Int. J. Electron. Commun. (AEÜ) 61 (2007) 235 – 242 www.elsevier.de/aeue Truly random number generators based on a non-autonomous chaotic oscillator Salih Ergün a , Serdar Özo ˜ guz b, ∗ a National Research Institute of Electronics and Cryptology, TÜB ˙ ITAK, P.O. Box 74, Gebze, Kocaeli 41470, Turkey b Faculty of Electrical-Electronics Engineering, ˙ Istanbul Technical University, Maslak, ˙ Istanbul 34390, Turkey Received 5 September 2005 Abstract A non-autonomous chaotic circuit which is suitable for high-frequency integrated circuit (IC) realization is presented. Simulation and experimental results verifying the feasibility of the circuit are given. We have numerically veriﬁed that the bit streams obtained from the stroboscopic Poincaré map of the system passed the four basic tests of FIPS-140-2 test suite. We also have veriﬁed that the binary data obtained from the hardware realization of this continuous-time chaotic oscillator in the same way pass the full NIST random number test suite. Then, in order to increase the output throughput and the statistical quality of the generated bit sequences, we propose a TRNG design which uses a dual oscillator architecture with the proposed continuous-time chaotic oscillator. Finally, we have experimentally veriﬁed that the binary data obtained by this oscillator sampling technique pass the tests of full NIST random number test suite without Von Neumann processing for a higher throughput speed while compared with the previous one where the proposed continuous-time chaotic oscillator is used alone.  2006 Elsevier GmbH. All rights reserved. Keywords: Chaotic oscillators; Random number generators 1. Introduction Nowadays, because of the increasing demand of electronic ofﬁcial and ﬁnancial transactions and digital signature ap- plications, the need for information secrecy has raised. In this manner, random number generators (RNGs) which have been used for only military cryptographic applications in the past got expanding usage for a typical digital communica- tion equipment. Almost all cryptographic systems require unpredictable values, therefore RNG is a fundamental component for cryp- tographic mechanisms. Generation of public/private key- pairs for asymmetric algorithms and keys for symmetric and ∗ Corresponding author. E-mail addresses: salih@uekae.tubitak.gov.tr (S. Ergün), serdar@ehb.itu.edu.tr (S. Özo˜ guz). 1434-8411/$ - see front matter  2006 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2006.05.006 hybrid cryptosystems require random numbers. The one- time pad, challenges, nonces, padding bytes and blinding values are created by using truly random number generators (TRNGs) [1]. Pseudo-random number generators (PRNGs) generate bits in a deterministic manner. In order to appear to be generated by a TRNG, the pseudo-random sequences must be seeded from a shorter truly random sequence [2]. Random numbers are also used during the authentication procedure between two cryptoequipments and initial value randomization of a cryptomodule that realizes an algorithm. Even if RNG design is known, any useful prediction about the output cannot be made. To fulﬁll the requirements for secrecy of one-time pad, key generation and any other cryp- tographic applications, the TRNG must satisfy the following properties: The output bit stream of the TRNG must pass all the statistical tests of randomness; the next random bit must be unpredictable; the same output bit stream of the TRNG must not be able to reproduced [3]. The best way to generate