In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wire-tapper also receives the transmitted signal via another MIMO channel. First we assumed that the channels are degraded and the wire-tapper has the worst channel.We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of enhanced channel to show that the secret superposition of Gaussian codes is optimal.We show that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. Then we extend the result of the degraded case to non-degraded case. We show that the secret superposition of Gaussian codes along with successive decoding cannot work when the channel is not degraded. we develop an Secret Dirty Paper Coding (SDPC) scheme and show that SDPC is optimal for this channel. Finally, We investigate practical characterizations for the specific scenario in which the transmitter and the eavesdropper have multiple antennas, while both intended receivers have a single antenna. We characterize the secrecy capacity region in terms of generalized eigenvalues of the receivers channel and the eavesdropper channel. We refer to this configuration as the MISOME case. In high SNR we show that the capacity region is a convex closure of two rectangular regions.
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning, and the Gelfand-Pinsker bining. This scheme matches Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation in which the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as Secret Superposition Scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar Lemma. We then assume that the channels are Additive White Gaussian Noise (AWGN) and show that secret superposition scheme with Gaussian codebook is optimal. The converse proof is based on the generalized entropy power inequality. Finally, we use a broadcast strategy for the slowly fading wire-tap channel when only the eavesdropper's channel is fixed and known at the transmitter. We derive the optimum power allocation for the layers which maximizes the total average rate.
1 Abstract-In this paper, we first consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-taper also receives the transmitted signal. We assume that the signals are transmitted over additive white Gaussian noise channels. We characterize the secrecy capacity region of this channel. Our achievable coding scheme is based on superposition coding and the random binning. We refer to this scheme as Secret Superposition Coding. The converse proof combines the converse proof for the conventional Gaussian broadcast channel and the perfect secrecy constraint. This capacity region matches the capacity region of the broadcast channel without security constraint. It also matches the secrecy capacity of the wire-tap channel. Based on the rate characterization of the secure Gaussian broadcast channel, we then use a multilevel coding approach for the slowly fading wire-tap. We assume that the transmitter only knows the eavesdropper's channel. In this approach, source node sends secure layered coding and the receiver viewed as a continuum ordered users. We derive optimum power allocation for the layers which maximizes the total average rate.
Abstract. Camellia, a 128-bit block cipher which has been accepted by ISO/IEC as an international standard, is increasingly being used in many cryptographic applications. In this paper, using the redundancy in the key schedule and accelerating the filtration of wrong pairs, we present a new impossible differential attack to reduced-round Camellia. By this attack 12-round Camellia-128 without F L/F L −1 functions and whitening is breakable with a total complexity of about 2 116.6 encryptions and 2 116.3 chosen plaintexts. In terms of the numbers of the attacked rounds, our attack is better than any previously known attack on Camellia-128.
A K-user secure Gaussian Multiple-Access-Channel (MAC) with an external eavesdropper is considered in this paper. An achievable rate region is established for the secure discrete memoryless MAC. The secrecy sum capacity of the degraded Gaussian MIMO MAC is proven using Gaussian codebooks. For the non-degraded Gaussian MIMO MAC, an algorithm inspired by interference alignment technique is proposed to achieve the largest possible total Secure-Degrees-of-Freedom (S-DoF). When all the terminals are equipped with a single antenna, Gaussian codebooks have shown to be inefficient in providing a positive S-DoF. Instead, a novel secure coding scheme is proposed to achieve a positive S-DoF in the single antenna MAC. This scheme converts the single-antenna system into a multiple-dimension system with fractional dimensions. The achievability scheme is based on the alignment of signals into a small sub-space at the eavesdropper, and the simultaneous separation of the signals at the intended receiver. Tools from the field of Diophantine Approximation in number theory are used to analyze the probability of error in the coding scheme. It is proven that the total S-DoF of K−1 K can be achieved for almost all channel gains. For the other channel gains, a multi-layer coding scheme is proposed to achieve a positive S-DoF. As a function of channel gains, therefore, the achievable S-DoF is discontinued.
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