The ramp quantum secret sharing proposed by Ogawa et al. has the highest possible coding rate given a threshold type access structure. On the other hand, in some quantum secret sharing schemes, it is known that some shares can be distributed to participants before a secret is given to the dealer. However, it is unclear whether some shares can be distributed before a secret is given in Ogawa et al.'s scheme. In this paper, we propose a method to distribute some shares before a secret is given in Ogawa et al.'s scheme, then determine a necessary and sufficient condition on sets of shares that can be distributed before a given secret.

Abstract We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert–Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explicit construction of strongly secure ramp secret sharing scheme by quantum stabilizers, which can support twice as large classical secrets as the McEliece–Sarwate strongly secure ramp secret sharing scheme of the same share size and the access structure.

We consider secret sharing schemes with a classical secret and quantum shares. One example of such schemes was recently reported whose access structure cannot be realized by any secret sharing schemes with classical shares. In this paper, we report further quantum secret sharing schemes whose access structures cannot be realized by any classical secret sharing schemes.

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.

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.

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.

The key rate of the B92 quantum key distribution protocol had not been reported before this research when the number of qubits is finite. We compute it by using the security analysis framework proposed by Scarani and Renner in 2008.

By extending the notion of minimum rank distance, this paper introduces two new relative code parameters of a linear code C1of length n over a field extension Fqmand its subcode C2⊆ C1. 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 C1-1 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.

It was recently shown that RGHW (relative generalized Hamming weight) exactly expresses the security of linear ramp secret sharing scheme. In this paper we determine the true value of the asymptotic metric for RGHW previously proposed by Zhuang et al. in 2013. Then we propose new asymptotic metrics useful for investigating the optimal performance of linear ramp secret sharing scheme constructed from a pair of linear codes. We also determine the true values of the proposed metrics in many cases.

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes [23], [22]. In this paper we elaborate on the implication of these parameters and we 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.

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.

We analyze the asymptotic key rate of the single photon B92 protocol by using Renner's security analysis given in 2005. The new analysis shows that the B92 protocol can securely generate key at 6.5% depolarizing rate, while the previous analyses cannot guarantee the secure key generation at 4.2% depolarizing rate.

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan [15] based on Gröbner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander [4]. By using the same principle, we also generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cabcurves proposed by Lee, Bras-Amorós and O'Sullivan [14] to general one-point AG codes, without any assumption. Finally we extend the latter 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 [3] that has not been done in the original proposal, and remove the unnecessary computational steps so that it can run faster.

The universal strongly secure network coding scheme allows communication at maximum rate while ensuring that, independently from the underlying network code, no part of the secret message is revealed to the wiretapper. Although Silva and Kschischang showed the existence of such a scheme, the explicit construction remained an open question. This paper demonstrates an explicit construction of the scheme that uses secret sharing schemes based on maximum rank distance (MRD) codes, which can be viewed as a special case of Ozarow-Wyner coset coding scheme.

We determine the capacity region of the secure multiplex coding with a common message, and evaluate the mutual information and the equivocation rate of a collection of secret messages to the second receiver (eavesdropper), which were not evaluated by Yamamoto et al.

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 ofconventional scheme are achieved with even smaller source length.

From an arbitrary given channel code over a discrete or Gaussian memoryless channel, we construct a wiretap code with the strong security. Our construction can achieve the wiretap capacity under mild assumptions. The key tool is the new privacy amplification theorem bounding the eavesdropped information in terms of the Gallager function.

Low-density parity-check (LDPC) codes become very popular in channel coding, since they can achieve the performance close maximum-likelihood (ML) decoding with linear complexity of the block length. Muramatsu et al. proposed a code using LDPC matrices for Slepian-Wolf source coding. However, since they employed ML decoding, their code is not universal, that is their decoder needs to know the probability distribution of the source. On the other hand, if there exists a universal code using LDPC matrices, we can arbitrary decrease the error probability for all sources whose achievable rate region contains the rate pair of encoders even if the probability distribution of sources is unknown. To this end, we show the existence of a universal Slepian-Wolf source code using LDPC matrices in the case where the source is stationary memoryless.

We improve the non-asymptotic key rate shown by Scarani and Renner by proposing several methods to construct tighter conservative confidence interval of the phase error rate than the one shown by them. In addition, we show that the accurate channel estimation method non-asymptotically increases the key rate over the amplitude damping channel as well as the asymptotic case in the BB84 protocol.

Silva et al. proposed a universal secure network coding scheme based on MRD codes, which can be applied to any underlying network code. This paper considers a stronger eavesdropping model where the eavesdroppers possess the ability to re-select the tapping links during the transmission. We give a proof for the impossibility of attaining universal security against such adversaries using Silva et al.'s code for all choices of code parameters, even with restricted number of tapped links. We also consider the cases with restricted tapping duration and derive some conditions for this code to be secure.

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.

We consider energy savings offered by network coding for multiple unicast in wireless networks. For d-dimensional wireless networks we show that the maximum possible benefit is at least 2d/¿¿d¿.

Wyner's source coding system is one of the most fundamental fixed-length source coding systems with side information available only at the decoder. In this coding system, Wyner 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, the closed form of this region is not clarified because the region is expressed by the union of indefinitely many sets. This paper deals with two correlated sources whose conditional distribution is represented by binary input output symmetric channels, and clarifies closed forms of the achievable rate region for Wyner's source coding system.

The axis compensation is a procedure in which the sender and the receiver compensate the axes of their transmitter and detector so that the bit sequence can be transmitted more reliably. We show the optimal axis compensations maximizing the key generation rate. We consider the case in which only the receiver is allowed to compensate his axis, and the case in which both the sender and the receiver are allowed to compensate their axes. For unital channels, we clarify that the optimal key generation rates for both cases coincide if they utilize the mismatched measurement outcomes in the channel estimation. We also clarify that the optimal key generation rates for both cases do not coincide in general if they do not utilize the mismatched measurement outcomes in the channel estimation.

The privacy amplification is a technique to distill a secret key from a random variable by a hash function so that the distilled key and an eavesdropper's random variable is statistically independent. There are two kinds of security criteria for the key distilled by the privacy amplification: the weak security criterion and the strong security criterion. As a technique to distill a secret key, it is known that the encoder of a Slepian-Wolf (the source coding with full side-information at the decoder) code can be used as a hash function for the privacy amplification if we employ the weak security criterion. In this paper, we show that the encoder of a Slepian-Wolf code cannot be used as a hash function for the privacy amplification if we employ the strong security criterion.

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.

We propose Dijkstra’s algorithm with bounded list size after QR decomposition for decreasing the computational complexity of near maximum-likelihood (ML) detection of signals over multiple-input-multiple-output (MIMO) channels. After that, we compare the performances of proposed algorithm, QR decomposition M-algorithm (QRM-MLD), and its improvement. When the list size is set to achieve the almost same symbol error rate (SER) as the QRM-MLD, the proposed algorithm has smaller average computational complexity.

We propose an information reconciliation protocol that uses two-way classical communication. In the case of the BB84 protocol and the six-state protocol, the key rates of the quantum key distribution (QKD) protocols that use our proposed information reconciliation protocol are higher than previously known protocols for wide range of error rates. We also clarify the relation between the proposed protocol and known QKD protocols and entanglement distillation protocols (EDPs).

Let$N(d,d^perp)$denote the minimum length$n$of a linear code$C$with$d$and$d^bot$, where$d$is the minimum Hamming distance of$C$and$d^bot$is the minimum Hamming distance of$C^bot$. In this correspondence, we show lower bounds and an upper bound on$N(d,d^perp)$. Further, for small values of$d$and$d^perp$, we determine$N(d,d^perp)$and give a generator matrix of the optimum linear code. This problem is directly related to the design method of cryptographic Boolean functions suggested by Kurosawa

This paper shows that the BB84 protocol with random privacy amplification is secure with a higher key rate than Mayers' estimate with the same error rate. Consequently, the tolerable error rate of this protocol is increased from 7.5% to 11%. We also extend this method to the case of estimating error rates separately in each basis, which enables us to securely share a longer key.

The propagation criterion, PC(/spl lscr/) of order k, is one of the most general cryptographic criteria of secure Boolean functions f. In this paper, we formalize its /spl epsiv/-almost version. The new definition requires that f(X)+f(X+/spl Delta/) is almost uniformly distributed while in the original definition, it must be strictly uniformly distributed. Better parameters are then obtained than the strict PC(/spl lscr/) of order k functions. To construct /spl epsiv/-almost PC(/spl lscr/) of order k functions, we introduce a notion of domain distance.

We improve performance of the asymptotically good quantum codes constructed by Ashikhmin, Litsyn and Tsfasman (see Phys. Rev. A, vol.63, no.3, p.032311, 2001), by using more rational points on algebraic curves.