We consider in this paper the problem of information reconciliation in the context of secret key agreement between two legitimate parties, Alice and Bob. Beginning the discussion with the secret key agreement model introduced by Ahlswede and Csiszár, the channel-type model with wiretapper, we study a protocol based on error correcting codes. The protocol can be adapted to changes in the communication channel extending the original source. The efficiency of the reconciliation is only limited by the quality of the code and, while transmitting more information than needed to reconcile Alice's and Bob's sequences, it does not reveal any more information on the original source than an ad-hoc code would have revealed.
We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method, based on the algebraic properties of octonions. Since the protocol does not use any postselection, it can be proven secure against arbitrary collective attacks, by using well-established theorems on the optimality of Gaussian attacks. By using this new coding scheme with an appropriate signal to noise ratio, the distance for secure…
Quantum key distribution performs the trick of growing a secret key in two distant places connected by a quantum channel. The main reason is that the legitimate users can bound the information gathered by the eavesdropper. In practical systems, whether because of finite resources or external conditions, the quantum channel is subject to fluctuations. A rate adaptive information reconciliation protocol, that adapts to the changes in the communication channel, is then required to minimize the leakage of information in the classical postprocessing. We consider here the leakage of a rate-adaptive …
We consider a key encapsulation mechanism (KEM) based on Module-LWE where reconciliation is performed on the 8-dimensional lattice $E_8$, which admits a fast CVP algorithm. Our scheme generates 256 bits of key and requires 3 or 4 bits of reconciliation per dimension. We show that it can outperform Kyber in terms of the modulus q with comparable error probability. We prove that our protocol is IND-CPA secure and improves the security level of Kyber by 7.3%.
Quantum key distribution (QKD) offers a practical solution for secure communication between two distinct parties via a quantum channel and an authentic public channel. In this work, we consider different approaches to the quantum bit error rate (QBER) estimation at the information reconciliation stage of the post-processing procedure. For reconciliation schemes employing low-density parity-check (LDPC) codes, we develop a novel syndrome-based QBER estimation algorithm. The algorithm suggested is suitable for irregular LDPC codes and takes into account punctured and shortened bits. Testing our …
In Part I of this two-part paper on confidential communication over wireless channels, we studied the fundamental security limits of quasi-static fading channels from the point of view of outage secrecy capacity with perfect and imperfect channel state information. In Part II, we develop a practical secret key agreement protocol for Gaussian and quasi-static fading wiretap channels. The protocol uses a four-step procedure to secure communications: establish common randomness via an opportunistic transmission, perform message reconciliation, establish a common key via privacy amplification, and…
We designed high-efficiency error correcting codes allowing to extract an errorless secret key in a continuous-variable quantum key distribution protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an AWGN channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a continuous-variable quantum key distribution with a Gaussian…
Quantum key distribution (QKD) is a cryptographic system that generates an information-theoretically secure key shared by two legitimate parties. QKD consists of two parts: quantum and classical. The latter is referred to as classical post-processing (CPP). Information reconciliation is a part of CPP in which parties are given correlated variables and attempt to eliminate the discrepancies between them while disclosing a minimum amount of information. The elegant reconciliation protocol known as \emph{Cascade} was developed specifically for QKD in 1992 and has become the de-facto standard for …
Although quantum key distribution (QKD) comes from the development of quantum theory, the implementation of a practical QKD system does involve a lot of classical process, such as key reconciliation and privacy amplification, which is called post-processing. Post-processing has been a crucial element to high speed QKD systems, even the bottleneck of it because of its relatively high time consumption. Low density parity check (LDPC) is now becoming a promising approach of overcoming the bottleneck due to its good performance in processing throughput. In this article we propose and simulate an e…
We define the direct and reverse secret-key capacities of a memoryless quantum channel as the optimal rates that entanglement-based quantum key distribution protocols can reach by using a single forward classical communication (direct reconciliation) or a single feedback classical communication (reverse reconciliation). In particular, the reverse secret-key capacity can be positive for antidegradable channels, where no forward strategy is known to be secure. This property is explicitly shown in the continuous variable framework by considering arbitrary one-mode Gaussian channels.
\emph{Group Testing} (GT) addresses the problem of identifying a small subset of defective items from a large population, by grouping items into as few test pools as possible. In \emph{Adaptive GT} (AGT), outcomes of previous tests can influence the makeup of future tests. Using an information theoretic point of view, Aldridge $2012$ showed that in the regime of a few defectives, adaptivity does not help much, as the number of tests required is essentially the same as for non-adaptive GT. \emph{Secure GT} considers a scenario where there is an eavesdropper who may observe a fraction $δ$ of the…
There have been several approaches to provisioning traffic between core network nodes in Internet Service Provider (ISP) networks. Such approaches aim to minimize network delay, increase network capacity, and enhance network security services. MATE (Multipath Adaptive Traffic Engineering) protocol has been proposed for multipath adaptive traffic engineering between an ingress node (source) and an egress node (destination). Its novel idea is to avoid network congestion and attacks that might exist in edge and node disjoint paths between two core network nodes. This paper builds an adaptive, rob…
Device-to-device (D2D) communication raises new transmission secrecy protection challenges, since conventional physical layer security approaches, such as multiple antennas and cooperation techniques, are invalid due to its resource/size constraints. The full-duplex (FD) jamming receiver, which radiates jamming signals to confuse eavesdroppers when receiving the desired signal simultaneously, is a promising candidate. Unlike existing endeavors that assume the FD jamming receiver always improves the secrecy performance compared with the half-duplex (HD) receiver, we show that this assumption hi…
Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart…
We consider the problem of designing secure and private codes for distributed matrix-matrix multiplication. A master server owns two private matrices and hires worker nodes to help compute their product. The matrices should remain information-theoretically private from the workers. Some of the workers are malicious and return corrupted results to the master. We design a framework for security against malicious workers in private matrix-matrix multiplication. The main idea is a careful use of Freivalds' algorithm to detect erroneous matrix multiplications. Our main goal is to apply this securit…
Several approaches have been proposed to the problem of provisioning traffic engineering between core network nodes in Internet Service Provider (ISP) networks. Such approaches aim to minimize network delay, increase capacity, and enhance security services between two core (relay) network nodes, an ingress node and an egress node. MATE (Multipath Adaptive Traffic Engineering) has been proposed for multipath adaptive traffic engineering between an ingress node (source) and an egress node (destination) to distribute the network flow among multiple disjoint paths. Its novel idea is to avoid netwo…
Physical layer security has recently been regarded as an emerging technique to complement and improve the communication security in future wireless networks. The current research and development in physical layer security is often based on the ideal assumption of perfect channel knowledge or the capability of variable-rate transmissions. In this work, we study the secure transmission design in more practical scenarios by considering channel estimation errors at the receiver and investigating both fixed-rate and variable-rate transmissions. Assuming quasi-static fading channels, we design secur…
An information theoretic approach to security and privacy called Secure And Private Information Retrieval (SAPIR) is introduced. SAPIR is applied to distributed data storage systems. In this approach, random combinations of all contents are stored across the network. Our coding approach is based on Random Linear Fountain (RLF) codes. To retrieve a content, a group of servers collaborate with each other to form a Reconstruction Group (RG). SAPIR achieves asymptotic perfect secrecy if at least one of the servers within an RG is not compromised. Further, a Private Information Retrieval (PIR) sche…
In this work, an adaptive and robust null-space projection (AR-NSP) scheme is proposed for secure transmission with artificial noise (AN)-aided directional modulation (DM) in wireless networks. The proposed scheme is carried out in three steps. Firstly, the directions of arrival (DOAs) of the signals from the desired user and eavesdropper are estimated by the Root Multiple Signal Classificaiton (Root-MUSIC) algorithm and the related signal-to-noise ratios (SNRs) are estimated based on the ratio of the corresponding eigenvalue to the minimum eigenvalue of the covariance matrix of the received s…
