A Rayleigh entropy estimation method for superlattice physical entropy source

Abstract

The present invention relates to a Rayleigh entropy estimation method for a superlattice physical entropy source, comprising the following steps: step 1, sampling and obtaining raw data in the form of a binary sequence from a physical entropy source of a superlattice device PUF to obtain an entropy source output; step 2, using Markov chain Monte Carlo sampling to obtain a sequence of length L from the entropy source output; step 3, estimating the Rayleigh entropy of the sampled sequence. The method involved in the present invention is different from the traditional simple and intuitive exploration of superlattices. The present invention adopts a cryptographic method to treat the superlattice device as a black box model to quantitatively evaluate its cryptographic security. The estimation of the Rayleigh entropy is of great significance to the parameter estimation of the random number post-processing algorithm and the understanding of its physical behavior characteristics.

Description

Technical Field

[0001] The invention relates to the fields of information security and cryptographic technology, and in particular to a Rayleigh entropy estimation method for a superlattice physical entropy source. Background Art

[0002] Random number generator (RNG) is a basic cryptographic security primitive used to generate keys, filler values, authentication, etc., and has been widely used in cryptographic systems. The security of RNG is the basis of many cryptographic algorithms, protocols, and even hardware attack countermeasures. In general, RNG is divided into two categories: deterministic (pseudo) random number generator (PRNG) and non-deterministic (true) random number generator (TRNG). PRNG uses a deterministic algorithm to generate random numbers, and its seed comes from physical random number technology. TRNG requires the use of external hardware to extract random numbers from physical phenomena instead of deterministic algorithms on computers, and the sequences generated by TRNG are statistically indistinguishable from uniform (called true random numbers). However, the direct output of the available physical entropy source is entropy-deficient, so post-processing of the physical entropy source is essential to generate full entropy sequences. This requirement is not only a provable security issue, but also an important practical issue, because low entropy may lead to attacks on real-world applications. Therefore, the necessity of entropy evaluation as the quality of the entropy source for TRNG randomness is self-evident.

[0003] The study of information points out that the amount of information depends on the degree of uncertainty of the message containing the information content. The greater the uncertainty of the information, the greater the amount of information sent, and the smaller the uncertainty of the information, the smaller the amount of information sent. In 1948, Shannon introduced the concept of entropy in statistical physics into information theory, and used entropy as a measure of the uncertainty of a random event or the amount of information. For cryptographic applications, a truly unpredictable random sequence with maximum entropy is required. There are many ways to measure entropy, including Shannon entropy, Rayleigh entropy, and minimum entropy. Rayleigh entropy is a necessary condition that has been proven to provide information-theoretic security extractors, so estimating Rayleigh entropy is crucial to the design of practical information systems.

[0004] Semiconductor superlattice (SSL) is a solid-state electronic device that is periodically grown from two semiconductor materials with matching lattices. Scholars from various countries have conducted research and exploration in two directions: the physical mechanism analysis of superlattice random oscillation phenomenon and the application of superlattice random numbers in the field of information security. This has opened a new chapter for the cross-integration of semiconductor superlattice and cryptography, and laid a good foundation for the research and development of superlattice cryptography. As a basic technology in the field of information security, superlattice cryptography has broad application prospects. At present, the application research of superlattice physical random number technology and superlattice key distribution technology has made many breakthroughs and reached the practical stage. However, there are still few studies on statistical tests and entropy estimation of superlattice physical entropy source black box models, especially in the application of random number generators. Rayleigh entropy is an important parameter in the post-processing design of physical random number generators. In addition, the estimation of Rayleigh entropy will further support the development of security detection and evaluation technology of superlattice devices, thereby promoting the vigorous development of superlattice cryptography. Summary of the invention

[0005] The Rayleigh entropy is estimated for the entropy source output of the superlattice physically unclonable functions (PUF), and the estimated entropy result provides the necessary entropy extraction parameters for the post-processing algorithm of the random number generator to extract a high-quality full entropy sequence. To achieve the above purpose, the present invention provides a Rayleigh entropy estimation method based on superlattice PUF, which uses a Markov Chain Monte Carlo sampling algorithm to simulate the sample distribution to calculate the Rayleigh entropy.

[0006] The technical solution of the present invention is: a method for estimating the Rayleigh entropy of a superlattice physical entropy source, comprising the following steps:

[0007] Step 1, sampling and obtaining raw data in the form of a binary sequence from a physical entropy source of a superlattice device PUF to obtain an entropy source output;

[0008] Step 2, using the entropy source output of Markov chain Monte Carlo sampling to obtain a sequence with a length of L;

[0009] Step 3: Calculate the Rayleigh entropy of the sequence.

[0010] Beneficial effects:

[0011] Many traditional cryptographic algorithms, protocols and even hardware attack countermeasures ultimately depend on the security of the random number generator. The security in the random number generator is closely related to the entropy of the original output. Information provided by encryption applications with insufficient entropy will lead to poor security and be easily attacked by malicious attacks. The present invention estimates the Rayleigh entropy of the superlattice physical original entropy source output, which can provide compression rate parameters for the digital post-processing process to achieve the required security level.

[0012] Entropy estimation provides an important assessment of the security of SSL-TRNG. According to the entropy estimation results and the properties of the SSL entropy source, SSL-TRNG uses semiconductor superlattices as physical entropy sources to generate true random numbers, which can generate full entropy sequences at high speed to meet the application of one-time passwords. At the same time, SSL-TRNG can provide random bits for cryptographic primitives (such as symmetric cryptography, public key cryptography, certificates, signatures), which play an important role in blockchain and the Internet of Things to protect core applications and resist intrusion. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Superlattice physics entropy source framework;

[0014] Figure 2 Flowchart of the algorithm for Markov Chain Monte Carlo sampling of a sequence of length L;

[0015] Figure 3 Flowchart of Rayleigh entropy estimation for superlattice physical entropy sources. DETAILED DESCRIPTION

[0016] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the protection scope of the present invention.

[0017] According to one embodiment of the present invention, a Rayleigh entropy estimation method for a superlattice physical entropy source is proposed, such as Figure 3 As shown, the following steps are included:

[0018] Step 1, sampling and obtaining raw data in the form of a binary sequence from a physical entropy source of a superlattice device PUF to obtain an entropy source output;

[0019] The physical entropy source is the core part of the random number generator, providing uncertainty associated with the physical process. Due to high-frequency chaotic oscillation, the output bandwidth of the superlattice PUF can reach 500MHz, which is a new physical entropy source implementation scheme. The superlattice PUF mentioned in the present invention already includes an evaluation circuit for analog electrical signals. Through the digitization process of the analog-to-digital converter (ADC), the chaotic current signal output by the superlattice device can be sampled and quantized into an original random sequence, so that the original data in the form of a binary sequence can be sampled from the physical entropy source of the superlattice PUF.

[0020] The application architecture of superlattice physical entropy source is as follows Figure 1As shown, it is mainly divided into three steps: the superlattice physical entropy source obtains the raw data in the form of binary sequence through digital sampling;

[0021] The entropy of the raw data output of digital sampling is estimated and analyzed. The result of entropy estimation is mainly used for the parameter design of the extractor in the digital post-processing algorithm.

[0022] The digital post-processing process extracts the true random number sequence and collects a large amount of data for randomness detection and analysis. When the quality of the random number passes the relevant detection standards, the obtained random number is output through the output interface.

[0023] Step 2, using the entropy source output of Markov chain Monte Carlo sampling to obtain a sequence with a length of L;

[0024] According to an embodiment of the present invention, Figure 2 As shown in the figure, it is the algorithm flow chart of Markov chain Monte Carlo sampling length L sequence, including the following process:

[0025] (1) The sample sequence obtained from step 1, that is, the original random sequence, is defined as S = (s1, ..., s L );L is the sample size;

[0026] (2) The different arrays in the sample sequence S become the state space of the Markov chain. The frequency of each different number in the sample sequence S is counted to obtain the initial state P(X) of the Markov chain. t )=p(x t ); Xt represents the state space of the Markov chain; xt represents the set of different numbers obtained from the sample sequence;

[0027] (3) Count the frequency of each state in the sample sequence S transferring to itself and other states, and obtain the transfer matrix Q, i.e., the Markov chain transfer operator, Q i，j =q(x (t+1) =j|x (t) =i); the subscript (i, j) indicates that the current state i transfers to the next state j; x(t) indicates the state of the Markov chain at time t; the q function represents the probability of the state of the Markov chain at time t transferring to time t+1;

[0028] (4) For t=0, 1, 2, ..., the following process is repeated to obtain a sampling sequence S′=(s′1, ..., s′ L );

[0029] The state of the Markov chain at the tth moment is X t =x t , sample y~N(x|x t), y represents the recommended transition state at time t, and N(x|xt) represents the set of next states of state xt at time t;

[0030] Sample u~Uniform[0,1] from uniform distribution; u represents the value obtained by random sampling from uniform distribution; the uniform distribution function Uniform[a,b] represents that the distribution probability in intervals of the same length is equally likely, and is defined by two parameters a and b, which are the minimum and maximum values ​​on the number axis.

[0031] If u<A(x t , y) = p(y)q(x t |y) then accept the transfer x t →y, the next state X of the Markov chain t+1 =y; where A function represents the acceptance probability, which is calculated by the state xt of the Markov chain at time t and the proposed state y. Otherwise, the transfer is not accepted, that is, the next state X of the Markov chain t+1 =x t (The final result is the sampling sequence S′=(s′1,...,s′ L )).

[0032] Step 3: Estimation of Rayleigh entropy for the sampling sequence

[0033] Rayleigh entropy is also known as Rényi entropy, named after Alfréd Rényi, and is a generalization of Hartley entropy, Shannon entropy, collision entropy, and minimum entropy. RénYi entropy with parameter α, where α ≥ 0, α ≠ 1, is defined as:

[0034] Indicates the frequency of the X state.

[0035] The estimation of Rayleigh entropy is mainly the entropy value of α when α is not 0, 1, 2, ∞. The frequency of each state in the sampling sequence obtained in step 2 is counted, and the Rayleigh entropy is calculated according to the formula. α is taken, and the frequency pi of the n states in the sampling sequence obtained in step 2 is counted, and substituted into the above formula to calculate the Rayleigh entropy.

[0036] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, and it should be clear that the present invention is not limited to the scope of the specific embodiments, for those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A Rayleigh entropy estimation method for a superlattice physical entropy source, characterized in that: The steps include: Step 1, sampling and obtaining raw data in the form of a binary sequence from a physical entropy source of a superlattice device PUF to obtain an entropy source output; Step 2, using Markov chain Monte Carlo sampling to obtain the entropy source output to obtain a sequence with a length of L; Step 3, calculating the Rayleigh entropy for the sequence; The step 3 comprises: With parameters The Rayleigh entropy is , is defined as: Indicates the frequency of state X; The estimate of Rayleigh entropy is Not for hour The entropy value of the state in the sampling sequence obtained in step 2 is calculated according to the formula to obtain the Rayleigh entropy, and the value of α is calculated. The frequency p of the n states in the sampling sequence obtained in step 2 is calculated. i , substitute it into the above formula to calculate the Rayleigh entropy.

2. The Rayleigh entropy estimation method of a superlattice physical entropy source according to claim 1, characterized in that: The step 1 comprises the following steps: The superlattice device includes an evaluation circuit for analog electrical signals, and the chaotic current signal output by the superlattice device is sampled and quantized into an original random sequence through a digitization process of an analog-to-digital converter, specifically including: (1) The superlattice physical entropy source obtains raw data in the form of binary sequence through digital sampling; (2) Estimating and analyzing the entropy of the raw data output of digital sampling. The results of entropy estimation are mainly used for parameter design of the extractor in the digital post-processing algorithm. (3) The digital post-processing process extracts the true random number sequence and collects multiple data for randomness detection and analysis. When the random number quality passes the detection standard, the obtained random number is output through the output interface.

3. The Rayleigh entropy estimation method of a superlattice physical entropy source according to claim 1, characterized in that: The step 2 comprises: (1) The sample sequence obtained from step 1, that is, the original random sequence, is defined as ; L is the sample size; (2) Sample sequence The different arrays in the Markov chain become the state space, and the statistical sample sequence The frequencies of different numbers in get the initial state of the Markov chain ; Xt represents the state space of the Markov chain; xt represents the set of different numbers obtained from the sample sequence; (3) Statistical sample sequence The frequency of each state transferring to itself and other states, and the transfer matrix is ​​obtained That is, the Markov chain transfer operator, ; The subscript (i, j) indicates that the current state i is transferred to the next state j; x (t) represents the state of Markov at time t; the q function represents the probability of the state of the Markov chain at time t transferring to time t+1; (4) Yes Cycle sampling to obtain the sampling sequence .

4. The Rayleigh entropy estimation method of a superlattice physical entropy source according to claim 3, characterized in that: The step (4) comprises: a) No. The state of the Markov chain at this moment is ,sampling , y represents the recommended transition state at time t, N(x|xt) represents the set of next states of state xt at time t; b) Sampling from a uniform distribution ; u represents the value obtained by random sampling from a uniform distribution; the uniform distribution function Uniform[a,b] represents that the probability of distribution in intervals of the same length is equally likely, and is defined by two parameters a and b, which are the minimum and maximum values ​​on the number axis; c) If Accept transfer , that is, the next state of the Markov chain ; Among them, the A function represents the acceptance probability, which is calculated by the state xt of the Markov chain at time t and the proposed state y; d) Otherwise, the transfer is not accepted, that is, the next state of the Markov chain , and finally we get the sampling sequence .

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