LFDs

LFD stands for Linear Feedback Shift Register. It is a type of pseudorandom number generator that produces a sequence of bits. The sequence is determined by a linear recurrence relation modulo two. An LFD consists of a shift register of n bits and a feedback function. The feedback function is a linear function of the bits in the register. At each step, the bits in the register are shifted one position to the right, and the leftmost bit is replaced by the output of the feedback function.

The output sequence of an LFD is periodic. The maximum period length is 2^n - 1, where n is the number of bits in the register. This maximum period is achieved when the feedback function is chosen such that the characteristic polynomial of the recurrence relation is primitive. LFDs are widely used in various applications due to their simplicity, speed, and good statistical properties. These applications include cryptography, stream ciphers, error-correcting codes, and simulation.

Different types of LFDs exist, often distinguished by their feedback polynomial or the specific implementation of the shift register. The choice of the feedback polynomial is crucial for determining the period and the statistical randomness of the generated sequence. While LFDs are efficient generators, their deterministic nature means that their output can be predicted if the feedback polynomial and the initial state are known. This characteristic makes them unsuitable for certain cryptographic applications where unpredictability is paramount without additional security measures.