Entropy Estimation for ADC Sampling-Based True Random Number Generators

True random number generators (TRNGs) are widely used in cryptographic systems, and their security is the base of many cryptographic algorithms and protocols. At present, entropy estimation based on a stochastic model is a well-recommended approach to evaluate the security of a specific TRNG structure. Besides, the generation speed is also an important property for TRNGs. For this purpose, an analog-to-digital converter (ADC) can be employed to sample the noisy signal to achieve high bit rate. However, no research focuses on the entropy estimation on the basis of the stochastic model toward ADC sampling. In this paper, we propose an entropy estimation for the ADC sampling-based TRNG through extending an existing model. In particular, we present an equivalent model to estimate the entropy of any single bit in the converted sample obtained by the ADC sampling. Furthermore, we propose a method of the entropy estimation for the multi-bit ADC output, which provides the lower bound of the entropy. By conducting simulations and hardware experiments on this type of TRNG, we confirm the correctness of the proposed entropy estimation theory. The prototype chip is fabricated in the SMIC 65-nm process, and the consumed power is 34 mW. The random bit sequences compatible with the AIS 31 standard are generated at a speed of 1323 Mb/s. The sequences are able to pass the rigorous statistical test suites, including NIST SP 800-22, Diehard, and TestU01 (containing the Big Crush test), after simple post-processing at a bit rate of around 33 Mb/s.