![]() It is achieved by means of rotations, instead of generic permutations, reducing the complexity of precomputation performed to obtain the valid configurations (rotations). The proposal requires the same resources than Condo et al’s PRNG but overcomes the oversize of Kang’s PRNG and the inconvenient of Condo et al’s PRNG related to the searching algorithm for valid configurations and reduces its computational cost. For this reason, we present in this article a much simpler implementation of the CLT method, mainly oriented to a hardware implementation, following the same strategy than Kang and Condo et al, that is, using only one LFSR. However, the proposals based on a unique LFSR require a lower implementation cost. The comparison reveals that the number of gates and other hardware resources are very similar, while the CLT, implemented in a field-programmable gate array (FPGA) using directly the numbers produced by several LFSR, showed worse results in the normality tests. In, a comparison is performed among the hardware implementation of three of the best-known methods: CLT, Box–Muller algorithm and polarization decision algorithm. Other proposals Kang and Condo are based on a unique LFSR that produces all the sequences in order to decrease the global complexity of the PRNG.Īlthough the application of CLT is not the only method to generate Gaussian random numbers, it will always be a reference to take in mind. Some authors propose the utilization of several LFSR to generate different and independent uniform distributed sequences to be summed later. The use of several of these sequences leads us to obtain an approximation of a Gaussian distribution by means of the sum of all of them. In this case, the samples produced by LFSR follow a uniform distribution. In other words, only when the tests results are greater than a given threshold, the permutation is considered a valid one.Īll of these proposals are focused on the application of the central limit theorem (CLT) that states that the distribution of samples mean approximates a normal distribution, as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population distribution shape. Once these permutations have been applied in the PRNG, the numbers generated follow a Gaussian distribution according to the results of the normality tests. Furthermore, a high computational cost is required for the searching of valid permutations. However, as the own authors claim, not all permutations can be applied. This generator, designed using a unique LFSR of length 17, reduces the cost of implementation. More recently, in 2015, Condo et al have proposed a PRNG using permutations over the successive states of an LFSR. The generation algorithm was based on an accumulator operated over decimated M-bits numbers, producing a final period of ( 2 N - 1 ) / ( 8 N ) which yields on an oversize LFSR. In 2010, Kang presented a method employing an LFSR of length N = 4 M bits to generate pseudorandom numbers with ( M + 4 ) bits. Some authors have previously proposed Gaussian PRNG using LFSR. ![]() Īlthough initially motivated by the potential cryptographic application, we explore in this paper the utilization of LFSR as a general purpose PRNG with Gaussian distribution instead of their native uniform distribution. CV-QKD schemes employ Gaussian modulation to send random amplitude and phase values that must be generated following a Gaussian distribution. ![]() On the other hand, quantum key distribution schemes (QKD) are evolving from the initial discrete variable proposals (DV-QKD) based on the transmission of polarized photons using non-orthogonal states towards continuous variable systems (CV-QKD) based in the transmission of coherent states which allow the use of standard communications components and, therefore, lower implementation cost. LFSR are also employed to design true random number generators (TRNG) in radio frequency identification (RFID) systems. The uniform distribution of the generated numbers allows LFSR to be widely used in communication and cryptographic applications, as part of the core of CDMA systems and stream ciphers belonging to the security standards and protocols of wireless and mobile telecommunication systems such as Bluetooth, IEEE 802.11 WLAN, GSM and LTE. Linear feedback shift registers (LFSR) have always been a basic resource for the pseudorandom number generation (PRNG) due to their low cost implementation, the good statistical properties of the values produced and the simplicity of their mathematical model that allows a priori analysis of the behavior of the system. ![]()
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