Random number generators in digital information systems make use of physical entropy sources such as electronic and photonic noise to add unpredictability to deterministically generated pseudo-random sequences1,2. However, there is a large gap between the generation rates achieved with existing physical sources and the high data rates of many computation and communication systems; this is a fundamental weakness of these systems. Here we show that good quality random bit sequences can be generated at very fast bit rates using physical chaos in semiconductor lasers. Streams of bits that pass standard statistical tests for randomness have been generated at rates of up to 1.7 Gbps by sampling the fluctuating optical output of two chaotic lasers. This rate is an order of magnitude faster than that of previously reported devices for physical random bit generators with verified randomness. This means that the performance of random number generators can be greatly improved by using chaotic laser devices as physical entropy sources. Random-number generators are important in digital information systems. However, the speed at which current sources operate is much slower than the typical data rates used in communication and computing. Chaos in semiconductor lasers might help to bridge the gap.

Fast physical random bit generation with chaotic semiconductor lasers

The intrinsic variability of switching behavior in memristors has been a major obstacle to their adoption as the next generation of universal memory. On the other hand, this natural stochasticity can be valuable for hardware security applications. Here we propose and demonstrate a novel true random number generator utilizing the stochastic delay time of threshold switching in a Ag:SiO2 diffusive memristor, which exhibits evident advantages in scalability, circuit complexity, and power consumption. The random bits generated by the diffusive memristor true random number generator pass all 15 NIST randomness tests without any post-processing, a first for memristive-switching true random number generators. Based on nanoparticle dynamic simulation and analytical estimates, we attribute the stochasticity in delay time to the probabilistic process by which Ag particles detach from a Ag reservoir. This work paves the way for memristors in hardware security applications for the era of the Internet of Things. Memristors can switch between high and low electrical-resistance states, but the switching behaviour can be unpredictable. Here, the authors harness this unpredictability to develop a memristor-based true random number generator that uses the stochastic delay time of threshold switching

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A novel true random number generator based on a stochastic diffusive memristor

Threshold Switching of Ag or Cu in Dielectrics: Materials, Mechanism, and Applications

We report a 12.5 Gb/s physical random number generator (RNG) that uses high-speed threshold detection of the spectrally-sliced incoherent light produced by a fiber amplifier. The system generates a large-amplitude, easily measured, fluctuating signal with bandwidth that is constrained only by the optical filter and electrical detector used. The underlying physical process (spontaneous emission) is inherently quantum mechanical in origin, and therefore cannot be described deterministically. Unlike competing optical RNG approaches that require photon counting electronics, chaotic laser cavities, or state-of-the-art analog-to-digital converters, the system employs only commonly available telecommunications-grade fiber optic components and can be scaled to higher speeds or multiplexed into parallel channels. The quality of the resulting random bitstream is verified using industry-standard statistical tests.

Fast physical random number generator using amplified spontaneous emission

This paper describes an all-digital PVT-variation tolerant true-random number generator (TRNG), fabricated in 45 nm high-k/metal-gate CMOS, targeted for on-die entropy generation in high-performance microprocessors. The TRNG harvests differential thermal-noise at the diffusion nodes of a pre-charged cross-coupled inverter pair to resolve out of metastability, generating one random bit/cycle. A self-calibrating 2-step tuning mechanism using coarse-grained configurable inverters and fine-grained programmable clock delay generators, along with an entropy-tracking feedback loop provide tolerance to 20% PVT variation-induced device mismatches, enabling lowest-reported energy-consumption of 2.9 pJ/bit with a dense layout occupying 4004 μm2, while achieving: (i) 2.4 Gbps random bit throughput, 7 mW total power consumption with 0.7 mW leakage power component, measured at 1.1 V, 50°C, (ii) random bitstreams that passes all NIST RNG tests with raw entropy/bit measured up to 0.9999999993, (iii) good distribution of 1's with 4-bit entropy of 3.97996 and high-entropy pattern probability of 0.066 (iv) wide operating supply voltage range with robust sub-threshold voltage performance of 14 Mbps, 5.6 μW, measured at 280 mV, 50°C, (v) 12 fine-grained high-entropy settings for the TRNG to dither in during steady-state operation, (vi) <;3% error while using an analytical ergodic Markov chain model for predicting pattern probabilities and (vii) 200x higher throughput and 9x higher energy-efficiency than previously reported implementations. Design modifications for robust operation in 22 nm high-volume manufacturing in the presence of 3σ process variations demonstrate scalability of the all-digital design to future technologies.

2.4 Gbps, 7 mW All-Digital PVT-Variation Tolerant True Random Number Generator for 45 nm CMOS High-Performance Microprocessors

The design of a high-speed IC random number source macro-cell, suitable for integration in a smart card microcontroller, is presented. The oscillator sampling technique is exploited and a jittered oscillator which features an amplified thermal noise source has been designed in order to increase the output throughput and the statistical quality of the generated bit sequences. The oscillator feedback loop acts as an offset compensation for the noise amplifier, thus solving one of the major issues in this kind of circuit. A numerical model for the proposed system has been developed which allows us to carry out an analytical expression for the transition probability between successive bits in the output stream. A prototype chip has been fabricated in a standard digital 0.18 /spl mu/m n-well CMOS process which features a 10 Mbps throughput and fulfills the NIST FIPS and correlation-based tests for randomness. The macro-cell area, excluding pads, is 0.0016 mm/sup 2/ (184 /spl mu/m /spl times/ 86 /spl mu/m) and a 2.3 mW power consumption has been measured.

A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC

The design of a high-speed integrated circuit random number source macro-cell, suitable to be integrated in a SmartCard microcontroller, is presented. The direct amplification of a thermal-noise source is exploited and an accurate and low-area offset zeroing system has been developed in order to increase the statistical quality of the output bit sequences. Moreover, an analytical model has been developed, allowing the estimation of the output bit correlation as a function of the main circuit parameters. Using a standard 0.18-/spl mu/m n-well CMOS process, a prototype has been fabricated and measured, obtaining a random behavior for an output data rate up to 40 Mb/s. The macro-cell area, excluding pads, is 0.025 mm/sup 2/ (220 /spl mu/m/spl times/116 /spl mu/m) and its power consumption is about 3.6 mW when clocked at 10 MHz.

A high-speed IC random-number source for SmartCard microcontrollers

The design of a high speed IC random number source macro-cell, suitable to be integrated in a Smart Card microcontroller, is presented. The direct amplification of thermal noise is exploited and an accurate and low area demanding offset zeroing system has been developed in order to increase the statistical quality of the generated bit sequences. Using a 0.18 /spl mu/m n-well CMOS process, a prototype has been fabricated and measured, obtaining a random behavior for an output data rate up to 40 Mb/s.

L. Germani

Papers

A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC

A high-speed IC random-number source for SmartCard microcontrollers

A high speed truly IC random number source for smart card microcontrollers