## 1 Introduction
The raw data itself follows Gaussian random distribution because these arise from a Gaussian random source; however, by applying some trivial operations on the raw data units, the desired uniform distribution can be reached, and the reconciliation can be performed with unconditional security, as we will show in detail in Section 3. A relevant difference of DV and CV protocols is that the physical quantum channel that connects the parties is characterized in a different way. For DVQKD the appropriate channel model is the Binary Symmetric Channel (BSC), which allows the use of the well-known channel-coding and error-correction tools in the post-processing phase. It also follows that for DVQKD there is a clear connection between the characteristics of the quantum channel and the world of traditional communication theory. On the other hand, for a CVQKD system the situation is more complicated, because the proper description of a Gaussian quantum channel requires several physical parameters (transmittance, variance, shot noise, excess noise, etc.) which allows no to draw a clear connection. To solve the situation for one-way CVQKD, the multidimensional reconciliation schemes [9; 10; 11; 12] have been introduced, which made possible the conversion of the physical AWGN (Additive White Gaussian Noise) quantum channel to a logical binary AWGN (BAWGN) channel, where the Gaussian random noise arises directly from the quantum-level transmission. Precisely, it works only for low dimensions and the resulted logical channel approximates only a binary Gaussian channel. As the accuracy of the physical-logical channel conversion gets closer to perfect, the resulting logical channel gets closer to a binary Gaussian channel. At low SNRs (Signal-to-Noise Ratio) the capacities of the Gaussian quantum channel and the binary Gaussian channel coincidence, and this is particularly convenient because for low SNRs, the problem of channel conversion can be reduced to the approximation of a binary Gaussian channel. From this follows, that the efficiency of the channel conversion procedure can be described by the relevant parameters of the resulting logical binary channel (such as its variance and capacity). This conversion efficiency has tremendous importance because it also determines the efficiency of the reconciliation process, i.e., the performance of the protocol. In the multidimensional reconciliation the conversion procedure required the use of the spherical space and its sophisticated operations [9; 10; 11], which is a complex process. The difficult computational steps of post-processing just cause further slowing down in the very sensitive key rates that are so difficult to establish. These requirements of the reconciliation phase are strongly undesired in a practical CVQKD scenario, so a simpler reconciliation would be desirable--for both one- and two-way systems. The problem of efficient post-processing is more crucial for two-way CVQKD, due to its more complex physical architecture. To exploit the real potential of two-way CVQKD systems, efficient post-processing is needed. It is still missing, which makes it not possible to attain the true performance of two-way CVQKD. This is the main reason why the theoretical maximum of key rates and ranges cannot be exceeded in the current practical scenarios; however, the protocol in its 'hardware level' is built to be strong, and would be capable of more performance than is currently available. To boost up the performance of the two-way CVQKD protocols over the current limits, we introduce an efficient reconciliation method that makes it possible to increase the key rates and to extend the currently available distance ranges. The mathematical apparatus that stands behind the multidimensional reconciliation puts a strict upper bound on the available dimensions, and limits its maximum [9; 10; 11; 42]. The reason is that in higher dimensions the required spherical division operations do not exist.