![]() 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. However, the proposed design is more efficient than the segmented leap-ahead method concerning space occupancy.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. It occupies more area and runs at a lower frequency compared with the original Fibonacci LFSR. Finally, the proposed design is implemented on a field-programmable gate array (FPGA). However, the period is almost equal to the original one when the system is realized in 32-bit or 64-bit form. The period of the proposed system is less than that of the original Fibonacci LFSR. The proposed design can generate different sequences of random numbers compare to those of the conventional methods. The second stage (segment 2) is executed only after every 2 n 1−1 clock cycles. The clock signal for the first segment is that of the external clock, whereas that for the second segment is modified by the clock controller. The system produces random numbers based on an external clock. The proposed design consists of blocks: segment 1, segment 2, and a clock controller. Two segments of Fibonacci LFSR are used to form a generator that can produce more varied random numbers. The proposed circuit is designed to produce different sequences of numbers. Therefore, this paper proposes a circuit for generating random numbers. Even though a lot of work has been done using this method to search for truly random numbers, it is an area that continues to attract interest. ![]() A popular method for generating random numbers is a linear-feedback shift register (LFSR). Much work has been conducted to generate truly random numbers and is still in progress. For a long time, random numbers have been used in many fields of application. ![]()
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