CN110399626B - Thermal noise jitter estimation method of true random number generator based on ring oscillator - Google Patents
Thermal noise jitter estimation method of true random number generator based on ring oscillator Download PDFInfo
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Abstract
The invention discloses a method and a circuit for estimating thermal noise jitter of a true random number generator based on a ring oscillator. The method comprises the following steps: 1) counting the edges of the oscillation signals within a certain interval to serve as a statistical sample; 2) calculating the average absolute difference of the samples; 3) multiplied by the mean absolute difference of the samples
The result of multiplying again by the average half period of the oscillating signal as the estimate of thermal noise jitter 4) in the count interval times the average absolute difference of the samples
Then, the result of multiplying the arithmetic square root of the mean ratio of the sampling interval and the counting interval is multiplied, and finally, the result of multiplying the average half period of the oscillation signal is multiplied as the estimated value of the thermal noise jitter in the sampling interval. The method carries out estimation based on the average absolute difference of the samples, and multiplication is not needed in the calculation process of the average absolute difference. The invention can accurately and quickly estimate the thermal noise jitter of the true random number generator based on the ring oscillator, and can be used for evaluating the true randomness of the true random number generator and online detecting the fault attack aiming at the true random number generator.
Description
Technical Field
The invention relates to a thermal noise jitter estimation method and a thermal noise jitter estimation circuit of a true random number generator based on a ring oscillator, which can be applied to the fields of randomness evaluation of the true random number generator, online detection aiming at fault attack of the true random number generator and the like.
Background
Ring oscillator based true random number generators (RO-TRNGs) are widely used in secure hardware such as secure smart cards, embedded cryptographic devices, cryptographic engines, etc. to provide random, unpredictable true random numbers for cryptographic algorithms or protocols. The structure is simple, and the logic circuit is easy to realize. One possible implementation of RO-TRNG is: oscillation signal S1 of frequency F generated by ring oscillator 1 composed of odd number of invertersf(ii) a Oscillation signal S2 generated by identically implemented, frequency-consistent ring oscillator 2fAfter frequency division by K times, the frequency is obtained
For sampled signals Ss，SsEach cycle pair S1 through D flip-flopfSampling is performed once and the sampling result is output as a random number, as shown in fig. 1.
The random behavior of the signal in the RO-TRNG can be characterized by a random model, the oscillator 1 signal S1 under the influence of uncorrelated noise (mainly thermal noise) and correlated noise (mainly flicker noise at low frequencies) in the logic circuitfTurn-over time interval TfSampling signal SsSampling time interval T ofsRandom variation, resulting in random variation of the sampling result within {0,1}, so the sampling result can be a true random number of its output. T isfMean value of (a)f、TsMean value of 2K mufCan be respectively defined as S1fAverage half period of (1) and (S)sAverage period of (1) thus
Can be measured by the frequency of the oscillation signal; t isfAnd TsStandard deviation of (a)f、σsCan be defined as S1fHalf cycle jitter and S ofsThe period of (2) is jittered. Due to two signals SsAnd S1fIs relative, S1 can be calculatedfEquivalently regarded as a steady signal, i.e. Tf＝μfAnd then S issConsidered to have an equivalent period jitter σ and referred to as the total jitter in the sampling interval. The jitter σ includes a thermal noise jitter σthAnd flicker noise jitter σflAnd both are independent. This equivalent stochastic model is shown in figure 2.
The randomness evaluation theory for RO-TRNG is that the thermal noise jitter sigma in the jitter sigma within a sampling intervalthAnd calculating the output entropy rate of the RO-TRNG as a parameter, and quantitatively measuring the true randomness of the RO-TRNG. In addition, the online test circuit can also monitor the sigmathAnd detecting whether fault attack interferes with the RO-TRNG. It is therefore necessary to dither the thermal noise σ in the total ditherthA quick and accurate assessment is performed.
Current jitter estimation methods for RO-TRNG mainly include estimation methods based on edge count standard deviation approximation as proposed by Yuan Ma et al. The method calculates the standard deviation of the oscillator 1 signal edge count over a time interval and approximates the jitter over that time interval. Specifically, the oscillator 2 signal S2fObtaining a counting signal after frequency division by M times, and taking each period of the counting signal as a counting interval TcAt TcIntrinsic pair oscillator 1 signal S1fThe rising edge and the falling edge of the counting result X are counted, and the sample standard deviation sigma of the counting result X is calculatedXBased on this method, σ can be expressedXμfAs a pair count interval TcInner total jitter sigmac(in the Equivalence stochastic model, σcCan be regarded as TcStandard deviation of) and then by σcApproximate total jitter within a sampling interval
There are three major problems with this approach: one, because X is the count interval ratio
The quantization value of 1 is the quantization step, so σ isXμfAs σcThe estimation value of (M) necessarily introduces quantization error, and in order to reduce the estimation relative error caused by the quantization error, the method needs to adopt larger counting interval, namely M takes a larger value; when M is a large value, low-frequency counting is adopted, so that even if the estimation relative error caused by quantization error is reduced, due to low-frequency counting, a large amount of low-frequency flicker noise jitter components are contained in the estimated total jitter, and therefore, the method cannot accurately estimate the thermal noise jitter; thirdly, calculating the sample standard deviation sigma of X in the estimation processXIn time, a large amount of square operations are needed, so the method has high consumption of computing resources and low computing efficiency. In 2014, the jitter estimation method based on the monte-malalo method proposed by Viktor Fischer et al was also used to estimate the overall jitter. To estimate the thermal noise jitter, an alternative approach is toThe thermal noise jitter is separated, for example, Haddad et al firstly estimates the total jitter by an estimation method based on edge counting standard deviation approximation, obtains the proportion of the thermal noise jitter by quadratic fitting, and further separates the thermal noise jitter, but the quadratic fitting required by the method is complex in calculation and is not suitable for circuit implementation.
Disclosure of Invention
Aiming at RO-TRNG, aiming at overcoming the problems that the jitter estimation method based on the edge counting standard deviation approximation cannot directly estimate the thermal noise jitter due to the fact that quantization errors are introduced to cause inaccurate estimation and the estimated total jitter contains a large amount of flicker noise jitter components, and simultaneously reducing the calculation resources required by the jitter estimation method when a circuit is implemented.
The invention also estimates the thermal noise jitter of the RO-TRNG by using the sample of the edge counting X, and the difference is that the invention approximately estimates the thermal noise jitter of the RO-TRNG based on the average absolute difference of X, reduces the estimation error caused by quantization and other factors, and reduces the flicker noise jitter component in the jitter estimation result to a negligible degree by high-frequency counting. The present invention can therefore achieve a direct approximate estimate of RO-TRNG thermal noise jitter. In addition, compared with standard deviation calculation, the mean absolute difference calculation process does not need square operation, so that the calculation amount in the estimation process is greatly reduced, the efficiency of the estimation method is improved, and the circuit implementation cost is also reduced. The specific principle is as follows:
1) flicker noise jitter and thermal noise jitter are independent of each other
At a sampling interval TsInner, total jitter σ and thermal noise jitter σthFlicker noise jitter σflThe relationship of (1) is:
σ2＝(σth)2+(σfl)2 (1)
at counting interval TcInner, total jitter σcAnd thermal noise jitter
Flicker noise dithering
The relationship of (1) is:
2) at high frequency counts, flicker noise jitter is negligible and the overall jitter can be approximated as thermal noise jitter
by setting different M, the total jitter sigma is measured multiple timescAnd then the constants a and b related to the equipment can be obtained through offline quadratic fitting operation.
In which the primary linear term is the proportion of thermal noise, i.e.
a, b are constants associated with the device, and it can be seen that when M decreases, the count interval T iscWhen reduced, the proportion of thermal noise (i.e. heat noise)
) And gradually increases. This means that with high frequency counting, the flicker noise jitter component of the overall jitter can be reduced to a negligible component. If it is estimated to be trueFor example, when the thermal noise jitter ratio is set to be at least r, i.e. when the thermal noise jitter ratio is set to be at least r
When the flicker noise jitter component can be ignored, it is required
(the ratio threshold r is a settable constant, and it is considered that when the thermal noise ratio is larger than r, the flicker noise jitter component in the total jitter can be ignored). Thus, at high frequency counts, as long as M is satisfied
I.e. the total jitter sigma in the counting intervalcApproximated as thermal noise jitter
I.e. at high frequency count, may have
3) Thermal noise jitter accumulation effect
Thermal noise is uncorrelated noise, so the square of thermal noise jitter is linearly accumulated along with the increase of time intervals, and the mean ratio of sampling intervals to counting intervals is
(the sampling signal is obtained by dividing the frequency of the oscillator 2 signal in fig. 1 by K times, and the counting signal is obtained by dividing the frequency of the oscillator 2 signal by M times), so the thermal noise jitter in the sampling interval and the thermal noise jitter in the counting interval have the following relationship:
4) at high frequency count, count interval TcApproximate distribution in an equivalent stochastic model
At high frequency count, thermal noise jitter accounts forDominance, therefore, in the equivalent stochastic model, TcApproximately obeying a normal distribution
5) At high frequency counts, the average absolute difference of edge counts can be used to accurately approximate thermal noise jitter within a count interval
Let the average absolute difference of edge count X mad (X) ═ E (| X-E (X) |), where E (·) is desired. By high frequency counting, based on 2), when M is small enough to satisfy the set
The flicker noise jitter component is negligible. At this time, the counting interval T under the equivalent model for different McAre all approximately normally distributed, i.e. have
For TcAnalysis of the standard deviation of (2) and the mean absolute difference of the edge counts X shows that for all ranges of M and TcThe method can be approximated:
the error of this approximate relationship is extremely small, and as shown in fig. 6, M is an abscissa, and the relative error of the approximate relationship shown in the formula (7) is an ordinate. Therefore, under high-frequency counting, the thermal noise jitter in the counting interval can be directly approximately estimated based on the average absolute difference of edge counting, and the estimation relative error can be ensured to be extremely small.
6) Estimating thermal noise jitter in a count interval using the average absolute difference of edge count samples at high frequency counts
As shown in the formula (7), the high frequency counting can be based on the mad (X) pair
For direct approximation, let the sample of edge count X be X1,…,xNN is the sample size and the sample mean is
Let the mean absolute difference of the samples be madXThen there is
Thus, thermal noise jitter in the count interval
The estimation of (d) is:
7) estimation of thermal noise jitter in sampling intervals at high frequency counts
According to the formulas (6) and (9), the method uses the estimation of the thermal noise jitter in the sampling interval by the edge counting samples as follows:
based on the above principle, the estimation steps of the invention for the thermal noise jitter are as follows:
1) for signal S2fPerforming M times of frequency division, wherein M satisfies the preset condition
Obtaining a count signal Sc；
2) Obtaining a series of samples x of the oscillator 1 signal edge count within a count interval with an edge counter1,…,xN；
3) Calculating the mean absolute difference mad of the samplesX；
4) Calculating an estimate of thermal noise jitter within a sampling interval
According to the thermal noise jitter estimation method, the invention designs the circuit system capable of continuously estimating the thermal noise jitter on the chip. The circuit system inputs two oscillator signals and estimates the thermal jitter based on equation (10)
As an output, it includes: the device comprises a frequency division module, an edge counting module, a mean value estimation module, an average absolute difference estimation module and a thermal noise jitter calculation module.
1) A frequency division module: the input terminal is connected with the oscillator 2, and the signal S2 generated by the oscillator 2 is inputfDividing the frequency by M times with a set integer M to output a count signal Sc。
2) An edge counting module: two input terminals, the first input terminal is connected with the oscillator 1, the second input terminal is connected with the output terminal of the frequency dividing module, and the signal S1 of the oscillator 1 is usedfAnd a count signal ScFor input, with ScIs a counting interval, outputs N pairs of counting intervals S1fSample x of the rising and falling edge count results1,…,xN。
3) The mean value estimation module: the input end is connected with the output end of the edge counting module by x1,…,xNFor input, the module uses the buffered last estimated mean value according to the stability of the mean value so as not to wait for the calculation of the mean value of the current estimated sample
Providing the output for other modules of the estimation to use, and obtaining the sample mean value of the estimation
Caching and reserving for next estimation;
4) a mean absolute difference estimation module: two input ends, the first input end is connected with the output end of the mean value estimation module, and the second input end is connected with the edge meterNumber the output end of the module to
And x1,…,xNFor input, the mean absolute difference of the counted samples is calculated according to the formula (8)
And as an output.
5) A thermal noise jitter calculation module: the input end is connected with the output end of the mean absolute difference estimation module and is used for madXFor input, an estimate of thermal noise jitter within a sampling interval is calculated according to equation (10)
And takes it as the output of the entire circuitry.
The method has the advantages that when the thermal noise jitter is estimated by using the quantized sample (namely the oscillation signal edge counting result of the RO-TRNG in a certain counting interval) which is directly measurable by a simple and digital circuit:
1) estimation errors such as quantization errors and the like in the estimation process can be reduced;
2) by utilizing the approximate estimation of average absolute difference, the low-frequency flicker noise jitter component in the jitter can be reduced to the negligible degree under the high-frequency counting, so that the approximate estimation can be directly carried out on the thermal noise jitter;
3) the square calculation is not needed in the calculation process of the mean absolute difference, the calculation is simple, and the efficiency is high;
4) the method is easy to realize by a digital circuit, consumes less computing resources, is suitable for online and offline evaluation of the RO-TRNG, and can be used for evaluating the true randomness of the true random number generator and online detection of fault attack aiming at the true random number generator.
Drawings
FIG. 1 is a schematic diagram of a RO-TRNG;
FIG. 2 is an RO-TRNG equivalent stochastic model;
FIG. 3 is a RO-TRNG thermal noise jitter estimation step of the present invention;
FIG. 4 is a circuit diagram of a thermal noise jitter estimation system of the present invention;
fig. 5 (a) to (e) are circuit diagrams of respective blocks of the thermal noise jitter estimation circuit system;
FIG. 6 is a diagram of the relative error in estimating thermal noise jitter according to the present invention;
fig. 7(a) and (b) are comparison graphs of absolute errors and relative errors in the estimation of the thermal noise jitter according to the present invention and the conventional estimation method based on edge count standard deviation approximation.
Detailed Description
An embodiment of the method and circuit for RO-TRNG thermal noise jitter estimation according to the present invention is described below with reference to the drawings and embodiments of the method and circuit, but is not limited thereto.
In the embodiment, to explain the implementation process and beneficial effects of the method in detail, the method and the existing estimation method based on edge counting standard deviation approximation are used to estimate the equivalent thermal noise jitter in a series of counting intervals through the sample of X, and the accuracy of the two is compared. Firstly, setting the average half period mu of the oscillation signalf1 is ═ 1; when M is less than or equal to 50, the high-frequency counting requirement is met, and the flicker noise component can be ignored. Specifically, the frequency division multiple is set to be M ∈ {5,6, …,49,50 }; corresponding to a series of counting intervals T in the equivalent random modelcThe distribution of (A) is as follows:
each counting interval TcThe inner ideal thermal noise jitter magnitude is:
based on each TcAll generate 10000 edge count samples x1,…,x10000And counting the interval T according to the steps of FIG. 3cEstimate internal thermal noise jitter by x1,…,x10000And first calculating the average absolute difference of a corresponding series of samples according to the formula (8): madXE {0.1266, 0.1379, 0.1469, …, 0.4040 }. The method is obtained for the series according to the formula (9)The estimate of the thermal noise jitter over the counting interval is:
the corresponding series of estimated absolute errors is:
as shown by the broken line 1 in fig. 7 (a). The corresponding series of estimated relative errors are:
as shown by the broken line 1 in fig. 7 (b).
If the method is based on the existing jitter estimation method based on the approximation of the edge counting standard deviation, the sample standard deviation based on X is matched with the TcEstimating the thermal noise jitter, and obtaining a series of jitter estimation values as follows:
the corresponding series of estimated absolute errors is:
as shown by fold line 2 in fig. 7 (a). The corresponding series of estimated relative errors are:
as shown by fold line 2 in fig. 7 (b).
The high accuracy of the method for estimating the thermal noise jitter can be seen from the numerical value, the graph (a) and the graph (b) of fig. 7.
On the other hand, in the embodiment, the method does not need to use multiplication for calculating the average absolute difference of the samples, and the estimation method based on the edge count standard deviation approximation generally needs 10000 times of multiplication corresponding to the sample size when calculating the standard deviation of the samples. Therefore, the method has high calculation efficiency and low resource consumption.
An implementation of the various blocks of the thermal noise jitter estimation circuitry of the present invention is given by fig. 4 and 5, in which:
the circuit system shown in fig. 4 includes a frequency division module, an edge counting module, a mean value estimation module, an average absolute difference estimation module, and a thermal noise jitter calculation module;
the frequency division module shown in fig. 5 (a) is implemented by using an integer frequency divider, and inputs a signal of the oscillator 2, and after frequency division by M times, a counting signal with a series of counting intervals is obtained;
the edge counting module shown in fig. 5 (b) is implemented by an edge counter (edge _ counter), which is connected to the oscillator 1 and the edge counting module, inputs the oscillator 1 signal and the counting signal, is controlled by the enable signal (en), and outputs a counting sample x after counting the edges of the oscillator 1 signal within the counting interval1,…,xN10000 samples are obtained after 10000 times of counting;
the mean estimation block shown in (c) of FIG. 5 is connected to the edge counting block by x1,…,xNFor inputting, the input is controlled by a clock signal (clk) and an enable signal (en), the input samples are accumulated in each clock period, 10000 times of accumulation are completed, and the accumulated result is divided by the sample amount N to 10000, so that a sample average value is obtained
Buffered in a buffer 2, the buffer 1 stores the mean value of the last estimated sample
The output state is kept until the buffer 1 is released after the estimation is finished, and the sample mean value stored in the buffer 2 is transferred to the buffer 1;
the mean absolute difference estimation block shown in (d) of FIG. 5 is connected to the edge count block and the mean estimation block by x1,…,xNAnd
for input, the sample average absolute difference mad is obtained and output after a series of operations in fig. 5(d) are performed controlled by a clock signal (clk) and an enable signal (en)X。
The thermal noise jitter calculation module shown in (e) of FIG. 5, connected with the mean absolute difference estimateModule by madXThe input is controlled by a clock signal (clk) and an enable signal (en), and a series of operations in fig. 5(e) are performed to obtain an estimated thermal noise jitter value in a sampling interval
And output.
The estimation of the RO-TRNG thermal noise jitter can be accurately and efficiently completed by the circuit.
The invention counts the sample average absolute difference mad of X by the edgeXWhen estimating RO-TRNG thermal noise jitter, in other embodiments, other approximations may be used
Numerical substitution of
As a constant factor; the proportional threshold r can be set according to requirements; the division multiple M is selectable to meet the setting
Optionally, M is not satisfied
The method and circuit may still be used as a coarse but fast jitter estimation method; the edge count sample size N may be more or less than 10000.
The above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person skilled in the art can modify the technical solution of the present invention or substitute the same without departing from the spirit and scope of the present invention, and the scope of the present invention should be determined by the claims.
Claims (5)
1. A method for estimating the thermal noise jitter of a ring oscillator based true random number generator, the ring oscillator based true random number generator comprising a ring oscillator 1 and a ring oscillator 2, the method comprising the steps of:
1) obtaining a series of samples of an edge count of a signal generated by the ring oscillator 1 over a count interval by an edge counter;
2) calculating an average absolute difference of a series of samples of the edge count;
3) under the high-frequency counting of the ring oscillator 2, calculating a thermal noise jitter estimation value in a counting interval according to the average absolute difference;
4) calculating a thermal noise jitter estimation value in a sampling interval according to the thermal noise jitter estimation value in the counting interval;
let a series of samples of edge count X be X1,…,xNThe average absolute difference is calculated using the following formula:
wherein x isiFor the (i) th sample,
is the sample mean;
the thermal noise jitter estimation value in the counting interval is calculated by adopting the following formula:
wherein, mufFor the average half period of the oscillation signal, derived from the oscillation signal frequency F,
the thermal noise jitter estimation value in the sampling interval is calculated by adopting the following formula:
wherein, the sampling signal is obtained by dividing the frequency of the ring oscillator 2 by K times, the counting signal is obtained by dividing the frequency of the oscillator 2 by M times, and the average ratio of the sampling interval to the counting interval is
2. The method of claim 1, wherein other approximations are used
Numerical substitution of
As a constant factor.
3. The method of claim 1, wherein M satisfies
To achieve accurate and fast estimation of the thermal noise jitter, where a and b are constants related to the device, and r is a threshold of the proportion of the thermal noise jitter.
4. The method of claim 1, wherein the M-choice is not satisfied
Where a, b are constants associated with the device and r is a threshold for the proportion of thermal noise jitter.
5. A ring oscillator based true random number generator thermal noise jitter estimation circuit employing the method of claim 1, comprising:
a frequency division module: the input end is connected with the oscillator 2, the signal of the oscillator 2 is input, M times of frequency division is carried out on the signal by a set integer M, and a counting signal is output;
an edge counting module: comprises two input ends, the first input end is connected with the oscillator 1, the second input end is connected with the output end of the frequency division module, the oscillator 1 signal and the counting signal are input, and the counting sample x of the edge of the oscillator 1 signal in N counting intervals is output1,…,xN；
The mean value estimation module: the input end is connected with the output end of the edge counting module and used for sampling x1,…,xNAs input, the mean value of the last estimated sample buffered is used
Providing the output for other modules of the estimation to use, and obtaining the sample mean value of the estimation
Caching and reserving for next estimation;
a mean absolute difference estimation module: comprises two input ends, the first input end is connected with the output end of the mean value estimation module, the second input end is connected with the output end of the counting module, so as to
And x1,…,xNFor input, the average absolute difference mad of the output samplesX；
A thermal noise jitter calculation module: the input end is connected with the output end of the mean absolute difference estimation module and is used for madXFor input, an estimate of thermal noise jitter within a sampling interval is calculated
And takes it as the output of the entire circuitry.
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