Disclaimer: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
A Truly Random Number Generator (TRNG) is a device that generates an unbiased and independent binary stream (sequence of 0s and 1s). One basic requirement for such a TRNG system to exist is an inherent never-ending source of entropy (randomness) in the system. The most commonly used source of entropy for a hardware-based TRNG device is the inherent noise in the analog circuitry which is due to the discrete nature of the electron charge and random motions of the electrons in the circuit. Truly random number generators are required in public key cryptography as well as digital signature schemes as essential tools for the generation of the key that is used for data protection. A TRNG is also used in lotteries and slot machines to replace the traditional methods of determining the winner. Furthermore, TRNGs can also be used in hardware-based compressive sensing and Monte Carlo sampling applications where long random sequences are required for the processing of data. With the advancement of technology towards enabling data processing (such as banking and emails) on small mobile device, several novel applications have recently appeared that require security on a very small hardware chip while the rate of data acquiring is also very high, and hence the need for high speed embedded TRNGs is growing very fast.
Certain nonlinear dynamical systems exhibit a long-term unpredictable behavior called chaos. One natural application for such unpredictability (and hence randomness) of the chaotic systems is the generation of a truly random bit sequence. In fact, one of the most prominent solutions for high speed embedded truly random number generation is based on the discrete-time chaotic maps. A chaotic-map TRNG operates by the amplification of the inherent noise of the analog circuitry in a (chaotic) map function. This is performed by feeding the output of the map back into the map as the input in each time step which leads to the amplification of the noise and thus unpredictable output behaviour. The state of the map output at each time step is transformed into a binary random variable using a bit generation function. Chaotic-map TRNGs as compared with other methods are faster (due to the discrete-time nature of the circuit) and easier to embed in integrated circuits. Therefore, they are the best candidate whenever high speed embedded TRNGs are required.
- A. Beirami and H. Nejati, "A Framework for Investigating the Performance of Chaotic-Map Truly Random Number Generators," to appear in IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 60, no. 7, July 2013. (pdf)
- A. Beirami, H. Nejati, and W. H. Ali, "Zigzag map: A variability-aware discrete-time chaotic-map truly random number generator," Electronics Letters, vol. 48, no. 24, pp. 1537-1538, November 2012. (pdf)
- H. Nejati, A. Beirami, and W. H. Ali, "Discrete-time chaotic-map truly random number generators: design, implementation, and variability analysis of the zigzag map," Analog Integrated Circuits and Signal Processing (ALOG), vol. 73, no. 1, pp. 363-374, October 2012. (pdf)
- A. Beirami, H. Nejati, and Y. Massoud, "A performance metric for discrete-time chaos-based truly random number generators," in Proc. of 51st IEEE Midwest Symposium on Circuits and Systems (MWSCAS 2008), Knoxville, TN, USA, August 2008, pp. 133-136. (pdf)
- H. Nejati, A. Beirami, and Y. Massoud, "A realizable modified tent map for true random number generation," in Proc. of 51st IEEE Midwest Symposium on Circuits and Systems (MWSCAS 2008), Knoxville, TN, USA, August 2008, pp. 621-624. (pdf)
Present and Past Participants
- Ahmad Beirami
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
- Hamid Nejati
- Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA.
- Warsame H. Ali
- Prairie view A&M university, Electrical and Computer Engineering Department, Prairie view, TX 77446, USA.
- Yehia Massoud
- Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA.
- Our paper titled "Zigzag map: A variability-aware discrete-time chaotic-map truly random number generator" was featured in Electronics Letters, vol. 48, no. 24, November 2012.
- Our paper titled "A performance metric for discrete-time chaos-based truly random number generators" was selected as top ten student papers at the 51st Midwest Symposium on Circuits and Systems, August 2008.