Universal random number generation robust to manufacturing error using AD converters based on beta map

Beta encoder is robust to manufacturing error, can be miniturized, and consumes less power. Application of beta encoder to random number generation is promising. The fundamental problem for random number generation is to maximize the rate of random number generation under the condition that the random number satisfies unpredictability and uniformity. We obtain the following results: 1. We proposed a method for estimating beta values on pipelined beta encoders which generate random numbers faster than the normal beta encoders. 2. We derived a rigorous upper bound of the mean square error of beta encoders using the theory of Fredholm determinants of Perron-Frobenius operators. 3. We showed that our previously proposed (beta)-ary to binary transformation method can achieve log(beta) of generating rate as the code length goes to infinity. 4. We reduce the computational complexity for evaluating the security performance of a coset coding.