On the assumption of mutual independence of jitter realizations in P-TRNG stochastic models

Haddad, Patrick; Téglia, Yannick; Bernard, Florent; Fischer, Viktor

doi:10.7873/date.2014.052

Cited by 16 publications

(29 citation statements)

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“…In particular, we want to obtain a number of oscillations close to 100. With such a number of oscillations, we can assume that their variation comes mainly from the thermal noise inside transistors and that the realizations of the counter values are independent as it was shown in [4]. Indeed, we observed that for a significantly smaller number of oscillations the accumulated entropy was insufficient and for a number of oscillations too high the jitter coming from the flicker noise could cause the dependence between subsequent output samples to be non-negligible.…”

Section: Implementation Resultsmentioning

confidence: 57%

“…Consequently, n(t) can be represented as a stationary Gaussian random process. 4 Let us now analyze variations in the width of the pulse transmitted over one inverter as explained earlier in this section, but now in the presence of noisy currents. Let us consider that at t = t ↑ , signal V in goes up from V GND to V CC , and we denote t a the time, at which the signal V out at the output of the inverter reaches (…”

Section: Modeling a Noisy Invertermentioning

confidence: 99%

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From Physical to Stochastic Modeling of a TERO-Based TRNG

et al. 2018

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Security in random number generation for cryptography is closely related to the entropy rate at the generator output. This rate has to be evaluated using an appropriate stochastic model. The stochastic model proposed in this paper is dedicated to the transition effect ring oscillator (TERO)-based true random number generator (TRNG) proposed by Varchola and Drutarovsky (in: Cryptographic hardware and embedded systems (CHES), 2010, Springer, 2010). The advantage and originality of this model are that it is derived from a physical model based on a detailed study and on the precise electrical description of the noisy physical phenomena that contribute to the generation of random numbers. We compare the proposed electrical description with data generated in two different technologies: TERO TRNG implementations in 40 and 28 nm CMOS ASICs. Our experimental results are in very good agreement with those obtained with both the physical model of TERO's noisy behavior and the stochastic model of the TERO TRNG, which we also confirmed using the AIS 31 test suites.

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Section: Implementation Resultsmentioning

confidence: 57%

Section: Modeling a Noisy Invertermentioning

confidence: 99%

From Physical to Stochastic Modeling of a TERO-Based TRNG

et al. 2018

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“…To compare the parameters of the proposed randomness monitoring process, we implemented tests based on counter differences and two other state-of-the-art tests (proposed in [HBFT14] and [FL14]) in the same device -Intel Cyclone V FPGA.…”

Section: Implementation Of the Variance Measurements In Hardware And mentioning

confidence: 99%

“…The circuitry corresponding to hardware implementation of the variance computation used by Haddad et al in [HBFT14] and for the one corresponding to Eq. (2) is depicted in Fig.…”

Section: Implementation Of the Variance Measurements In Hardware And mentioning

confidence: 99%

“…Evaluating the contribution of thermal and low frequency noises to the generated randomness is no simple task. In [HBFT14], Haddad et al computed the variance of the jitter for different accumulation times and then computed the jitter component originating from the thermal noise by curve fitting. This method has two disadvantages: 1) its precision depends to a great extent on the precision of the curve fitting algorithm; 2) it is not suitable for monitoring the jitter inside the device.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation and Monitoring of Free Running Oscillators Serving as Source of Randomness

Allini¹,

Skorski²,

Petura³

et al. 2018

TCHES

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In this paper, we evaluate clock signals generated in ring oscillators and self-timed rings and the way their jitter can be transformed into random numbers. We show that counting the periods of the jittery clock signal produces random numbers of significantly better quality than the methods in which the jittery signal is simply sampled (the case in almost all current methods). Moreover, we use the counter values to characterize and continuously monitor the source of randomness. However, instead of using the widely used statistical variance, we propose to use Allan variance to do so. There are two main advantages: Allan variance is insensitive to low frequency noises such as flicker noise that are known to be autocorrelated and significantly less circuitry is required for its computation than that used to compute commonly used variance. We also show that it is essential to use a differential principle of randomness extraction from the jitter based on the use of two identical oscillators to avoid autocorrelations originating from external and internal global jitter sources and that this fact is valid for both kinds of rings. Last but not least, we propose a method of statistical testing based on high order Markov model to show the reduced dependencies when the proposed randomness extraction is applied.

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Embedded electronic circuits for cryptography, hardware security and true random number generation: an overview

Acosta

Addabbo

Tena-Sánchez

2016

Circuit Theory & Apps

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We provide an overview of selected crypto-hardware devices, with a special reference to the lightweight electronic implementation of encryption/decryption schemes, hash functions, and true random number generators. In detail, we discuss the hardware implementation of the chief algorithms used in private-key cryptography, public-key cryptography, and hash functions, discussing some important security issues in electronic crypto-devices, related to side-channel attacks (SCAs), fault injection attacks, and the corresponding design countermeasures that can be taken. Finally, we present an overview about the hardware implementation of true random number generators, discussing the chief electronic sources of randomness and the types of post-processing techniques used to improve the statistical characteristics of the generated random sequences.A. J. ACOSTA, T. ADDABBO AND E. TENA-SÁNCHEZ resource consumption. This matter sets the point for the lightweight cryptography, that is, the subfield of cryptography aiming to provide solutions tailored for resource-constrained devices.According to Elsevier Scopus, the largest database of research peer-reviewed literature, since 2010, about 40k documents are returned if searching the keyword 'cryptography' [6]. A huge subset of these papers deals with conceptual, algorithmic, software, hardware solutions that may be taken into account in lightweight cryptography. In the face of such a vast literature, in this work, we provide a brief overview of selected crypto-hardware devices, with a special reference to the lightweight electronic implementation of encryption/decryption schemes, hash functions, and true random number generators (TRNGs).This paper is organized as in the following. In Section 2, we introduce some terminology and present an overview of the hardware implementation of the chief algorithms used in private-key cryptography, public-key cryptography (PKC), and hash functions. In Sections 3 and 4, we introduce some important security concerns about electronic crypto-devices, discussing SCAs, fault injection attacks, and the corresponding countermeasures that can be taken in the hardware design. Finally, Sections 5-8 are devised to provide an overview about the electronic implementation of TRNGs. In detail, in Sections 5 and 6, we discuss about security flaws, statistical defects, and predictability of TRNGs, presenting the chief sources of randomness used nowadays for their hardware implementation. In Sections 7 and 8, we discuss an overview of the different post-processing techniques aimed to improve the statistical characteristics of the generated random sequences and the evaluation methods used to assess the reliability of cryptographic TRNGs. Conclusion and References close the paper. CRYPTOGRAPHIC ALGORITHMSCryptographic algorithms aim to convert secret data into an unreadable code for non authorized persons, protecting secret information from theft or alteration and also enabling authentication. For better understanding, in the next sections, we define the following...

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On the assumption of mutual independence of jitter realizations in P-TRNG stochastic models

Cited by 16 publications

References 13 publications

From Physical to Stochastic Modeling of a TERO-Based TRNG

From Physical to Stochastic Modeling of a TERO-Based TRNG

Evaluation and Monitoring of Free Running Oscillators Serving as Source of Randomness

Embedded electronic circuits for cryptography, hardware security and true random number generation: an overview

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