This paper analyzes the cryptographic security of J3Gen, a promising pseudo random number generator for low-cost passive Radio Frequency Identification (RFID) tags. Although J3Gen has been shown to fulfill the randomness criteria set by the EPCglobal Gen2 standard and is intended for security applications, we describe here two cryptanalytic attacks that question its security claims: (i) a probabilistic attack based on solving linear equation systems; and (ii) a deterministic attack based on the decimation of the output sequence. Numerical results, supported by simulations, show that for the specific recommended values of the configurable parameters, a low number of intercepted output bits are enough to break J3Gen. We then make some recommendations that address these issues.

A new proposal to generate pseudorandom numbers with Gaussian distribution is presented. The generator is a generalization to the extended field $GF\left(2^n\right)$ of the one using cyclic rotations of linear feedback shift registers (LFSRs) originally defined in $GF\left(2\right)$. The rotations applied to LFSRs in the binary case are no longer needed in the extended field due to the implicit rotations found in the binary equivalent model of LFSRs in $GF\left(2^n\right)$. The new proposal is aligned with the current trend in cryptography of using extended fields as a way to speed up the bitrate of the pseudorandom generators. This proposal allows the use of LFSRs in cryptography to be taken further, from the generation of the classical uniformly distributed sequences to other areas, such as quantum key distribution schemes, in which sequences with Gaussian distribution are needed. The paper contains the statistical analysis of the numbers produced and a comparison with other Gaussian generators.

This paper presents a new proposal to generate optimal pseudorandom numbers with Gaussian distribution. The generator is especially designed for low-cost hardware implementation, although the software version is also considered. For this reason, Linear Feedback Shift Registers in conjunction with cyclic rotations are employed. The proposal presents a low implementation cost and overcomes the limitations of the previous Gaussian generators based on linear feedback shift registers by means of a less complex algorithm to find optimal configurations. As a consequence, it turns into a really usable generator. Moreover, a further improvement, based on the simulated annealing algorithm, is applied in order for the random values to be better adjusted to the normal distribution.

Many stream ciphers employ linear feedback shift registers (LFSRs) to generate pseudorandom sequences. Many recent LFSRs are defined in $GF\left(2^n\right)$ to take advantage of the n-bit processors, instead of using the classic binary field. In this way, the bit generation rate increases at the expense of a higher complexity in computations. For this reason, only certain primitive polynomials in $GF\left(2^n\right)$ are used as feedback polynomials in real ciphers. In this article, we present an efficient implementation of the LFSRs defined in $GF\left(2^n\right)$. The efficiency is achieved by using equivalent binary LFSRs in combination with binary n-bit grouped operations, n being the processor word’s length. This improvement affects the general considerations about the security of cryptographic systems that uses LFSR. The model also allows the development of a faster method to test the primitiveness of polynomials in $GF\left(2^n\right)$.