Universal Secure Multiplex Network Coding with Dependent and Non-Uniform Messages

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.Comment: 10 pages, 1 figure, IEEEtrans.cls. Online published in IEEE Trans. Inform. Theor

Secure network coding with adaptive and active attack

Ning Cai and the author jointly studied secure network codes over adaptive and active attacks, which were rarely studied until these seminal papers. This paper reviews the result for secure network code over adaptive and active attacks. We focus on two typical network models, a one-hop relay network and a unicast relay network

Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets

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.Comment: Publisher's Open Access PDF. arXiv admin note: text overlap with arXiv:1811.0521

New Parameters of Linear Codes Expressing Security Performance of Universal Secure Network Coding

The universal secure network coding presented by Silva et al. realizes secure and reliable transmission of a secret message over any underlying network code, by using maximum rank distance codes. Inspired by their result, this paper considers the secure network coding based on arbitrary linear codes, and investigates its security performance and error correction capability that are guaranteed independently of the underlying network code. The security performance and error correction capability are said to be universal when they are independent of underlying network codes. This paper introduces new code parameters, the relative dimension/intersection profile (RDIP) and the relative generalized rank weight (RGRW) of linear codes. We reveal that the universal security performance and universal error correction capability of secure network coding are expressed in terms of the RDIP and RGRW of linear codes. The security and error correction of existing schemes are also analyzed as applications of the RDIP and RGRW.Comment: IEEEtran.cls, 8 pages, no figure. To appear in Proc. 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton 2012). Version 2 added an exact expression of the universal error correction capability in terms of the relative generalized rank weigh

Secure Quantum Network Code without Classical Communication

We consider the secure quantum communication over a network with the presence of a malicious adversary who can eavesdrop and contaminate the states. The network consists of noiseless quantum channels with the unit capacity and the nodes which applies noiseless quantum operations. As the main result, when the maximum number m1 of the attacked channels over the entire network uses is less than a half of the network transmission rate m0 (i.e., m1 < m0 / 2), our code implements secret and correctable quantum communication of the rate m0 - 2m1 by using the network asymptotic number of times. Our code is universal in the sense that the code is constructed without the knowledge of the specific node operations and the network topology, but instead, every node operation is constrained to the application of an invertible matrix to the basis states. Moreover, our code requires no classical communication. Our code can be thought of as a generalization of the quantum secret sharing

Secure Multiplex Coding with a Common Message

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.Comment: 5 pages, no figure, IEEEtran.sty, final version to appear in Proc. ISIT 201