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The polynomials are represented in bitwise little endian: Bit 0 (least significant bit) represents the coefficient of \(x^0\), bit \(k\) represents the coefficient of \(x^k\), etc. The most interesting classes of PRNG are Linear Feedback Shift Registers (LFSR) and Non-Linear Shift Registers (NLFSR), those have such major strengths as good statistic properties, effective software and hardware implementation, regular structure is convenient for embodiment in an integrated form. The LFSR generators are easy in hardware and. The implementation is optimized for clarity, not for speed. One of the pseudo random signal generators class is a linear feedback shift register generators LFSR 5, 6. Pick a characteristic polynomial of some degree \(n\), where each monomial coefficient is either 0 or 1 (so the coefficients are drawn from \(\text\) modulo the characteristic polynomial equals \(x^0\).įor each \(k\) such that \(k < n\) and \(k\) is a factor of \(2^n - 1\), \(x^k\) modulo the characteristic polynomial does not equal \(x^0\).įast skipping in \(Θ(\log k)\) time can be accomplished by exponentiation-by-squaring followed by a modulo after each square. Its setup and operation are quite simple: Here we will focus on the Galois LFSR form, not the Fibonacci LFSR form. A2U2 stream cipher and the proposed CA based stream cipher is compared which explores the quality of random number generated and hence increases the security of the cipher.A linear feedback shift register (LFSR) is a mathematical device that can be used to generate pseudorandom numbers. The quality of random numbers from the proposed CA-based stream cipher is tested by using the DIEHARD test and entropy test. This paper explores the combination of LFSRs and CA as the key components of an efficient stream cipher design which can be implemented on Field Programmable Gate Arrays (FPGAs).

A CA-based architecture will likely form the basis for the development of ultra-high speed and compact quantum-based computers. Where linear feedback shift registers (LFSRs) combined with nonlinear feedback shift registers (NFSRs) have typically been used for PRNGs, the use of cellular automata (CA) is another viable option. The proposed stream cipher design based upon a recent published design known as A2U2. Pseudo-random number generators (PRNGs) are the main key component of stream ciphers used for encryption purposes.