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In this paper, a novel true random bit generator (TRBG) based on a double-scroll attractor is proposed. The double-scroll attractor is obtained from a simple model which is qualitatively similar to Chua's circuit. In order to face the challenge of using the proposed TRBG in cryptography, the proposed TRBG is subjected to statistical tests which are the well-known Federal Information Processing Standards-140-1 and Diehard test suite in the area of cryptography. The proposed TRBG successfully passes all these tests and can be implemented in integrated circuits.