A Linear Feedback Shift Register (LFSR) is a mathematical algorithm used for generating a sequence of binary digits. It is commonly used in the field of cryptography, digital signal processing, and error-correcting codes. The LFSR algorithm involves a shift register, which is a sequence of flip-flops that can be shifted left or right by one position at each clock cycle. The output of the LFSR is obtained by taking a linear combination of the bits in the shift register, where the coefficients are either 0 or 1.
The LFSR algorithm works by taking the initial state of the shift register, which is usually a random sequence of binary digits. At each clock cycle, the bits in the shift register are shifted one position to the left or right, and a new bit is inserted into the shift register. The new bit is obtained by taking a linear combination of the bits in the shift register, where the coefficients are determined by a feedback polynomial. The feedback polynomial determines which bits are combined to produce the new bit, and which bits are discarded. The output of the LFSR is obtained by reading the output bit of the shift register at each clock cycle. The output sequence is typically a pseudo-random sequence, which appears to be random but is actually deterministic.
The MFSR algorithm is used in a variety of applications, including cryptography, digital communications, and circuit testing. In cryptography, the MFSR can be used to generate pseudorandom keys for encryption algorithms. In digital communications, the MFSR can be used to generate pseudorandom noise sequences for scrambling signals. In circuit testing, the MFSR can be used to generate test patterns for digital circuits.
The MFSR algorithm is a powerful tool for generating pseudorandom sequences. It is relatively easy to implement in hardware and software, and it can be used in a variety of applications. However, it is important to be aware that the output sequences of an MFSR are not truly random. They are deterministic and can be predicted given the initial state of the register.
The Matrix Shift Register Algorithm (MFSR) works by generating a sequence of bits from a linear feedback shift register (LFSR). The LFSR is a circuit that has a number of bits, each of which can be either a 0 or a 1. The bits are shifted one position to the right at each clock cycle, and the output bit is determined by a linear function of the previous state of the register.
The MFSR algorithm extends the LFSR algorithm by adding a matrix to the linear function. The matrix can be any square matrix, but it is typically chosen to be a Hadamard matrix. The Hadamard matrix is a matrix that has the property that the sum of each row and column is equal to 1.
The output bit of the MFSR algorithm is determined by the following equation:
output_bit = matrix * previous_state + previous_output
where:
matrixis the Hadamard matrixprevious_stateis the previous state of the LFSRprevious_outputis the previous output bit
The MFSR algorithm can generate more complex and unpredictable sequences than the LFSR algorithm because the matrix introduces non-linearity into the function. This makes it more difficult to predict the output of the MFSR algorithm from its previous state.
http://127.0.0.1:8000/docs - this is a main page with documentation to this API, if you are going to run locally.
https://generatorapi-1-a7624134.deta.app/docs - this is the same API but deployed to the remote server.
https://prbs-generator.netlify.app - this is the URL to get complete application.