, for these codes, the relative generalized Hamming weights are often much larger than the corresponding generalized Hamming weights.

DOI： 10.1109/TIT.2014.2345375

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

We show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil (2008) [1] for primary codes are consequences of each other. This implies that the Feng-Rao decoding algorithm can be applied to decode primary codes up to half their designed minimum distance. The technique applies to any linear code for which information on well-behaving pairs is available. Consequently we are able to decode efficiently a large class of codes for which no non-trivial decoding algorithm was previously known. Among those are important families of multivariate polynomial codes. Matsumoto and Miura (2000) [30] (see also Beelen and Hoholdt, 2008 [3]) derived from the Feng-Rao bound a bound for primary one-point algebraic geometric codes and showed how to decode up to what is guaranteed by their bound. The exposition in Matsumoto and Miura (2000) [30] requires the use of differentials which was not needed in Andersen and Geil (2008) [1]. Nevertheless we demonstrate a very strong connection between Matsumoto and Miura's bound and Andersen and Geil's bound when applied to primary one-point algebraic geometric codes. (c) 2013 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.ffa.2013.03.005

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan (2009) based on Grobner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander (2010). Our generalization enables us to apply the fast algorithm to compute a Grobner basis of a module proposed by Lee and O'Sullivan (2009), which was not possible in another generalization by Lax (2012). (C) 2013 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.jsc.2013.03.001

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG  

Source coding with a helper is one of the most fundamental fixed-length source coding problem for correlated sources. For this source coding, Wyner and Ahlswede-Korner showed the achievable rate region which is the set of rate pairs of encoders such that the probability of error can be made arbitrarily small for sufficiently large block length. However, their expression of the achievable rate region consists of the sum of indefinitely many sets. Thus, their expression is not useful for computing the achievable rate region. This paper deals with correlated sources whose conditional distribution is related by a binary-input output-symmetric channel, and gives a parametric form of the achievable rate region in order to compute the region easily.

DOI： 10.1587/transfun.E95.A.2493

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

DOI： 10.1587/transfun.E95.A.2067

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Other Link： https://www.wikidata.org/entity/Q57735066

Language：English   Publishing type：Research paper, summary (national, other academic conference)  

We propose a new method for constructing small-bias spaces through a combination of Hermitian codes. For a class of parameters our multisets are much faster to construct than what can be achieved by use of the traditional algebraic geometric code construction. So, if speed is important, our construction is competitive with all other known constructions in that region. And if speed is not a matter of interest the small-bias spaces of the present paper still perform better than the ones related to norm-trace codes reported in [12]. © 2012 Springer-Verlag.

DOI： 10.1007/978-3-642-31662-3_3

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/Allerton.2012.6483264

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2012.6283510

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

DOI： 10.1155/2010/605421

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2010.5513791

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2010.5513653

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2010.5513253

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2010.5513794

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Language：English   Publishing type：Research paper, summary (national, other academic conference)   Publisher：IEEE COMPUTER SOC  

Rate-compatible asymmetric Slepian-Wolf coding with non-binary LDPC codes of moderate code length is presented. The proposed encoder and decoder use only one single mother code. With the proposed scheme, better compressed rate and lower error rate than those of conventional scheme are achieved with even smaller source length.

DOI： 10.1109/DCC.2010.96

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

We study the information reconciliation (IR) scheme for quantum key distribution (QKD) protocols. The IR for the QKD can be seen as the asymmetric Slepian-Wolf problem, which low-density parity-check (LDPC) codes can solve with efficient algorithms, i.e., the belief propagation. However, the LDPC codes are needed to be chosen properly from a collection of codes optimized for multiple key rates, which leads to complex decoder devices and performance degradation for unoptimized key rates. Therefore, it is desired that establish an IR scheme with a single LDPC code which supports multiple rates. To this end, in this paper, we propose an IR scheme with a rate-compatible non-binary LDPC code. Numerical results show the proposed scheme achieves IR efficiency comparable to the best know conventional IR scheme with lower decoding error rates. © 2010 IEEE.

DOI： 10.1109/ISITA.2010.5649550

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2009.5205945

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DOI： 10.1587/transfun.E92.A.2141

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DOI： 10.1007/978-3-540-93806-4_33

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DOI： 10.1587/transfun.E92.A.525

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

We construct a practically implementable classical processing for the Bennett-Brassard 1984 (BB84) protocol and the six-state protocol that fully utilizes the accurate channel estimation method, which is also known as the quantum tomography. Our proposed processing yields at least as high a key rate as the standard processing by Shor and Preskill. We show two examples of quantum channels over which the key rate of our proposed processing is strictly higher than the standard processing. In the second example, the BB84 protocol with our proposed processing yields a positive key rate even though the so-called error rate is higher than the 25% limit. © 2008 The American Physical Society.

DOI： 10.1103/PhysRevA.78.042316

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2008.4595344

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2008.4595082

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1007/978-3-540-69499-1_14

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Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：Institute of Electronics, Information and Communication, Engineers, IEICE  

We consider the mismatched measurements in the BB84 quantum key distribution protocol, in which measuring bases are different from transmitting bases. We give a lower bound on the amount of a secret key that can be extracted from the mismatched measurements. Our lower bound shows that we can extract a secret key from the mismatched measurements with certain quantum channels, such as the channel over which the Hadamard matrix is applied to each qubit with high probability. Moreover, the entropic uncertainty principle implies that one cannot extract the secret key from both matched measurements and mismatched ones simultaneously, when we use the standard information reconciliation and privacy amplification procedure. Copyright © 2008 The Institute of Electronics, Information and Communication Engineers.

DOI： 10.1093/ietfec/e91-a.10.2870

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Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)  

We propose a quantum-key-distribution protocol that enables three parties to agree at once on a shared common random bit string in the presence of an eavesdropper without use of entanglement. We prove its unconditional security and analyze the key rate. © 2007 The American Physical Society.

DOI： 10.1103/PhysRevA.76.062316

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

DOI： 10.1109/ISIT.2007.4557180

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Language：English   Publishing type：Research paper, summary (national, other academic conference)  

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Language：English   Publishing type：Rapid communication, short report, research note, etc. (scientific journal)   Publisher：Institute of Electronics, Information and Communication, Engineers, IEICE  

We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give estimates on the time complexity and the required symbol size of the proposed algorithm. We also estimate the probability of a random choice of local encoding vectors by all intermediate nodes giving a network error-correcting codes attaining the Singleton bound. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors. Copyright © 2007 The Institute of Electronics, Information and Communication Engineers.

DOI： 10.1093/ietfec/e90-a.9.1729

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DOI： 10.1103/PhysRevA.76.032312

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DOI： 10.1093/ietfec/E88-A.1.322

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DOI： 10.1103/PhysRevA.64.022314

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Country：Japan

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