CN106066785A - A kind of real random number generator accumulated jitter method of estimation based on ring oscillator - Google Patents

Abstract

The present invention discloses a kind of real random number generator accumulated jitter method of estimation based on ring oscillator and circuit.The method include the steps that 1) count as statistical sample using oscillator signal edge in the sampling interval；2) sample variance is calculated；3) whether judgment sample variance is more than d ∈ [1/12,0.2098], if sample variance is more than d ∈ [1/12,0.2098], accumulated jitter estimated value is the square root that counts after sample variance subtracts 1/12, and otherwise estimated value is sample standard deviation.This method utilizes the frequency distribution of sample to calculate sample variance, cuts down explicit formula and calculates a large amount of multiplyings needed for sample variance；The estimating circuit of design is with sampled signal, oscillator signal for input, and the estimated value of accumulated jitter square is output, including edge counting module, Estimation of Mean module, sample space generation module, sample Frequency statistics module, accumulated jitter estimation module.The present invention can estimate real random number generator accumulated jitter based on ring oscillator accurately and efficiently, in conjunction with entropy Assessment theory, can assess its truly random property.

Description

A kind of real random number generator accumulated jitter method of estimation based on ring oscillator

Technical field

The present invention relates to a kind of real random number generator based on ring oscillator (RO-based TRNG) accumulated jitter Method of estimation and circuit, can be applicable to the truly random property evaluation areas of real random number generator.

Background technology

RO-based TRNG provide true random number for cryptographic system, because it has simple in construction, is suitable for digital circuit Feature and be widely used in various secure hardware device.RO-based TRNG is by the sampled signal pair of fixed frequency The quick oscillation signal with shake that ring oscillator produces is sampled, and sampled result exports as random data, such as Fig. 1 Shown in Fig. 2.The available truly random property of RO-based TRNG determines the safety of its output data.According to up-to-date RO- BasedTRNG entropy Assessment theory, the accumulated jitter in the sampling interval, it is in the nature sampled signal cycle and oscillator signal half period ratio The standard deviation of T, which determines RO-based TRNG truly random property quality degree.Accordingly, it would be desirable to RO-based TRNG is accumulated Shake has method of estimation accurately, and method of estimation need to possess efficient circuit implementing scheme, thus completes the truly random of TRNG Property assessment.

Owing to digital circuit cannot accurately measure T, therefore accumulated jitter can not be estimated by the sample of T.At present, it is applied to The main method that RO-based TRNG accumulated jitter is estimated is the quantized value with T, oscillator signal edge in the namely sampling interval CountingSample be statistical sample, by the sample standard deviation of X estimating directly as RO-based TRNG accumulated jitter Evaluation.But, when accumulated jitter being estimated by the sample of X, necessarily introduce quantization error, therefore, straight for the sample standard deviation of X Connect and be inaccurate as accumulated jitter estimated value, the too high assessment of property truly random to TRNG can be caused.

2014, Viktor Fischer et al., based on Meng Temaluo method, utilized TRNG output bit sequence to build new Statistical sample, using the standard deviation of new samples as the estimation to accumulated jitter, give estimating with accumulated jitter square simultaneously Evaluation is output, comprises statistical sample and builds module, the circuit design of sample variance computing module.Although but this method Claim the estimation difference level that can reach less than 5%, but the construction method of statistical sample and structure circuit are complex, and sample This variance computational methods and counting circuit have employed formula of variance and directly calculate, and required multiplying amount is suitable with sample size, sample This amount typically requires and reaches 10000, and therefore the method assessment is inefficient.

RO-based TRNG accumulated jitter is estimated by the present invention by the sample of edge counting X, estimates standard improving Really while property, devise accumulated jitter estimating circuit on efficient sheet.

Summary of the invention

When edge be counted as RO-based TRNG accumulated jitter sample estimates in order to overcome, introduce quantization error and lead Cause the inaccurate problem estimated, reduce on accumulated jitter method of estimation sheet simultaneously and realize higher operand.The invention provides A kind of method that accumulated jitter is accurately made estimation, the method can improve the computing effect realizing algorithm for estimating on sheet simultaneously Rate, furthermore present the design of estimating circuit system.

The present invention estimates RO-based TRNG accumulated jitter with the sample of edge counting X equally, general based on quantization error Rate is distributed, and determines the variance of X and the relation of the variance of T (sampled signal cycle and oscillator signal half period ratio), and then revises tired In long-pending shake estimation procedure, introduce the accumulated jitter estimation difference that quantization error causes., calculate in the sample variance of X meanwhile, Calculate sample variance by the sample frequency distribution of statistics X, reduce formula of variance and directly calculate required multiplying amount.Tool The estimation principle of body is as follows:

1) quantization error approximation probability distribution:

Accounting for main noise in digital circuit is Gauss noise like, and T under its influence, approximates Gaussian distributed: T～N (μ,μ·σ²)；

Quantization error F=T-X, at Var (X) ＞ d, during d ∈ [1/12,0.2098], its approximation is obeyed [0,1] and is the most uniformly divided Cloth F～U (0,1).

2) approximation relation of the variance of the variance of X and T

During Var (X)≤d, the variance of X and the variance relation of T:

Var(T)≈Var(X) (1)

During Var (X) ＞ d, the variance of modified chi and the relation of the variance of T:

Var (X)=Var (E (X | T))+E (Var (X | T)) (2)

Wherein, E () represents the expectation of stochastic variable.

Section 1 on the right of equation, when T regards as a stochastic process, has

E (X | T)=T-E (F) ≈ T-1/2 (3)

Var (E (X | T)) ≈ Var (T-1/2)=Var (T) (4)

On the right of equation, Section 2 has

$\begin{array}{c}Var\left(X\right|T)=E\left(X^2\right|T)-E^2\left(X\right|T)\\ =\underset{N\→\mathrm{\∞}}{\lim }({\left(t_1-f_1\right)}^2+{\left(t_2-f_2\right)}^2+\mathrm{...}+{\left(t_N-f_N\right)}^2)/N\end{array}$

$\begin{array}{c}-\underset{N\→\mathrm{\∞}}{\lim }{(t_1-f_1+t_2-f_2+\mathrm{...}+t_N-f_N)}^2/N^2\\ =\underset{N\→\mathrm{\∞}}{\lim }(f_1^2+f_2^2+\mathrm{...}+f_N^2)/N-\underset{N\→\mathrm{\∞}}{\lim }{(f_1+f_2+\mathrm{...}+f_N)}^2/N^2\\ =E\left(F^2\right)-E^2\left(F\right)\\ =Var\left(F\right)\≈1/12\end{array}---\left(5\right)$

Wherein, t₁,t₂,…,t_NRepresent a series of samples of T, f₁,f₂,…,f_NRepresent a series of samples of F.

When obtaining Var (X) ＞ d according to (2) (4) (5), the variance of X and the variance relation of T:

Var(X)≈Var(T)+1/12 (6)

3) accumulated jitter and the variance approximation relation of X

The standard deviation being in the nature T of accumulated jitter, can be such as lower aprons, wherein J by (1) (6)_CExpression accumulated jitter:

$J_C=\sqrt{Var\left(T\right)}\≈\left\{\begin{array}{ccc}\sqrt{Var\left(X\right)},& if& Var\left(X\right)\≤d\\ \sqrt{Var\left(X\right)-1/12},& if& Var\left(X\right)>d\end{array}\right.---\left(7\right)$

4) by sample variance s of X²Estimate accumulated jitter and accumulated jitter square

${\hat{J}}_C=\sqrt{s^2}\≈\left\{\begin{array}{ccc}\sqrt{s^2},& if& s^2\≤d\\ \sqrt{s^2-1/12},& if& s^2>d\end{array}\right.---\left(8\right)$

${{\hat{J}}_C}^2=\left\{\begin{array}{ccc}{s}^2,& if& s^2\≤d\\ s^2-1/12,& if& s^2>d\end{array}\right.---\left(9\right)$

5) scope of quantile d

First, for making radical computing set up, d have to be larger than equal to 1/12.

Ideal value J for accumulated jitter_C, withDuring as estimated value, absolute error isWithDuring as estimated value, absolute error isAccording to the distribution of T, when Var (T) fixes, its The fractional part of mean μ is closer to 0.5, s²The least, s²E can be made time sufficiently small₂＞ E₁.Consider extreme case, if μ's is little Fractional part is 0.5, preferable accumulated jitter J_C∈ [0.001,0.7], according to the distribution of each T(U can be set to appoint Meaning positive integer) generate X sample, respectively withWithEstimate J_C, as in Fig. 8, (a) figure shows, s²During ＞ 0.2098 (retaining 4 position effective digitals), there is E₂＜ E₁；If the fractional part of μ is 0, estimate J in the same way_C, as in Fig. 8, (b) figure shows Show there is E all the time₂＜ E₁。

More than Zong He, the optional scope of d is [1/12,0.2098].

6) by sample X₁,…,X_NFrequency distribution calculate sample variance s in (8) formula, (9) formula²

The Estimation of Mean of X is:

$\stackrel{\‾}{X}=\underset{i=1}{\overset{N}{\Σ}}{X}_i/N---\left(10\right)$

The average of X Yu T, sample average approximation relation:

E (T)=E (X+F)=E (X)+E (F) ≈ E (X)+1/2 (11)

$\stackrel{\‾}{T}\≈\stackrel{\‾}{X}+1/2---\left(12\right)$

In the RO-based TRNG that the digital circuit of reality application is realized, typically there is J_C＜ 2, therefore the sample of X is empty Between be regarded asWherein N is sample size, each sample in sample space On this point counting sample, obtaining 2K sample frequency corresponding to sample point is Y₁,…Y_2K, by Y₁,…Y_2K、S、Calculate The sample variance of X is:

In sum, (8) formula is the method for estimation to accumulated jitter, and (13) formula is the method calculating sample variance.

Based on above estimation principle, the accumulated jitter method of estimation that the present invention proposes comprises the following steps:

1) with a series of sample X of oscillator signal edge counting in the edge counter acquisition sampling interval₁,…,X_N；

2) sample variance s is calculated by sample frequency distribution²；

3) quantile d ∈ [1/12,0.2098] is chosen, it is judged that s²Whether more than d, if more than d, the estimated value of accumulated jitter ForIf s²Less than or equal to d, the estimated value of accumulated jitter is

According to accumulated jitter method of estimation, the present invention designs the sustainable circuit system estimating accumulated jitter in slice System.Circuits System input oscillator signal, sampling clock, and based on (9) formula with the estimated value of accumulated jitter squareFor exporting, Comprising:

1) edge counting module: input oscillator signal, sampled signal, counted oscillator signal edge in the output sampling interval Sample X₁,…,X_N；

2) Estimation of Mean module: input connects the outfan of edge counting module, with X₁,…,X_NFor inputting, in order to not Waiting the calculating of this sample estimates average, this module estimates average with the last of cachingFor output, it is provided that give this Other modules of secondary estimation use, and this estimation obtains sample averageCache and remain estimated service life next time；

3) sample space generation module: input connects the outfan of Estimation of Mean module, withFor input, output Sample space

4) sample Frequency statistics module: two inputs, first input connects the outfan of edge counting module, and second defeated Enter end and connect the outfan of sample space generation module, with X₁,…,X_N、 For inputting, to X₁,…,X_NAt sample pointUpper counting, obtains sample frequency Y₁,…,Y_2KAs output；

5) accumulated jitter estimation module: three inputs, first input connects the outfan of Estimation of Mean module, the Two inputs connect the outfan of sample space generation module, and the 3rd input connects the output of sample Frequency statistics module End, with Y₁,…,Y_2KFor inputting, according to (9), (13) formula calculates the estimated value of accumulated jitter squareAnd as the output of whole Circuits System.

It is an advantage of the invention that and using simple, digital circuit direct measurable quantized samples (i.e. RO-based TRNG Sampling interval in oscillator signal edge counting) estimate accumulated jitter time:

1), after causing accumulated jitter estimation difference in view of quantized samples introducing quantization error, it is made that the most suitable repairing Just, can accurately accumulated jitter be estimated；

2) when calculating sample variance, calculate variance by the frequency distribution of sample, reduce formula of variance and calculate method institute The multiplying amount suitable with sample size needed, improves operation efficiency；

3) method proposed is prone to digital circuit, it is adaptable to the truly random property assessment of RO-based TRNG.

Accompanying drawing explanation

Fig. 1 is RO-based TRNG structural representation；

Fig. 2 is that oscillator signal is sampled schematic diagram by RO-based TRNG sampled signal；

Fig. 3 is accumulated jitter method of estimation step；

Fig. 4 is sample variance computational methods step；

Fig. 5 is accumulated jitter estimating system circuit diagram；

In Fig. 6, (a)-(e) is accumulated jitter estimating circuit system modules circuit diagram；

(a) in Fig. 7, (b) be this method with existing without modification method to the estimated result of accumulated jitter and estimation difference The comparison diagram of level；

(a) in Fig. 8, (b) be respectively withWithEstimate accumulated jitter J_CTime, error E₁、E₂Magnitude relationship Schematic diagram, wherein the abscissa of (a) figure is J_C/ 0.001, the vertical coordinate on the left side is to estimate J_CTime absolute error value, the right vertical Coordinate is sample variance s²Value；B the abscissa of () figure is J_C/ 0.001, vertical coordinate is to estimate J_CTime absolute error value.

Detailed description of the invention

Below in conjunction with the accompanying drawings and this method and the embodiment of circuit, illustrate that the present invention is to RO-Based TRNG accumulated jitter A kind of implementation estimated and circuit implementations, but it is not limited to this.

In an embodiment, for describing implementation process and the beneficial effect of this method in detail, by the sample of X to a series of Accumulated jitter is done and is estimated, the ideal standard difference of the T that namely distributed constant is different is done and estimated.These a series of T are distributed as: { N (192.6,0.2647²), N (385.2,0.3744²), N (577.8,0.4585²), N (770.4,0.5294²), N (963, 0.5919²), N (1155.6,0.6484²), N (1155.6,0.6484²), N (1540.8,0.7488²), N (1733.4, 0.7942²), N (1926,0.8371²), N (2118.6,0.8780²), N (2311.2,0.9170²), corresponding preferable accumulation is trembled Move and be:

{0.2647,0.3744,0.4585,0.5294,0.5919,0.6484,0.7004,0.7488,0.7942, 0.8371,0.8780,0.9170}, as shown in Fig. 7 (a) middle polyline 1.

Each distribution produces quantized samples X of 10000 T₁,…,X₁₀₀₀₀, according to the step of Fig. 3 and Fig. 4, accumulation is trembled Move and make estimation, by X₁,…,X₁₀₀₀₀First calculate correspondence a series of sample averages:

A series of sample space is generated by sample average:

$\begin{array}{c}\{S:\{187+i|i=1,\mathrm{...},10\},S:\{380+i|i=1,\mathrm{...},10\},S:\{572+i|i=1,\mathrm{...},10\},\\ S:\{765+i|i=1,\mathrm{...},10\},S:\{958+i|i=1,\mathrm{...},10\},S:\{1150+i|i=1,\mathrm{...},10\},\\ S:\{1343+i|i=1,\mathrm{...},10\},S:\{1535+i|i=1,\mathrm{...},10\},S:\{1728+i|i=1,\mathrm{...},10\},\\ S:\{1920+i|i=1,\mathrm{...},10\},S:\{2113+i|i=1,\mathrm{...},10\},S:\{2306+i|i=1,\mathrm{...},10\left\}\right\}\end{array},$

The sample a series of frequency distribution on sample space are:

{{0,0,0,104,9266,630,0,0,0,0},{0,0,8,2944,6902,146,0,0,0,0},{0,0,0, 390,6317,3255,38,0,0,0},

{0,0,36,2180,6465,1308,11,0,0,0},{0,5,458,4556,4492,487,2,0,0,0},0,2, 74,1684,5548,2523,167,2,0,0},

{0,3,435,3405,4825,1278,54,0,0,0},{0,1,67,1349,4604,3424,540,15,0,0},

{0,15,387,2667,4653,2058,212,8,0,0},{0,2,90,1079,3842,3851,1046,90,0, 0},

{0,16,319,2149,4296,2713,479,28,0,0},{2,84,905,3141,3948,1692,217,11, 0,0}}, (13) formula being calculated a series of sample variance is:

{0.0706,0.2330,0.2932,0.3591,0.4432,0.5102,0.5826,0.6407,0.7232, 0.7854,0.8365,0.9277}, according to (8) formula, take quantile d=1/6, obtain this method to these a series of accumulated jitter Estimated value is:

{0.2657,0.3869,0.4580,0.5252,0.5999,0.6534,0.7066,0.7466,0.7999, 0.8379,0.8679,0.9189}, as shown in Fig. 7 (a) middle polyline 2.Corresponding a series of estimation relative erroies are:

0.3%, 3.3%, 0.1%, 0.8%, 1.4%, 0.8%, 0.9%, 0.3%, 0.7%, 0.1%, 1.1%, 0.2%}, as shown in Fig. 7 (b) broken line 1.

If by existing error free correction method of estimation, by the sample standard deviation of X directly as the estimated value of accumulated jitter, The a series of accumulated jitter obtained are estimated as:

{0.2657,0.4827,0.5415,0.5992,0.6657,0.7143,0.7633,0.8004,0.8504, 0.8862,0.9146,0.9632}, as shown in Fig. 7 (a) broken line 3.Corresponding a series of estimation relative erroies are:

0.3%, 28.9%, 18.1%, 13.2%, and 12.5%, 10.2,9.0%, 6.9%, 7.1%, 5.9%, 4.2%, 5.0%}, as shown in Fig. 7 (b) broken line 2.

No matter from (a) figure of numerical value or Fig. 7, (b) figure, it can be seen that the Gao Zhun that accumulated jitter is estimated by this method Really property.

On the other hand, in the sample variance of the present embodiment calculates, calculate variance by sample frequency distribution, only use 20 Secondary multiplying, formula directly calculates variance then needs 10000 multiplication that sample size is suitable, the high efficiency feature of this method Especially pronounced.

A kind of implementation of accumulated jitter estimating circuit system modules in the present invention is given by Fig. 5 and Fig. 6, Wherein:

In Fig. 6, the edge counting module shown in (a) figure uses edge counter (edge_counter) to realize, input vibration Signal and sampled signal, controlled by enabling signal (en), to output counting sample after oscillator signal edge counting in the sampling interval X₁,…,X_N, complete 10000 times to count to get 10000 samples；

Estimation of Mean module shown in (b) figure in Fig. 6, connects edge counting module, with X₁,…,X_NFor inputting, by clock Signal (clk), enable signal (en) control, and in each clock cycle, the sample to input does cumulative, after completing 10000 times to add up By accumulation result divided by sample size N=10000, obtain sample averageIt is cached to buffer2, buffer1 and stores the last time The sample average estimatedAnd holding output state, until this discharges buffer1, buffer2 internal memory after estimating to terminate The sample average of storage transfers to buffer1；

Sample space generation module shown in (c) figure in Fig. 6, connects Estimation of Mean module, withFor input, by time Clock signal, enable signal control, rightCarry out the sequence of operations shown in Fig. 6 (c), obtain and export comprising 10 samples The sample space of this point

In Fig. 6, the sample Frequency statistics module shown in (d) figure is realized by enumerator, connects edge counting module and sample is empty Between generation module, with X₁,…,X_NIt is input with S, by clock signal, enables signal control, to the sample inputted at each sample Do Frequency statistics on Dian, obtain and export frequency Y₁,…,Y₁₀；

Accumulated jitter estimation module shown in (e) figure in Fig. 6, connects Estimation of Mean module, sample space module, sample frequency Number statistical module, withS、Y₁,…,Y₁₀For input, clock and enable signal control, carry out institute in Fig. 6 (e) successively The sequence of operations shown, obtains sample variance s², then judge s²Whether more than 1/6, if more than 1/6, export s²-1/12 conduct The estimated value of accumulated jitter square, otherwise exports s²Estimated value as accumulated jitter square.Above circuit gets final product precise and high efficiency Complete the estimation to RO-based TRNG accumulated jitter.

The present invention is with sample variance s of edge counting X²Estimate accumulated jitter J_CTime, can belong to other in other embodiments Numerical value in [1/12,0.2098] substitutes 1/6 as quantile；S is calculated with the sample frequency distribution of X²Time, sample space S bag The sample point contained is not limited to 10, can increase the sample point that S comprises；Sample size N is more or less than 10000.

Above example is only limited in order to technical scheme to be described, the ordinary skill of this area Technical scheme can be modified or equivalent by personnel, without departing from the spirit and scope of the present invention, and this The protection domain of invention should be as the criterion with described in claims.

Claims (6)

1. a real random number generator accumulated jitter method of estimation based on ring oscillator, its step includes:

1) as statistical sample, a series of sample is obtained by edge counter with the sample of oscillator signal edge counting in the sampling interval This；

2) sample variance s is calculated by sample frequency distribution², as the statistic of accumulated jitter estimation；

3) quantile d ∈ [1/12,0.2098] is chosen, it is judged that s²Whether more than d, if more than d, then the estimated value of accumulated jitter isIf s²Less than or equal to d, then the estimated value of accumulated jitter is

2. the method for claim 1, it is characterised in that step 2) calculate sample variance s by sample frequency distribution²'s Method is: set sample average asSample space is Wherein N is sample size, and sample is counted by each sample point in sample space, obtains 2K sample corresponding to sample point This frequency is Y₁,…Y_2K, by Y₁,…Y_2K、S、The sample variance calculating X is:

3. the method for claim 1, it is characterised in that step 3) based on quantization error probability distribution, by accumulated jitter Estimated value is modified to:

4. the real random number generator accumulated jitter based on ring oscillator using method described in claim 1 estimates electricity Road, it is characterised in that including:

Edge counting module: input oscillator signal, sampled signal, counting sample in oscillator signal edge in the output sampling interval X₁,…,X_N；

Estimation of Mean module: input connects the outfan of edge counting module, with sample X₁,…,X_NFor inputting, with caching Last estimation averageFor output, it is provided that using to this other module estimated, this estimation obtains sample averageCache and remain estimated service life next time；

Sample space generation module: input connects Estimation of Mean module outfan, withFor input, export sample space S；

Sample Frequency statistics module: comprise two inputs, first input connects the outfan of edge counting module, and second Individual input connects the outfan of sample space generation module, with X₁,…,X_N, S for input, to X₁,…,X_NSample point is counted Number, obtains sample frequency as output；

Accumulated jitter estimation module: comprise three inputs, first input connects the outfan of Estimation of Mean module, and second Individual input connects the outfan of sample space generation module, and the 3rd input connects the output of sample Frequency statistics module End, withS, sample frequency are input, calculate the estimated value of accumulated jitter squareAnd as whole circuit system The output of system.

5. circuit as claimed in claim 4, it is characterised in that the sample space of described sample space generation module output is:

6. circuit as claimed in claim 5, it is characterised in that described accumulated jitter estimation module calculates sample side according to following formula Difference:

Then the estimated value of accumulated jitter square is calculated according to following formula

${{\hat{J}}_C}^2=\left\{\begin{array}{ccc}{s}^2,& if& s^2\≤d\\ s^2-1/12,& if& s^2>d\end{array}\right..$