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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