Generalization of Galois Linear Feedback Register
Chang-Soo Park, Gyeong-Yeon Cho · Journal of the Institute of Electronics Engineers of Korea · 2006
This thesis proposes Arithmetic Shift Register(ASR) which can be used as pseudo random number generator. Arithmetic Shift. Register is defined as progression that multiplies random number D , not 0 or 1 at initial value which is not 0, and it is represented as ASR-D in this thesis. Irreducible polynomial that t which makes satisfies uniquely as over. is the characteristic polynomial of ASR-D , and the cycle of Arithmetic Shift Register has maximum cycle as . Galois Linear Feedback Shift Register corresponds to ASR-2-1. Therefore, Arithmetic Shift Register proposed in this thesis generalizes Galois Linear Feedback Shift Register. Linear complexity of ASR-D over is and in comparison with existing Linear Feedback Shift Register stability is high. The Software embodiment of arithmetic shift register proposed in this thesis is efficient than that of existing Linear Shift Register and hardware complexity is equal. Arithmetic shift register proposed in this thesis can be used widely in various fields such as cipher, error correcting codes, Monte Carlo integral, and data communication etc along with existing linear shift register.