arXiv subjects
Publications and source records attributed to Ryutaroh Matsumoto.
In the secure network coding for multicasting, there is loss of information rate due to inclusion of random bits at the source node. We show a method to eliminate that loss of information rate by using multiple statistically independent messages to be kept secret from an eavesdropper. The proposed scheme is an adaptation of Yamamoto et al.'s secure multiplex coding to the secure network coding.
We show that the capacity region of the broadcast channel with confidential messages does not change when the strong security criterion is adopted instead of the weak security criterion traditionally used. We also show a construction method of coding for the broadcast channel with confidential messages by using an arbitrary given coding for the broadcast channel with degraded message sets.
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.
The privacy amplification is a technique to distill a secret key from a random variable by a function so that the distilled key and eavesdropper's random variable are statistically independent. There are three kinds of security criteria for the key distilled by the privacy amplification: the normalized divergence criterion, which is also known as the weak security criterion, the variational distance criterion, and the divergence criterion, which is also known as 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 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 function for the privacy amplification if we employ the criteria other than the weak one.
We construct a universal secure network coding. Our construction just modifies the transmission scheme at the source node and works with every linear coding at an intermediate node. We relax the security criterion such that the mutual information between the message and the eavesdropped signal is sufficiently small instead of strictly zero. Our construction allows the set of eavesdropped links to change at each time slot.
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 improve the non-asymptotic key rate shown by Scarani and Renner by proposing several methods to construct tighter conservative confidence intervals of the phase error rate than 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.
In all papers on the BB84 protocol, the transmission probability of each bit value is usually set to be equal. In this paper, we show that by assigning different transmission probability to each transmitted qubit within a single polarization basis, we can generally improve the key generation rate of the BB84 protocol and achieve a higher key rate.
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.
The information reconciliation in a quantum key distribution protocol can be studied separately from other steps in the protocol. The problem of information reconciliation can be reduced to that of distributed source coding. Its solution by LDPC codes is reviewed. We list some obstacles preventing the LDPC-based distributed source coding from becoming a more favorable alternative to the Cascade protocol for information reconciliation in quantum key distribution protocols. This exposition does not require knowledge of the quantum theory.
We consider a modified version of the BB84 quantum key distribution protocol in which the angle between two different bases are less than $π/4$. We show that the channel parameter estimate becomes the same as the original protocol with sufficiently many transmitted qubits. On the other hand, the statistical correlation between bits transmitted in one basis and those received in the other basis becomes stronger as the angle between two bases becomes narrower. If the angle is very small, the statistical correlation between bits transmitted in one basis and those received in the other basis is as strong as those received in the same basis as transmitting basis, which means that the modified protocol can generate almost twice as long secret key as the original protocol, provided that Alice and Bob choose two different bases with almost the same probability. We also point out that the reverse reconciliation often gives different amount of secret key to the direct reconciliation over Pauli channels with our modified protocol.
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 for unital channels. We consider the case in which only Bob is allowed to compensate his axis, and the case in which both Alice and Bob are allowed to compensate their axes. In the former case, we show that we should utilize the mismatched measurement outcomes in the channel estimation phase. In the latter case, we show that we do not have to utilize the mismatched measurement outcomes in the channel estimation phase.
We construct a practically implementable classical processing for the 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 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.
Using tools from algebraic geometry and Groebner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.
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.
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 (QRD-MLD), and its improvement. When the list size is set to achieve the almost same symbol error rate (SER) as the QRD-MLD, the proposed algorithm has smaller average computational complexity.
Let Lambda be a numerical semigroup. Assume there exists an algebraic function field over GF(q) in one variable which possesses a rational place that has Lambda as its Weierstrass semigroup. We ask the question as to how many rational places such a function field can possibly have and we derive an upper bound in terms of the generators of Lambda and q. Our bound is an improvement to a bound by Lewittes which takes into account only the multiplicity of Lambda and q. From the new bound we derive significant improvements to Serre's upper bound in the cases q=2, 3 and 4. We finally show that Lewittes' bound has important implications to the theory of towers of function fields.