CN113300830A - Data transmission method, device and storage medium based on weighted probability model - Google Patents

Data transmission method, device and storage medium based on weighted probability model Download PDF

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CN113300830A
CN113300830A CN202110573726.4A CN202110573726A CN113300830A CN 113300830 A CN113300830 A CN 113300830A CN 202110573726 A CN202110573726 A CN 202110573726A CN 113300830 A CN113300830 A CN 113300830A
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hash value
probability model
binary sequence
binary
weighted probability
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CN113300830B (en
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王杰林
欧阳斌
周浪
李增应
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Hunan Yaosheng Communication Technology Co ltd
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0618Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
    • H04L9/0631Substitution permutation network [SPN], i.e. cipher composed of a number of stages or rounds each involving linear and nonlinear transformations, e.g. AES algorithms
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/0001Systems modifying transmission characteristics according to link quality, e.g. power backoff
    • H04L1/0006Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the transmission format
    • H04L1/0007Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the transmission format by modifying the frame length
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/24Testing correct operation
    • H04L1/245Testing correct operation by using the properties of transmission codes
    • H04L1/246Testing correct operation by using the properties of transmission codes two-level transmission codes, e.g. binary
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0643Hash functions, e.g. MD5, SHA, HMAC or f9 MAC
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0869Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds

Abstract

The invention discloses a data transmission method, equipment and a storage medium based on a weighted probability model.A first binary sequence is converted into a hash value according to a hash value generation method, wherein the hash value generation method is based on S-box subsection iteration and XOR operation, linear correlation is eliminated, and the probability of 0 of each section of subsequence symbol is different, and a weighting coefficient used by each symbol code is changed due to a nonlinear round function, so that the length of the weighted probability model after being coded has randomness; the nonlinear round function of the weighting coefficient is constructed by linearly calculating the probability interval corresponding to each symbol, so that the coding results are different when the length of the message, the probability of the symbol and the arrangement sequence of the symbol are different, and the safety of information transmission is greatly improved; compared with the prior scheme, the method has the advantages that the abstract length can be customized, the adjustment can be performed according to the information security level, the information security can be guaranteed, and the pressure of information network transmission, check operation and storage is reduced.

Description

Data transmission method, device and storage medium based on weighted probability model
Technical Field
The present invention relates to the field of information communication technologies, and in particular, to a data transmission method, device, and storage medium based on a weighted probability model.
Background
The Hash algorithm can compress the message with any length to the message abstract with fixed length, and is widely applied to the fields of digital signature, file verification, information encryption and the like. Currently, the standard Hash algorithm mainly includes several series such as MD (Message-Digest) Message Digest algorithm, sha (secure Hash algorithm), lattice-based Hash algorithm, and mac (Message Authentication code) Message Authentication code. The MD information digest algorithm mainly comprises series of MD2, MD4, MD5 and the like, and the mainstream SHA secure hash algorithm mainly comprises series of SHA-1 and SHA-2(SHA-224, SHA-256, SHA-384, SHA-512) and series of SHA-3(KECCAK algorithm). The MAC algorithm is mainly a hash function algorithm with HMAC containing keys, keys are added on the basis of the original MD and SHA algorithms, and mainly comprises HmacMD series (HmacMD2, HmacMD4, HmacMD5) and HmacSHA series (HmacSHA1, HmacSHA224, HmacSHA256, HmacSHA38 and HmacSHA512), and the digest length is consistent with the original MD series and SHA series. The abstract lengths are different, and the operation structures in the algorithms are different, so that a system needs to integrate a large number of hash algorithms with different abstract lengths to adapt to the safety requirement, and system resources and cost waste is caused. With the arrival of quantum computing, the computing performance is greatly improved, and the safety system can only guarantee safety by adopting a hash algorithm of a longer message digest or a hash algorithm of a more reliable operation structure. However, the longer the message digest is, the greater burden is also brought to network transmission, check operation and storage, and the hash algorithm with a complex operation structure has operational burden.
Disclosure of Invention
The present invention is directed to at least solving the problems of the prior art. Therefore, the invention provides a data transmission method, equipment and a storage medium based on a weighted probability model.
The first aspect of the present invention provides a data transmission method based on a weighted probability model, which is applied to a transmitting end, and comprises the following steps:
converting the first binary sequence into a hash value according to a hash value generation method, wherein the hash value generation method comprises the following steps:
dividing the first binary sequence with the bit length of n into n/m subsequences linearly and respectively generating m randomly2A first binary two-dimensional table and a second binary two-dimensional table of bits;
according to the position of the symbol i in the subsequence, searching a corresponding first bit value from the first binary two-dimensional table, and searching a corresponding second bit value from the second binary two-dimensional table;
carrying out XOR operation on the symbols in the subsequences and the corresponding first bit values to obtain a second binary sequence Y corresponding to each segment of the subsequences;
calculating an information entropy H (Y) from said second binary sequence Y and r (i) from said second bit value, wherein said
Figure BDA0003083495920000021
L represents a preset positive integer, v represents the bit length of each sub-sequence, and s represents an integer greater than 3;
constructed with said r (i),
Figure BDA0003083495920000022
And
Figure BDA0003083495920000023
as a weighted probability model of the coding parameters and coding the second binary sequence Y according to the weighted probability model, wherein the coding parameters are determined by the weighted probability model
Figure BDA0003083495920000024
C represents the number of symbols 0 in the second binary sequence Y;
converting the coding result output by the weighted probability model into a third binary sequence;
if the bit length of the third binary sequence is equal to L + t, performing exclusive-or operation on the last t bits and the first L bits to obtain a sub hash value corresponding to each segment of the subsequence;
summarizing the sub-hash values corresponding to each segment of the sub-sequence to obtain hash values;
and sending the first binary sequence and the hash value to a receiving end so that the receiving end verifies the hash value.
According to the embodiment of the invention, at least the following technical effects are achieved:
(1) the method comprises the steps that a first binary sequence is converted into a hash value according to a hash value generation method, wherein the provided hash value generation method is based on S-box segmented iteration and exclusive-or operation, and linear correlation is eliminated; because the probability of each sub-sequence symbol 0 and symbol 1 is different, and the weighting coefficient used for coding each symbol is changed by round functions, the length after the weighted probability model is coded has randomness. The bit length of the hash value is random, i.e. L is a random value, and the collision probability is smaller than that when L is fixed.
(2) The method converts the first binary sequence into the hash value according to the hash value generation method, wherein the hash value generation method constructs a nonlinear round function of a weighting coefficient by linearly calculating the probability interval corresponding to each symbol in the message, so that the length of the message, the probability of the symbol and the arrangement sequence of the symbol are different, the coding results are different, if the difference occurs in the message, the avalanche effect is caused, and the safety of information transmission is greatly improved.
(3) Compared with the Hash algorithm of the length of the fixed Hash value of MD, SHA and MAC, which is the mainstream at present, the digest length of the method can be customized and can be adjusted according to the information security level, so that the information security can be ensured, and the pressure of the network transmission, the check operation and the storage of the message can be effectively reduced.
In a second aspect of the present invention, a data transmission method based on a weighted probability model is provided, which is applied to a receiving end, and includes the following steps:
receiving a first binary sequence and a hash value sent by a sending end, wherein the hash value is obtained by a hash value generation method performed by the first binary sequence, and the hash value generation method comprises the following steps:
dividing the first binary sequence with the bit length of n into n/m subsequences linearly and respectively generating m randomly2A first binary two-dimensional table and a second binary two-dimensional table of bits;
according to the position of the symbol i in the subsequence, searching a corresponding first bit value from the first binary two-dimensional table, and searching a corresponding second bit value from the second binary two-dimensional table;
carrying out XOR operation on the symbols in the subsequences and the corresponding first bit values to obtain a second binary sequence Y corresponding to each segment of the subsequences;
calculating an information entropy H (Y) from said second binary sequence Y and r (i) from said second bit value, wherein said
Figure BDA0003083495920000041
L represents a preset positive integer, v represents the bit length of each sub-sequence, and s represents an integer greater than 3;
constructed with said r (i),
Figure BDA0003083495920000042
And
Figure BDA0003083495920000043
as a weighted probability model of the coding parameters and coding the second binary sequence Y according to the weighted probability model, wherein the coding parameters are determined by the weighted probability model
Figure BDA0003083495920000044
C represents the number of symbols 0 in the second binary sequence Y;
converting the coding result output by the weighted probability model into a third binary sequence Z;
if the bit length of the third binary sequence Z is equal to L + t, performing XOR operation on the last t bits and the first L bits to obtain a sub hash value corresponding to each segment of the subsequence;
summarizing the sub-hash values corresponding to each segment of the sub-sequence to obtain hash values;
executing the received first binary sequence to the hash value generation method, and feeding back a successful identifier if the execution result is the same as the hash value; and if the execution result is not the same as the hash value, feeding back a failure identifier.
According to the embodiment of the invention, at least the following technical effects are achieved:
(1) the method comprises the steps that a first binary sequence is converted into a hash value according to a hash value generation method, wherein the provided hash value generation method is based on S-box segmented iteration and exclusive-or operation, and linear correlation is eliminated; because the probability of each sub-sequence symbol 0 and symbol 1 is different, and the weighting coefficient used for coding each symbol is changed by round functions, the length after the weighted probability model is coded has randomness. The bit length of the hash value is random, i.e. L is a random value, and the collision probability is smaller than that when L is fixed.
(2) The method converts the first binary sequence into the hash value according to the hash value generation method, wherein the hash value generation method constructs a nonlinear round function of a weighting coefficient by linearly calculating the probability interval corresponding to each symbol in the message, so that the length of the message, the probability of the symbol and the arrangement sequence of the symbol are different, the coding results are different, if the difference occurs in the message, the avalanche effect is caused, and the safety of information transmission is greatly improved.
(3) Compared with the Hash algorithm of the length of the fixed Hash value of MD, SHA and MAC, which is the mainstream at present, the digest length of the method can be customized and can be adjusted according to the information security level, so that the information security can be ensured, and the pressure of the network transmission, the check operation and the storage of the message can be effectively reduced.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic diagram of a first binary two-dimensional table provided by the present invention;
FIG. 2 is a diagram of a second binary two-dimensional table provided by the present invention;
fig. 3 is a schematic flowchart of a data transmission method based on a weighted probability model according to a first embodiment of the present invention;
fig. 4 is a schematic flowchart of a data transmission method based on a weighted probability model according to a second embodiment of the present invention;
fig. 5 is a schematic flowchart of a method for performing data transmission based on a weighted probability model by a sending end of a data transmission system based on a weighted probability model according to a third embodiment of the present invention;
fig. 6 is a flowchart illustrating a receiving end of a data transmission system based on a weighted probability model executing a data transmission method based on the weighted probability model according to a third embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
Before describing the embodiments of the present invention, the principle of the present invention will be described:
a first, weighted probability model;
let the source sequence X ═ X1,X2,...,Xi,...,Xn) Is a finite value or a discrete sequence of several possible values, XiE.g., a ═ {0,1, 2. There is then a probability space for all values in a:
Figure BDA0003083495920000061
since the random process must be transferred to a certain symbol, at any time:
Figure BDA0003083495920000062
thus, an arbitrary symbol XiThe distribution function of (a) is:
Figure BDA0003083495920000063
p(0)≤F(x)≤1,s∈A。
let X be a {0, 1.. k }, P { X be a } - (P (a) } (a ∈ a)), and the weighted probability quality function be
Figure BDA0003083495920000064
p (a) is a probability mass function, 0 ≦ p (a ≦ 1), r is a weight coefficient, and:
F(a)=∑i≤ap(i) (2)
if F (a, r) satisfies F (a, r) ═ rf (a), F (a, r) is referred to as a weighted cumulative distribution function, and is simply referred to as a weighted distribution function. It is apparent that the weighted probability sum of all symbols is
Figure BDA0003083495920000071
Let discrete source sequence X ═ X1,X2,...,Xn),XiBelongs to A, and let F (X)i-1)=F(Xi)-p(Xi) The weighted distribution function for sequence X is denoted as F (X, r). When n is 1:
F(X,r)=rF(X1-1)+rp(X1)
when n is 2:
F(X,r)=rF(X1-1)+r2F(X2-1)p(X1)+r2p(X1)p(X2)
when n is 3:
F(X,r)=rF(X1-1)+r2F(X2-1)p(X1)+r3F(X3-1)p(X1)p(X2)+r3p(X1)p(X2)p(X3)
order to
Figure BDA0003083495920000072
By analogy, the following steps are obtained:
Figure BDA0003083495920000073
the set of weighted distribution functions satisfying equation (3) is defined as a weighted probability model, referred to as a weighted model for short, and is denoted as { F (X, r) }. If XiE.g., a is {0,1}, then, F (X, r) } is referred to as a binary weighting model. Order:
Hn=F(X,r) (4)
Figure BDA0003083495920000074
Ln=Hn-Rn (6)
wherein XiE.a, n is 1,2, …. When r is 1:
Figure BDA0003083495920000075
from the formulae (4), (5) and (6), H can be obtainednSection coding (arithmetic coding), which is F (X,1), is a lossless coding method based on a weighted distribution function when r is 1.
Due to XiMust take the value in A, so p (X)i)>0. It is obvious that the formulas (4), (5) and (6) are interval columns, [ L ]i,Hi) Is the variable X of the source sequence X at time i (i ═ 0,1,2, …, n)iSubscript, R, on corresponding intervali=Hi-LiIs the length of the interval. According to formulas (4), (5) and (6), when i is 0, R is0=H0=1,L0When i is equal to 0, then i is equal to 1,2, …, and n is represented by the following formula:
Figure BDA0003083495920000081
Li=Li-1+Ri-1F(Xi-1,r)
Hi=Li+Ri (8)
carrying out weighted probability model coding operation on the source sequence X by the formula (8), LnAnd the real number is a weighted probability model coding result. L isnAnd obtaining a binary sequence through binary conversion.
Secondly, weighting probability model information entropy;
let the discrete memoryless information source sequence X ═ X (X)1,X2,…,Xn)(XiE.g., a ═ {0,1,2, …, k }), and when r ═ 1,
Figure BDA0003083495920000082
defined by shannon information entropy, the entropy of X is:
Figure BDA0003083495920000083
when r ≠ 1, the definition has a probability
Figure BDA0003083495920000084
Random variable X ofiThe self information quantity is as follows:
I(Xi)=-logk+1p(Xi) (10)
set of { XiC is present in (i ═ 1,2, …, n, a ∈ a) }aA. When the value of r is determined, the total information amount of the source sequence X is:
Figure BDA0003083495920000085
the average amount of information per symbol is then:
Figure BDA0003083495920000086
let H (X, r) be:
Figure BDA0003083495920000091
when the value of r is determined, the binary length encoded by the weighted probability model is nH (X, r) (bit). The simplest source sequence is a binary source sequence, the bit length of a binary source sequence X is set to be n, a symbol 0 and a symbol 1 in the X have probabilities p (0) and p (1), and the sequence with the length L (bit) is obtained after the weighted probability model coding. When k is 1, it can be obtained from formula (11):
-nlog2r+nH(X)=L (12)
wherein h (X) the entropy of the sequence X, i.e. h (X) ═ p (0) log2p(0)-p(1)log2p (1), formula (12) is simplified to obtain:
Figure BDA0003083495920000092
according to the lossless coding theorem, H (X) is the lossless coding limit of the discrete memoryless source sequence X, so that the weighted model function F (X, r) can restore the source sequence X without distortion when H (X, r) is more than or equal to H (X). When H (X, r)<H (X), the weighted model function F (X, r) cannot restore the source X, i.e. when L<nH (X) time code result LnThe source X cannot be recovered.
From equations (12) and (13), when H (X) > L/n, r >1, H (X, r) < H (X), and thus the weighted model functions F (X, r) satisfying equation (13) and r >1 are both one-way Hash functions (Hash functions).
Third, collision limit;
order: the probabilities of the symbol 0 and the symbol 1 in the hash value obtained by the weighted probability model hash algorithm of any binary sequence are equal.
And (3) proving that: setting binary sequence to be obtained by weighted probability model Hash algorithmThe bit length of the hash value is L, the binary sequence of the hash value is marked as Y, and the information entropy is H (Y) -p (0) log2p(0)-p(1)log2p (1). According to the above, nH (X, r) ═ nlog2r + nh (X) (n is the bit length of the binary sequence X), so lh (y) -nlog2r + nH (X). If and only if h (y) is 1, equation (12) is true, that is, r satisfies equation (13). Otherwise r does not satisfy equation (13). Further, if and only if p (0) ═ p (1) ═ 0.5, h (Y) ═ 1, the probabilities of symbol 0 and symbol 1 in sequence Y are equal.
According to the above, the equal probability of the symbols in the hash value obtained by the hash of the invention can be obtained. Assuming that the bit length of the hash value is L, the range of the value space is {0,1, …,2 }L-1}. Let d be 2LThe hash collision probability for N trials from the hash collision (or "birthday attack") probability is:
Figure BDA0003083495920000101
fourthly, nonlinear piecewise iterative operation and a round function of the weighting coefficient;
common Hash algorithms, AES, and DES symmetric encryption algorithms all employ a round function of nonlinear byte substitution to eliminate linear correlation, commonly referred to as S-boxes. Based on the theory of function, the present embodiment employs piecewise iteration and xor operation to eliminate linear correlation, and constructs a nonlinear round function of weighting coefficients based on equation (13).
(1) Carrying out segmented iteration and XOR operation on the sequence X;
the bit length of the sequence X is n, and the bit length of each segment is m2The sequence X is then divided linearly into
Figure BDA0003083495920000102
And (4) section. Order to
Figure BDA0003083495920000103
v is the number of bits per segment, obviously
Figure BDA0003083495920000104
Time of flight
Figure BDA0003083495920000105
When v is m2. Randomly generating m2The bits are stored in a two-dimensional table of 16 x 16, as shown in fig. 1, where x and y are row and column indices.
Due to the symbol X in the j sectioniIs i (i is 1,2, …, m)2) The table lookup operation in the table of fig. 1 is:
x=(i+Xi)mod m,y=(i+Xi)/m (15)
the bit value f (x, y) is obtained. XiAnd f (x, Y) are subjected to exclusive-or operation, and the binary sequence after the exclusive-or operation is marked as Y:
Figure BDA0003083495920000106
after the exclusive-or operation, the probabilities of the symbol 0 and the symbol 1 in the sequence Y are calculated, and the r value of the current segment is calculated by substituting equation (13).
(2) A non-linear round function of the weighting coefficients;
when L is set and weighted probability model coding is performed on each binary sequence, if r is not associated with i (i is 1,2, …, m)2) If the weighting coefficient is changed, the r is called as a static weighting coefficient; if r varies with i, it is called the dynamic weighting coefficient, and is denoted as r (i). Randomly generating m2The integers 0 to 255 are stored in a 16 x 16 two-dimensional table, as shown in fig. 2, where x and y are subscripts of the rows and columns, and the calculation of x and y is the same as equation (15). From a look up of the table of FIG. 2, the values g (x, y), r (i) are given as the non-linear round functions:
Figure BDA0003083495920000111
in the formula (17), s may be an integer greater than 3, and an actual value depends on the calculation accuracy of the computer, and s is 4 in the experiment of the embodiment of the present invention. When r is<2(H(X)-L/n)The coding result will exceed L bits. Let the coding result be LzIf L + t bits, t more bits are added, and the binary sequence of the jth segment hash value is addedIs denoted by Z, Z is lnThrough binary-converted binary sequences. Due to the fact that
Figure BDA0003083495920000112
Goes to 0, so t is not present>And L is the case. Let L be 1,2, …, t, then the last t bits are xored with the first L bits:
Figure BDA0003083495920000113
formula (10) wherein Zl-1And ZL+l-1Is the L-1 th and L + L-1 th binary symbols of the sequence Z.
Obtaining a real number L corresponding to the j section through weighted probability model coding based on the formula (17)vThen, the hash value Z of the current segment can be obtained by equation (18).
A first embodiment;
referring to fig. 3, an embodiment of the present invention provides a data transmission method based on a weighted probability model, including the following steps:
s101, the sending end converts the first binary sequence into a hash value according to a hash value generation method, wherein the hash value generation method comprises the following steps:
s1011, linearly dividing the first binary sequence with the bit length of n into n/m subsequences, and respectively generating m randomly2A first binary two-dimensional table and a second binary two-dimensional table of bits.
S1012, according to the position of the symbol i in the subsequence, searching a corresponding first bit value from the first binary two-dimensional table, and searching a corresponding second bit value from the second binary two-dimensional table.
And S1013, carrying out XOR operation on the symbols in the subsequences and the corresponding first bit values to obtain a second binary sequence Y corresponding to each section of the subsequences.
The hash value generation method is a step of encoding a binary source sequence X with the length of n by adopting a weighted probability model. In steps S1011 to S1013, assuming that the first binary sequence is the sequence X, first, the sequence X is linearly divided into
Figure BDA0003083495920000121
A segment; when in use
Figure BDA0003083495920000122
Time of flight
Figure BDA0003083495920000123
Or when
Figure BDA0003083495920000124
When v is m2V represents the bit length of each sub-sequence segment, and the jth sub-sequence segment of the sequence X is obtained, wherein v bits are total; secondly, the ith symbol X of the jth sub-sequence is obtainediCalculating X and y, X ═ i + Xi)mod m,y=(i+Xi) M, looking up the corresponding first bit value from the first binary two-dimensional table, e.g. obtaining f (x, y) from the table in fig. 1, and then performing
Figure BDA0003083495920000125
And finally, until each symbol of each sub-sequence section finds a corresponding first bit value, and executing exclusive OR operation to obtain a second binary sequence Y corresponding to each sub-sequence section.
S1014, calculating information entropy H (Y) according to the second binary sequence Y, and calculating r (i) according to the second bit value, wherein
Figure BDA0003083495920000126
L represents a preset positive integer, v represents the bit length of each sub-sequence, and s represents an integer greater than 3.
S1015, construction with r (i),
Figure BDA0003083495920000127
And
Figure BDA0003083495920000128
as a weighted probability model of the coding parameters and coding the second binary sequence Y according to the weighted probability model, wherein
Figure BDA0003083495920000129
c represents the number of symbols 0 in the second binary sequence Y.
In steps S1014 and S1015, L is first set, and preferably, the initial value of L is 512. Then, the number c of symbols 0 in the sequence Y is obtained
Figure BDA0003083495920000131
And h (y) ═ plog2p-(1-p)log2(1-p). Then, X and y are calculated, X ═ i + Xi)mod m,y=(i+X) M, the corresponding second bit value is looked up from a second binary two-dimensional table, e.g. the table in fig. 2, to obtain g (x, y). Finally, r (i),
Figure BDA0003083495920000132
And
Figure BDA0003083495920000133
and
Figure BDA0003083495920000134
and obtaining the coding parameters of the weighted probability model.
And S1016, converting the coding result output by the weighted probability model into a third binary sequence.
S1017, if the bit length of the third binary sequence is equal to L + t, performing exclusive OR operation on the last t bits and the first L bits to obtain a sub hash value corresponding to each sub sequence.
And S1018, summarizing the sub hash value corresponding to each sub sequence to obtain the hash value.
In steps S1016 to S1018, L is assumed as the coding result output from the weighted probability modelzCalculating t, t ═ L and t + t bitsz-L. Then, when l is less than or equal to t,
Figure BDA0003083495920000135
until all t bits are exclusive-ored with the first L bits, where L is 1,2. Finally, summarizing each segment of sub hash value to obtainTo the corresponding hash value of the final first binary sequence.
S102, the sending end sends the first binary sequence and the hash value to the receiving end so that the receiving end can verify the hash value.
The method takes arithmetic coding (interval coding) as an operation core, defines the coding result length of the Hash algorithm through a weighted probability distribution function, provides a brand-new Hash value generation method, and applies the proposed brand-new Hash value generation method to the remote communication of an information sending end and a receiving end, and the embodiment of the method has the following beneficial effects:
(1) the method comprises the steps that a first binary sequence is converted into a hash value according to a hash value generation method, wherein the provided hash value generation method is based on S-box segmented iteration and exclusive-or operation, and linear correlation is eliminated; because the probability of each sub-sequence symbol 0 and symbol 1 is different, and the weighting coefficient used for coding each symbol is changed by round functions, the length after the weighted probability model is coded has randomness. The bit length of the hash value is random, i.e. L is a random value, and the collision probability is smaller than that when L is fixed. (2) The method converts the first binary sequence into the hash value according to the hash value generation method, wherein the hash value generation method constructs a nonlinear round function of a weighting coefficient by linearly calculating the probability interval corresponding to each symbol in the message, so that the length of the message, the probability of the symbol and the arrangement sequence of the symbol are different, the coding results are different, if the difference occurs in the message, the avalanche effect is caused, and the safety of information transmission is greatly improved. (3) Compared with the Hash algorithm of the length of the fixed Hash value of MD, SHA and MAC, which is the mainstream at present, the digest length of the method can be customized and can be adjusted according to the information security level, so that the information security can be ensured, and the pressure of the network transmission, the check operation and the storage of the message can be effectively reduced.
As an alternative embodiment, the method further comprises the steps of: s103, if the feedback response of the receiving end is not received, the sending end obtains a new hash value from the first binary sequence according to a hash value generation method, wherein L is re-assigned to be equal to L + d, and d represents a random number; and S104, the sending end sends the new hash value, the reassigned L and the first binary sequence to the receiving end so that the receiving end verifies the new hash value.
In this embodiment, since the digest length of the method can be customized, after the feedback of the receiving end is not received, the value of L can be adaptively adjusted, for example, the value of L is increased in this embodiment, so that the information security can be improved, for example, as the number of times of verification increases, the randomness of L increases, so that the probability of collision is closer to 0, and the information transmission security is higher. Wherein d is preferably a random number in the range of 0 to 128.
As an alternative embodiment, the method further comprises the steps of: and the sending end sets the transmission times, and stops sending the new hash value if the feedback response of the receiving end is not received in the transmission times. The purpose of this embodiment is to set a transmission threshold value to avoid infinite retransmission, and to reduce the network transmission, check calculation, and storage pressure of messages.
A second embodiment;
referring to fig. 4, an embodiment of the present invention provides a data transmission method based on a weighted probability model, including the following steps:
s201, a receiving end receives a first binary sequence and a hash value sent by a sending end, wherein the hash value is obtained by a hash value generation method carried out on the first binary sequence, and the hash value generation method comprises the following steps:
s2011, linearly dividing a first binary sequence with the bit length of n into n/m subsequences, and respectively randomly generating m2A first binary two-dimensional table and a second binary two-dimensional table of bits.
S2012, according to the position of the symbol i in the subsequence, the corresponding first bit value is looked up from the first binary two-dimensional table, and the corresponding second bit value is looked up from the second binary two-dimensional table.
S2013, carrying out exclusive OR operation on the symbols in the subsequences and the corresponding first bit values to obtain a second binary sequence Y corresponding to each section of subsequence.
S2014, calculating the signal according to the second binary sequence YEntropy H (Y) and calculating r (i) according to the second bit value, wherein
Figure BDA0003083495920000151
L represents a preset positive integer, v represents the bit length of each sub-sequence, and s represents an integer greater than 3.
S2015, constructing a mixture of r (i),
Figure BDA0003083495920000152
And
Figure BDA0003083495920000153
as a weighted probability model of the coding parameters and coding the second binary sequence Y according to the weighted probability model, wherein
Figure BDA0003083495920000154
c represents the number of symbols 0 in the second binary sequence Y.
And S2016, converting the coding result output by the weighted probability model into a third binary sequence.
S2017, if the bit length of the third binary sequence is equal to L + t, carrying out exclusive OR operation on the last t bits and the first L bits to obtain a sub hash value corresponding to each sub sequence.
S2018, summarizing the sub hash values corresponding to the sub sequences to obtain the hash values.
S202, the receiving end executes the received first binary sequence to generate a hash value, and if the execution result is the same as the hash value, a successful identifier is fed back; and if the execution result is not the same as the hash value, feeding back a failure identifier.
Since this embodiment is based on the same inventive concept as the first embodiment, the principle part will not be described again.
The method takes arithmetic coding (interval coding) as an operation core, defines the coding result length of the Hash algorithm through a weighted probability distribution function, provides a brand-new Hash value generation method, and applies the proposed brand-new Hash value generation method to the remote communication of an information sending end and a receiving end, and the embodiment of the method has the following beneficial effects:
(1) the method comprises the steps that a first binary sequence is converted into a hash value according to a hash value generation method, wherein the provided hash value generation method is based on S-box segmented iteration and exclusive-or operation, and linear correlation is eliminated; because the probability of each sub-sequence symbol 0 and symbol 1 is different, and the weighting coefficient used for coding each symbol is changed by round functions, the length after the weighted probability model is coded has randomness. The bit length of the hash value is random, i.e. L is a random value, and the collision probability is smaller than that when L is fixed. (2) The method converts the first binary sequence into the hash value according to the hash value generation method, wherein the hash value generation method constructs a nonlinear round function of a weighting coefficient by linearly calculating the probability interval corresponding to each symbol in the message, so that the length of the message, the probability of the symbol and the arrangement sequence of the symbol are different, the coding results are different, if the difference occurs in the message, the avalanche effect is caused, and the safety of information transmission is greatly improved. (3) Compared with the Hash algorithm of the length of the fixed Hash value of MD, SHA and MAC, which is the mainstream at present, the digest length of the method can be customized and can be adjusted according to the information security level, so that the information security can be ensured, and the pressure of the network transmission, the check operation and the storage of the message can be effectively reduced.
As an optional implementation, the method further comprises the following steps: s203, the receiving end receives the first binary system, the new hash value and the reassigned L sent by the sending end, wherein the new hash value is a result obtained by the sending end through executing a hash value generation method on the first binary system sequence based on the reassigned L. S204, the receiving end executes the hash value generation method on the first binary sequence according to the reassigned L, and if the execution result is the same as the new hash value, a successful identifier is fed back; and if the execution result is not the same as the new hash value, feeding back a failure identifier.
In this embodiment, since the digest length of the method can be customized, if the sending end does not receive the response fed back by the receiving end, the receiving end will receive the first binary, the new hash value and the reassigned L sent by the sending end again, and the sending end adjusts the value of the L, which can improve the security of information.
As an optional implementation, the method further comprises the following steps: s205, the receiving end obtains a new hash value and a reassigned L of the sending end, wherein the new hash value is a result obtained by the sending end through executing a hash value generation method on the first binary sequence based on the reassigned L. S206, the receiving terminal executes the hash value generation method on the first binary sequence according to the reassigned L, and if the execution result is the same as the new hash value, a successful identifier is fed back; and if the execution result is not the same as the new hash value, feeding back a failure identifier.
The difference between this embodiment and steps S203 and S204 is that this embodiment does not need to receive the first binary sequence retransmitted by the transmitting end, and therefore, in the foregoing transmission process, the receiving end already stores the first binary sequence, and therefore, the first binary sequence does not need to be checked for retransmission. For example: the first binary sequence does not need to be retransmitted when j is 2, and the first binary sequence must be retransmitted when j is 1, so as to reduce the retransmission load.
A third embodiment;
referring to fig. 5 to 6, an embodiment of the present invention provides a data transmission system based on a weighted probability model, where the system includes a transmitting end and a receiving end, and the system is capable of executing a hash value generation method (denoted by using an english notation WPMHA in the figure), where the hash value generation method includes the following steps:
l is the bit length of the user-defined hash value, and the step of encoding the binary source sequence X with the length of n by adopting a weighted probability model is as follows:
(1) initializing parameters, p ═ c ═ L0=0,H0=R0=1,i=t=Lz=0,m=16,j=l=1,s=4,v=m2-1,
Figure BDA0003083495920000171
(2) Linearly dividing the sequence X into
Figure BDA0003083495920000172
A segment;
(3) when in use
Figure BDA0003083495920000173
Time of flight
Figure BDA0003083495920000174
(4) Acquiring a jth binary sequence of the sequence X, wherein v bits are total;
(5) obtaining the ith symbol X of the jth sectioni
(6) Calculating X and y, X ═ i + Xi)mod m,y=(i+Xi)/m;
(7) Looking up a table 1 to obtain f (x, y);
(8)
Figure BDA0003083495920000181
(9) repeating (5) to (9) if i ≦ v;
(10) i is 0, counting the number c of the symbols 0 in the sequence Y to obtain
Figure BDA0003083495920000182
And h (y) ═ plog2p-(1-p)log2(1-p);
(11) Calculating X and y, X ═ i + Xi)mod m,y=(i+Xi)/m;
(12) Looking up table 2 to obtain g (x, y);
(13) calculating r (i),
Figure BDA0003083495920000183
And
Figure BDA0003083495920000184
and
Figure BDA0003083495920000185
(14) a weighted model coding operation, if Yi=0,
Figure BDA0003083495920000186
Otherwise
Figure BDA0003083495920000187
And is
Figure BDA0003083495920000188
(15) Repeating (11) to (15) if i ≦ v;
(16)Lv=Lv+T,T=Lv
(17)Lvbinary-converted into a binary sequence Z;
(18) counting the bit length L of ZzAnd calculating t, t ═ Lz-L;
(17) When l is less than or equal to t,
Figure BDA0003083495920000189
(18) repeating (17) to (18) for l + 1;
(19)i=0,j=j+1;
(20) if it is
Figure BDA00030834959200001810
Repeating (3) to (20);
(21) and finishing the encoding, and outputting Z, wherein Z is a hash value.
The flow of the system executing the data transmission method based on the weighted probability model is as follows:
first, the transmitting end (see fig. 5);
(1) initializing a parameter, defining an amplification d (d may be a random number in a certain range, such as a random number belonging to {1,2., m }, or an integer with a self-definition greater than 0), where i is 3, L is a value (e.g., L is 512, L is a bit length of a hash value in a hash value generation method), sign is 0;
(2) the sending end obtains a hash value A of the information (the information is marked as Data) by using a hash value generation method and sends the hash value A;
(3) the sending end sends information Data and waits for the receiving end to return sign;
(4) when the time is out or sign is 1, i is i +1, and L is L + d;
(5) and (5) repeating the steps (2) to (5) when i is greater than 0, and ending otherwise.
Second, the receiving end (see fig. 6);
(1) initializing parameters, wherein the checking times i are 3, and sign is 0;
(2) receiving a hash value A;
(3) receiving information Data;
(4) calculating a hash value B of the Data based on a hash value generation method according to the length of the hash value A;
(5) when A is equal to B, replying the success mark sign which is 0 and ending, otherwise, discarding Data, j is j-1;
(6) and if j is greater than 0, replying a failure identifier sign which is 1, otherwise, ending.
The following is an experimental analysis of the safety of this example:
first, experimental results:
(1) customizing the length bytelngth of the hash value;
inputting: abcdefghi jklmnnopqrstuvwyz 123456789;
the output bytelngth is the hash value of 4,8,15,20,32 (in bytes), respectively (table 1 below is the hash value of custom different lengths).
Figure BDA0003083495920000201
TABLE 1
(2) The hash values obtained by experiments for the input data were different, and the probability p (0) of the symbol 0 in the hash value was close to 0.5 (p (0) in the case where the hash value length was 128 bits (16 bytes) in table 2; and p (0) in the case where the hash value length was 512 bits (64 bytes) in table 3).
Figure BDA0003083495920000202
Figure BDA0003083495920000211
TABLE 2
Figure BDA0003083495920000212
Figure BDA0003083495920000221
TABLE 3
From the experimental results, the hash length of the present embodiment can be customized, and the probabilities of the symbol 0 and the symbol 1 in the hash value approach to be equal. The hash value generation method provided in the first part of this embodiment is used as a core of an adaptive attack strength security system, a simulation experiment is implemented based on a TCP/IP protocol Socket, and Data and a column value a are subjected to random bit error processing during Data transmission. The experiment sets d to be 1-128 random numbers, i ═ j ═ 3, the initial value of each simulation L is 512 bits, and when the simulation times are not less than 105, the experimental conclusion is that: adaptive attack strength can be achieved based on the security system of fig. 5 and 6.
Secondly, safety analysis is carried out;
piecewise iteration, exclusive-or operation, and round functions are means to combat linear and differential attacks. According to the encoding procedures provided in the second and third parts of this embodiment, first, since X is Xi0 and XiWhen table 1 or table 2 is looked up, the two-dimensional coordinates (x, y) are random, so the values of f (x, y) and g (x, y) are random. Secondly, the probability of the symbol 0 in the sequence X is fixed, but the probability p of the symbol 0 in each binary sequence is different, and the precision of p determines the value space, so that h (y) is unknown. Due to 2(H (Y)-L/v)And
Figure BDA0003083495920000231
are all unknown, so LvIs unknown. Due to Lv=Lv+ T, i.e. the coding result is iteratively operated in additive fashion, so that LvThe bit variation has randomness during operation. Thus, sufficient conditions can be analyzed: when encoding the ith symbol of the sequence E, f (x, y), g (x, y),r(i)、RiAnd LiAnd code XiThe hash values are kept consistent, i.e., the same hash value can be generated. Uncertainty exists in the sufficiency condition, and the probability that each section meets a certain sufficiency condition can be analyzed.
(1)XiE {0,1}, f (X, y) only works on the symbol XiThe probability of v bits per segment and the correct selection of f (x, y) per symbol is
Figure BDA0003083495920000232
(2) g (x, y) only acts on the weight coefficient r (i) with the probability of (1) correctly selecting g (x, y) for each symbol being
Figure BDA0003083495920000233
(3) Let the precision of p be u-bit binary, and obtain the probability p of 0 symbol in each binary sequence to exist 2uPossible values of r 2(H(Y)-L/v)Therefore, it is
Figure BDA0003083495920000234
(4) T and LvHas a binary digit of L and an iterative operation of Lv=T+LvThen L isvAnd the probability that T is both correct is
Figure BDA0003083495920000235
The same encoding result can be obtained when the above sufficient conditions are all satisfied. f (x, y) and g (x, y) are S boxes, and linear correlation is eliminated to a certain extent based on S box segmentation iteration and XOR operation. Because the probability of each section of sequence symbol 0 and symbol 1 is different, and the weighting coefficient used by each symbol coding is changed by a round function, the length after the weighted probability model coding has randomness. The bit length of the hash value calculated by the hash value generation method provided by the embodiment is random, that is, L is a random value, and the collision probability is smaller than that when L is fixed. And the longer the hash value, the smaller the collision probability. Thus, the safety system based on fig. 5 and 6 increases the randomness of L as the number of checks increases, so that the probability of a collision is closer to 0.
A fourth embodiment;
one embodiment of the present invention provides a data transmission device based on a weighted probability model; the data transmission device based on the weighted probability model can be any type of intelligent terminal, such as a mobile phone, a tablet computer, a personal computer and the like. Specifically, the data transmission device based on the weighted probability model comprises: one or more control processors and memory, in this example a control processor. The control processor and memory may be connected by a bus or other means, in this example by a bus.
Memory, which is a non-transitory computer-readable storage medium, may be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as program instructions/modules corresponding to the weighted probability model-based data transmission device in the embodiments of the present invention; the control processor implements the weighted probability model-based data transfer method of the above-described method embodiments by executing non-transitory software programs, instructions, and modules stored in the memory. The memory may include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function; further, the memory may include high speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory optionally includes a memory remotely located from the control processor, and the remote memories may be connected to the weighted probability model based data transfer device via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof. The one or more modules are stored in the memory and, when executed by the one or more control processors, perform the weighted probability model-based data transfer method of the above-described method embodiments.
Embodiments of the present invention also provide a computer-readable storage medium, which stores computer-executable instructions, which are executed by one or more control processors, for example, may cause the one or more control processors to execute the data transmission method based on the weighted probability model in the above method embodiments.
Through the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be implemented by software plus a general hardware platform. Those skilled in the art will appreciate that all or part of the processes of the methods of the above embodiments may be implemented by hardware related to instructions of a computer program, which may be stored in a computer readable storage medium, and when executed, may include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read Only Memory (ROM), a Random Access Memory (RAM), or the like.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (10)

1. A data transmission method based on a weighted probability model is applied to a sending end and comprises the following steps:
converting the first binary sequence into a hash value according to a hash value generation method, wherein the hash value generation method comprises the following steps:
dividing the first binary sequence with the bit length of n into n/m subsequences linearly and respectively generating m randomly2A first binary two-dimensional table and a second binary two-dimensional table of bits;
according to the position of the symbol i in the subsequence, searching a corresponding first bit value from the first binary two-dimensional table, and searching a corresponding second bit value from the second binary two-dimensional table;
carrying out XOR operation on the symbols in the subsequences and the corresponding first bit values to obtain a second binary sequence Y corresponding to each segment of the subsequences;
calculating an information entropy H (Y) from said second binary sequence Y and r (i) from said second bit value, wherein said
Figure FDA0003083495910000011
L represents a preset positive integer, v represents the bit length of each sub-sequence, and s represents an integer greater than 3;
constructed with said r (i),
Figure FDA0003083495910000012
And
Figure FDA0003083495910000013
as a weighted probability model of the coding parameters and coding the second binary sequence Y according to the weighted probability model, wherein the coding parameters are determined by the weighted probability model
Figure FDA0003083495910000014
C represents the number of symbols 0 in the second binary sequence Y;
converting the coding result output by the weighted probability model into a third binary sequence;
if the bit length of the third binary sequence is equal to L + t, performing exclusive-or operation on the last t bits and the first L bits to obtain a sub hash value corresponding to each segment of the subsequence;
summarizing the sub-hash values corresponding to each segment of the sub-sequence to obtain hash values;
and sending the first binary sequence and the hash value to a receiving end so that the receiving end verifies the hash value.
2. The weighted probability model-based data transmission method according to claim 1, further comprising the steps of:
if the feedback response of the receiving end is not received, obtaining a new hash value by the first binary sequence according to the hash value generation method, wherein the L is re-assigned, so that the L is L + d, wherein d represents a random number;
and sending the new hash value, the L after reassignment and the first binary sequence to a receiving end so that the receiving end verifies the new hash value.
3. The weighted probability model-based data transmission method according to claim 2, further comprising the steps of:
and setting the transmission times, and stopping sending the new hash value if the feedback response of the receiving end is not received in the transmission times.
4. The weighted probability model-based data transmission method of claim 1, wherein L is 512.
5. The weighted probability model-based data transmission method as claimed in claim 2, wherein d is a random number from 0 to 128.
6. A data transmission method based on a weighted probability model is characterized in that the method is applied to a receiving end and comprises the following steps:
receiving a first binary sequence and a hash value sent by a sending end, wherein the hash value is obtained by a hash value generation method performed by the first binary sequence, and the hash value generation method comprises the following steps:
dividing the first binary sequence with the bit length of n into n/m subsequences linearly and respectively generating m randomly2A first binary two-dimensional table and a second binary two-dimensional table of bits;
according to the position of the symbol i in the subsequence, searching a corresponding first bit value from the first binary two-dimensional table, and searching a corresponding second bit value from the second binary two-dimensional table;
carrying out XOR operation on the symbols in the subsequences and the corresponding first bit values to obtain a second binary sequence Y corresponding to each segment of the subsequences;
calculating an information entropy H (Y) from said second binary sequence Y and r (i) from said second bit value, wherein said
Figure FDA0003083495910000031
L represents a preset positive integer, v represents the bit length of each sub-sequence, and s represents an integer greater than 3;
constructed with said r (i),
Figure FDA0003083495910000032
And
Figure FDA0003083495910000033
as a weighted probability model of the coding parameters and coding the second binary sequence Y according to the weighted probability model, wherein the coding parameters are determined by the weighted probability model
Figure FDA0003083495910000034
C represents the number of symbols 0 in the second binary sequence Y;
converting the coding result output by the weighted probability model into a third binary sequence;
if the bit length of the third binary sequence is equal to L + t, performing exclusive-or operation on the last t bits and the first L bits to obtain a sub hash value corresponding to each segment of the subsequence;
summarizing the sub-hash values corresponding to each segment of the sub-sequence to obtain hash values;
executing the received first binary sequence to the hash value generation method, and feeding back a successful identifier if the execution result is the same as the hash value; and if the execution result is not the same as the hash value, feeding back a failure identifier.
7. The weighted probability model-based data transmission method of claim 6, further comprising the steps of:
receiving the first binary, a new hash value and the reassigned L sent by the sending end, wherein the new hash value is a result obtained by the sending end through executing the hash value generation method on the first binary sequence based on the reassigned L;
executing the hash value generation method on the first binary sequence according to the reassigned L, and feeding back a successful identifier if the execution result is the same as the new hash value; and if the execution result is not the same as the new hash value, feeding back a failure identifier.
8. The weighted probability model-based data transmission method of claim 6, further comprising the steps of:
acquiring a new hash value of the sending end and the reassigned L, wherein the new hash value is a result obtained by the sending end by executing the hash value generation method on the first binary sequence based on the reassigned L;
executing the hash value generation method on the first binary sequence according to the reassigned L, and feeding back a successful identifier if the execution result is the same as the new hash value; and if the execution result is not the same as the new hash value, feeding back a failure identifier.
9. A data transmission device based on a weighted probability model, characterized by: comprises at least one control processor and a memory for communicative connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the weighted probability model based data transfer method of any one of claims 1 to 5 and/or the weighted probability model based data transfer method of any one of claims 6 to 8.
10. A computer-readable storage medium characterized by: the computer-readable storage medium stores computer-executable instructions for causing a computer to perform the weighted probability model-based data transfer method of any one of claims 1 to 5 and/or the weighted probability model-based data transfer method of any one of claims 6 to 8.
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