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International Conference on Intelligent Systems and Embedded Design (ISED)

The HDL Implementation of High Precision Gaussian Random Number Generator for QKD Using FPGA

Krishnaveni. Guduru, Puli Kishore Kumar

Published Dec 20, 2024• 1 citation
Publisher

Abstract

In quantum cryptography, the Gaussian Random Number(GRN) plays a crucial role. The Box-Muller is exact method for generating Gaussian random numbers but it requires very complex arithmetic operations. The polarization decision method uses less arithmetic operations and less I/O pins. In this paper we have proposed novel floating point architecture to produce Gaussian random numbers(GRN). In this Floating point architecture initially a software approach is followed to obtain for Uniform Random Number(URN) and perform mathematical computation techniques to generate GRN, hence the overall architecture complexity is reduced when compared to fixed polarization decision method. The proposed floating point architecture achieves precision value 0.001 and 30% less in bonded IOBS which results in simplification of routing and enhance the timing performance. The design is implemented and performed using Xilinx on ZC706 FPGA.

DOI
10.1109/ised63599.2024.10957178

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In quantum cryptography, the Gaussian Random Number(GRN) plays a crucial role. The Box-Muller is exact method for generating Gaussian random numbers but it requires very complex arithmetic operations. The polarization decision method uses less arithmetic operations and less I/O pins. In this paper we have proposed novel floating point architecture to produce Gaussian random numbers(GRN). In this Floating point architecture initially a software approach is followed to obtain for Uniform Random Number(URN) and perform mathematical computation techniques to generate GRN, hence the overall architecture complexity is reduced when compared to fixed polarization decision method. The proposed floating point architecture achieves precision value 0.001 and 30% less in bonded IOBS which results in simplification of routing and enhance the timing performance. The design is implemented and performed using Xilinx on ZC706 FPGA.
Abstract Quantum key distribution is the process of using quantum communication to establish a shared key between two parties. It has been demonstrated the unconditional security and effective communication of quantum communication system can be guaranteed by an excellent Gaussian random number (GRN) generator with high speed and an extended random period. In this paper, we propose to construct the Gaussian random number generator by using field‐programmable gate array (FPGA), which is able to process large data in high speed. We also compare three algorithms of GRN generation: Box‐Muller algorithm, polarization decision algorithm, and central limit algorithm. We demonstrate that the polarization decision algorithm implemented in FPGA requires less computing resources and also produces a high‐quality GRN through the null hypothesis test.
Based on the research of the current situation of continuous variables quantum cryptographic key QCK and in order to guarantee the effect of communication, we aim to build a quantum communication system based on Reverse Reconciliation Protocol. Thus, a good Gaussian Random Number Generator based on FPGA (Field Programmable Gate Array) is proposed in this paper which can run fast and acquire a high throughput per slice. In this paper, Gaussian random number generator is based on the analysis of Box-Muller algorithm. Besides, seeds for Gaussian random number are input by mechanical keyboard which joggles randomly. Implementation results on Altera FPGA show that the proposed hardware design could generate Gaussian random number with period of 232−12^{32}-1232−1. Finally, we get the mean values, variances, maximum deviations and distribution diagrams of the generated Gaussian random numbers(GRN) by importing these data into Matlab. To assess the quality of these generated GRN, we further compare them to these GRN generated by Matlab.
The continuous-variable quantum key distribution experimental system requires the randomness and speed of a Gaussian modulator. We present the hardware design for a Gaussian random number (GRN) generator based on the Box–Muller method, which can be implemented on a field-programmable gate array (FPGA). An external high-speed true random number generator application-specific integrated circuit (ASIC) is used to this end. The ASIC operates faster and more independently compared with other Gaussian algorithms based on a linear feedback shift register. The trigonometric and logarithmic functions are calculated using the nonuniform piecewise linear approximation. The calculation of the Gaussian random modulus and phase value is realized using this hardware. Compared with an arbitrary waveform generator, the GRN can be uploaded to a computer to estimate the security key rate. Furthermore, the GRN generator accurately provides a Gaussian probability density function that passes the Jarque–Bera inspection and Lilliefors tests. The proposed FPGA-based system is demonstrated to convert eight-channel 320-Mbps uniform random numbers to 40-MHz 16-bit GRN in real time. Finally, the control of the optical module and Gaussian modulation is realized via the FPGA-based outputs of four dual-channel, 16-bit, 1-giga samples per second digital-to-analog converters.
Our work aims to introduce an FPGA-based electronics architecture designed to enhance the security of quantum key distribution (QKD) networks. The core focus is on integrating a true random number generator (TRNG) IP in an FPGA-based QKD control electronics implemented on Xilinx’s ZYNQ UltraScale+ based FPGA boards. The work presents the challenges in integrating an existing TRNG IP with QKD FPGA design, different bit and timing requirements, the subsequent speed mismatch issues, support for multiple QKD protocols (Coherent One-Way (CoW) and Differential Phase Shift (DPS)) and user-defined QKD implementations. The integrated design also supports external QRNG/TRNG over USB/Ethernet.
There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around 90%90\%90% reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.
The Box-Muller transform is a widely used method to generate Gaussian samples from uniform samples. Quantum amplitude encoding methods encode the multi-variate normal distribution in the amplitudes of a quantum state. This work presents the Quantum Box-Muller transform which creates a superposition of binary-encoded grid points representing the multi-variate normal distribution. The gate complexity of our method depends on quantum arithmetic operations and, using a specific set of known implementations, the complexity is quadratic in the number of qubits. We apply our method to Monte-Carlo integration, in particular to the estimation of the expectation value of a function of Gaussian random variables. Our method implies that the state preparation circuit used multiple times in amplitude estimation requires only quantum arithmetic circuits for the grid points and the function, in addition to a single controlled rotation. We show how to provide the expectation value estimate with an error that is exponentially small in the number of qubits, similar to the amplitude-encoding setting with error-free encoding.