A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number N of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large N for successful key generation. Here we report a Gaussian-modulated coherent state CVQKD system that is able to overcome these challenges and can generate composable keys secure against collective attacks with N ≈ 2 × 108 coherent states. With this advance, possible due to improvements to the security proof and a fast, yet low-noise and highly stable system operation, CVQKD implementations take a significant step towards their discrete-variable counterparts in practicality, performance, and security.

Continuous-variable quantum key distribution (QKD) utilizes an ensemble of coherent states of light to distribute secret encryption keys between two parties. An essential ingredient of the QKD protocol is highly efficient information reconciliation. To achieve highly efficient reconciliation, error-correcting codes with a low channel coding rate are inevitable in the most common schemes of multilevel coding and multistage decoding (MLC-MSD) and multidimensional reconciliation. Multiedge-type (MET) low-density parity-check (LDPC) codes are well suited for highly efficient reconciliation at low rates. Here, we calculate the optimal channel coding rates in the MLC-MSD scheme for reverse reconciliation, introduce the concept of generalized extrinsic information transfer charts for MET-LDPC codes, which constitute a simple and fast asymptotic analysis tool, and present a set of MET-LDPC codes with asymptotic efficiency >97% for channel coding rates 0.1, 0.05, 0.02, and 0.01. We believe that our codes will find wide application in implementations of continuous-variable quantum key distribution based on Gaussian modulation.

This paper proposes the Symbolic-Stochastic Chase Decoding Algorithm (S-SCA) for the Reed-Solomon (RS) and BCH codes. By efficient usage of void space between constellation points for q-ary modulations and using soft information at the input of the decoder, the S-SCA is capable of outperforming conventional Symbolic-Chase algorithm (S-CA) with less computational cost. Since the S-SCA starts with the randomized generation of likely test-vectors, it reduces the complexity to polynomial order and also it does not need to find the least reliable symbols to generate test-vectors. Our simulation results show that by increasing the number of test-vectors, the performance of the algorithm can approach the ML bound. The S-SCA(1K) provides near 2 dB gain in comparison with S-CA(1K) for (31, 25) RS code using 32-QAM. Furthermore, the algorithm provides near 3 dB further gain with 1K iteration compared with S-CA(65K) when (255, 239) RS code is used in an AWGN channel. For the Rayleigh fading channel and the same code, the algorithm provides more that 5 dB gain. Also for (63, 57) BCH codes and 8-PSK modulation the proposed algorithm provides 3dB gain with less complexity.This decoder is Soft-Input Soft-Output (SISO) decoder and is highly attractive in low power applications. Finally, the Symbolic-Search Bitwise-Transmission Stochastic Chase Algorithm (SSBT-SCA) was introduced for RS codes over BPSK transmission that is capable of generating symbolic test-vectors that reduce complexity and mitigate burst errors.The authors are with the DRAFT F n q (codeword space). The parameter d is the radius in which the codeword can be recovered [1].When a small fraction of the F n q space is used for codewords, a large d can be created. Specifically for Reed-Solomon (RS) codes, the code minimum distance is d = n − k + 1, which provides the largest possible code minimum distance for any linear code with the same input/output length.RS codes and Bose, Chaudhuri, and Hocquenghem (BCH) codes are linear codes suitable for high rate applications due to their large minimum distance. RS codes can be considered as a non-binary form of the BCH codes. In the same length n and approximately same rate, the BCH codes outperform RS codes, but the main reason that RS codes have frequent usage is that they can correct burst errors, which can occur in many applications like data storage devices.These codes are widely used in storage channels, satellite telecommunications (ETS 300 456), space telemetry systems (CCSDS and NTSS), digital video broadcasting (DVB-x) and wireless broadband systems (IEEE 802.x).The decoding problem is the problem of finding a codeword C ∈ F n q within a specific distance from a received code R ∈ R n q . The brute-force decoding method suffers from exponential complexity while the code length is increased linearly. The most common decoding algorithm for RS/BCH codes is hard decision decoding Berlekamp-Massey (HDD-BM) algorithm [2]. The HDD-BM algorithm has a running time complexity of O(n 2 ) and produces unique decoded message, w...

Distributing cryptographic keys over public channels in a way that can provide information-theoretic security is the holy grail for secure communication. This can be achieved by exploiting quantum mechanical principles in so-called quantum key distribution (QKD). Continuous-variable (CV) QKD based on coherent states, in particular, is an attractive scheme for secure communication since it requires only standard telecommunication technology that can operate at room temperature. However, a recently discovered side-channel created in the process of state preparation leads to a leakage of information about the transmitted quantum state, opening a security loophole for eavesdroppers to compromise the security of the CVQKD system. Here, we present a CVQKD system without this modulation leakage vulnerability. Our implementation is based on a baseband modulation approach and uses an in-phase and quadrature (IQ) modulator for state preparation and radio frequency heterodyne detection together with carefully designed digital signal processing for state measurement. We consider practical aspects in the implementation and demonstrate the generation of a composable secret key secure against collective attacks. This work is a step towards protecting CVQKD systems against practical imperfections of physical devices and operational limitations without performance degradation.

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