CN111651774B - Universal method for converting generated probability model into encoder and encryption method - Google Patents

Universal method for converting generated probability model into encoder and encryption method Download PDF

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CN111651774B
CN111651774B CN201910160645.4A CN201910160645A CN111651774B CN 111651774 B CN111651774 B CN 111651774B CN 201910160645 A CN201910160645 A CN 201910160645A CN 111651774 B CN111651774 B CN 111651774B
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CN111651774A (en
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王平
程海波
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Peking University
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Abstract

The invention discloses a general method for converting a probability model into an encoder and an encryption method. The general method for converting the generated probability model into the encoder automatically realizes the high-efficiency and safe encoder by using the generated probability model of any message and codes the message. By utilizing the technical scheme of the invention, the high-efficiency and safe encoder can be automatically realized on the probability model generated by any message, so that the encryption under the low-entropy key is realized, and the encryption method is safe, high-efficiency and universal.

Description

Universal method for converting generated probability model into encoder and encryption method
Technical Field
The invention belongs to the technical field of computer information security, relates to a computer information encryption method, and particularly relates to a general method for converting a probability model into an encoder in an encryption method under a low-entropy key.
Background
Passwords generated and remembered by users exhibit a low entropy property due to the limitations of human memory. Unlike the random long key of a typical encryption algorithm, the user's password is usually a string of meaningful characters, which are easily guessed. Therefore, in the conventional password-based encryption algorithm (PKCS #5), once ciphertext is leaked, an attacker can obtain plaintext by making a brute force guess about a key (i.e., password).
In 2014, Ari Juels and Thomas ristearpat propose a brand-new Encryption method, honeyencrypt, add a distribution-transformation encoder (DTE) on top of the traditional Encryption scheme, can guarantee that ciphertext can be decrypted under any key to obtain a plausible plaintext, so that an attacker can not judge whether attack is successful or not. However, this approach requires designing different DTEs for different message distributions. For messages that follow a simple distribution, such as a random distribution, a normal distribution, etc., it is simple to design a corresponding encoder. However, for messages such as natural language text, genetic data, password wallet, etc., the distribution is very complex, and the complex probability model needs to be used for characterization, and designing a corresponding encoder is a significant challenge.
Existing DTE design methods individually design corresponding encoders for specific types of messages. For example, in 2015, zhiconv Huang et al designed a corresponding encoder for gene data, and Rahul Chatterjee et al designed a corresponding encoder for password wallets. In 2016, Maximian Golla et al designed a new encoder for password wallets. The encoder of zhiconv Huang et al is relatively complex, while the encoders of Rahul Chatterjee et al and Maximilian Golla et al have significant security holes. More importantly, the encoders are all directed to specific types of messages and have no versatility.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a general method for converting a probability model into an encoder, which can automatically realize an efficient and safe encoder by utilizing a random message generation probability model, and further provides an encryption method under a low-entropy key (such as a password).
The invention provides a definition of a generative probability model, wherein the generative probability model PM is a quintuple
Figure BDA0001984512950000011
Figure BDA0001984512950000012
In order to be a space for the message,
Figure BDA0001984512950000013
in order to generate the set of rules,
Figure BDA0001984512950000014
for all legal generation of a sequence of rules, the function G is
Figure BDA0001984512950000015
To
Figure BDA0001984512950000016
Represents a message generating a sequence of rules, the function P is
Figure BDA0001984512950000021
Is determined. Here, the
Figure BDA0001984512950000022
Are all finite sets and the function G is the fill-shot. The generative probability model gives
Figure BDA0001984512950000023
A probability distribution P' of the first and second,
Figure BDA0001984512950000024
i.e. P' (M) represents the sum of the probabilities of all the generation rule sequences that can generate the message M. A generation rule prefix is a prefix of a legal generation rule sequence, specifically (r)1,r2,…,ri-1) Is a generating rule prefix, if and only if there is a legal generating sequence whose length is greater than or equal to i, its first i-1 items are respectively r1,r2,…,ri-1。
The encoder encodes a corresponding message M into a bit string, which is referred to as a seed.
The technical scheme provided by the invention is as follows:
a general method for converting a generated probability model into an encoder automatically realizes an efficient and safe encoder by utilizing the generated probability model of any message, and encodes the message, thereby realizing safe and efficient encryption; the method comprises the following steps:
defining the generative probability model PM as a quintuple
Figure BDA0001984512950000025
Message space
Figure BDA0001984512950000026
The probability distribution P' (M) above represents the sum of the probabilities of all the generation rule sequences that can generate the message M; encoding the message M into a bit string as a seed;
A. in constructing the encoder, a rule prefix (r) is generated for each1,r2,…,ri-1) After calculating the prefix of the generation rule, each generation rule riCorresponding seed intervalAnd storing the generation rule riThe corresponding seed partition, i.e. the seed partition table, specifically performs the following operations (as shown in fig. 1):
A1. to generate a regular sequence prefix (r)1,r2,…,ri-1) Each generation rule r of the latter possibilityiUsing a conditional probability density function table P (r) for generating a probability modeli|r1,r2,…,ri-1) Constructing cumulative distribution function table F (r) in lexical orderi|r1,r2,…,ri-1)；
A2. Let riAll possible values are ri,1,ri,m,…,ri,mAnd then:
A3.
Figure BDA0001984512950000027
A4. the value F (r) in the cumulative distribution function tablei,j|r1,r2,…,ri-1) Converting into a bit string with length of l (length of l) by roundl(s)＝round(2ls), round (x) represents the nearest integer to x; the bit string is a generating rule ri,jIn generating rule prefix (r)1,r2,…,ri-1) The upper bound of the seed interval is the previous rule ri,j-1The upper bound of the seed interval of (1) (if j is 1, the lower bound is 0)
A5. Storing the converted cumulative distribution function table, i.e. each generation rule sequence prefix (r)1,r2,…,ri-1) A corresponding seed compartment table.
B. The encoder, when encoding the message M, performs the following operations (as shown in fig. 2):
B1. parsing all Generation rule sequences G of M-1(M)；
B2.G-1(M) is the set of all generation rule sequences RS that can generate the message M;
B3. generating a regular sequence RS for each of M, and (r) for RS1,r2,…,rn) Each of the generation rules riAfter generating a regular sequence prefix of (r)1,r2,…,ri-1) In the corresponding seed interval table, two are searched for riCorresponding seed interval, and calculating the length l of the seed intervali(i.e., the number of seeds in the interval, let riThe upper and lower boundaries of the corresponding seed interval in the table are b and a, respectively, and then the seed interval is [ a, b]And the interval length is b-a +1), thereby calculating the number of seeds corresponding to the RS
Figure BDA0001984512950000031
Wherein n ismaxIs composed of
Figure BDA0001984512950000032
The length of the longest generation rule sequence;
B4. according to probability distribution
Figure BDA0001984512950000033
Randomly selecting a generation rule sequence RS';
B5. in specific implementation, a generation rule is randomly selected according to probability distribution. For example, there are two generation rule sequences RS1 and RS2, and the calculated probabilities are 0.3 and 0.7, respectively, then one generation rule sequence is randomly selected according to the probability, i.e., RS1 is selected with a probability of 0.3, and RS2 is selected with a probability of 0.7.
B6. Binary search RS ═ (r)1,r2,…,rn) Each of the generation rules riAfter generating a regular sequence prefix of (r)1,r2,…,ri-1) And randomly selecting a bit string s in the corresponding seed interval in the seed interval tablei；
B7. All s areiAre connected in sequence and are filled with random bits at the end to nmaxl long bit string, and outputting the bit string as a seed S.
The b8.c. decoder, when decoding the seed S, performs the following operations:
C1. decomposing a seed into a bit string s of length liN is total tomaxA plurality of;
C2. sequentially searching and generating a regular sequence prefix of (r)1,r2,…,ri-1) In the seed interval table, search s in the tableiObtaining the corresponding generation rule r between the seed regionsi(ii) a Thereby, a generation rule sequence RS ═ (r) corresponding to the seed S is obtained1,r2,…,rn)；
C3. And generating a message M (G) (RS) by using a generating function G, and outputting the message M.
The method is used for converting the generated probability model into the encoder, the invention also provides an encryption method of the low-entropy key, and the operation flow is as follows:
1) encryption:
a) inputting a plaintext message M and a secret key K, and converting the encoder coding message M by using a probability model to obtain a seed S.
b) And encrypting the seed S by using the key K to obtain a ciphertext C. The encryption method can be traditional password-based encryption, and only the encryption method needs to be guaranteed to successfully decrypt any secret key. For example, PBKDF2 (passed-Based Key Derivation Function 2) performs S expansion on Key K to obtain a long Key, and then encrypts S using the long Key in CTR mode (Counter mode) using AES (Advanced Encryption Standard).
2) And (3) decryption:
a) and for the input ciphertext C and the key K, decrypting the ciphertext C by using the key K to obtain the seed S.
b) And decoding the seed S by using a probability model conversion encoder to obtain a message M.
Through the steps, any message can be encoded and decoded, and safe and efficient encryption is realized.
The invention has the beneficial effects that:
by utilizing the technical scheme provided by the invention, the probability model is generated by self-defining, and a safe and efficient encoder can be automatically generated according to the generated probability model of the message, so that the process of designing the specific encoder for the specific message is saved, the process of designing the Honey Encryption scheme corresponding to the message is accelerated, the message is encoded and encrypted efficiently and safely, and the universality is realized. .
Drawings
FIG. 1 is a block diagram of a process for generating a seed interval table using the method of the present invention.
Fig. 2 is a block diagram of a flow of encoding using the encoder of the present invention.
FIG. 3 is a block diagram of a process for generating a seed interval table using a Markov chain model provided by the present invention.
Fig. 4 is a block diagram of a flow of encoder encoding using the markov chain model provided by the present invention.
Detailed Description
The invention will be further described by way of examples, without in any way limiting the scope of the invention, with reference to the accompanying drawings.
The invention provides a universal encryption method for converting a probability model into an encoder. In the following embodiments, the probability model is generated by using a Markov chain model, and the concrete implementation of the method of the present invention is further described by a Markov chain model (Markov chain model).
A Markov chain model is constructed, and a 0 th order Markov chain model is a generative probability model for generating messages character by character independently. Noting Σ as an alphabet
Figure BDA0001984512950000041
Where n denotes the length of the message (for ease of explanation, it is assumed here that the length of the message is the same). For message M ═ c1c2…cnThe model has only one generating sequence generating M, i.e. the character sequence c1c2…cn. And due to the memoryless of the 0-th order Markov chain model, P' (M) ═ P (c)1)P(c2)…P(cn) Therefore, the model has only one probability density function table, i.e., a probability table for each character, as shown in table 1.
TABLE 1 probability density function table for Markov chain model
Figure BDA0001984512950000042
Figure BDA0001984512950000051
TABLE 2 cumulative distribution function table for Markov chain model
Figure BDA0001984512950000052
TABLE 3 Markov chain model seed Interval Table (l ═ 20)
Character(s) Upper bound of seed interval
a 00000000010000011001
b 00000000010110111100
c 00000000100010011010
… …
9 11111111111111111111
Constructing a seed interval table of a Markov chain probability model conversion encoder: the probability table is first converted into a cumulative distribution function table in a lexicographic order and then the function ro is usedundlAnd converting the numerical values in the table into bit strings, thereby obtaining a seed interval table required by the encoder.
Markov chain probability model transform coder coding message M ═ c1c2…cnThe process comprises the following steps: for each character ciThe corresponding seed interval is searched in a binary mode in sequence, and a seed s is randomly selected from the intervaliAnd then s isiAnd then connected in sequence to obtain the seed of the message M, as shown in fig. 4. The specific encoding process is explained by taking the message abc as an example (l ═ 20, n ═ 3): for three characters a, b, c, searching corresponding seed regions [00000000000000000000,00000000010000011001 ]],[00000000010000011010,00000000010110111100],[00000000010110111101,00000000100010011010](ii) a Randomly selecting a seed from the interval, wherein the seed is 00000000000010100001, 00000000010000100010 and 00000000011111111100 respectively; the three seeds are connected in sequence as the seed 000000000000101000010000000001000010001000000000011111111100 for the message abc.
The flow of decoding the seed S by the Markov chain probability model transform coder is as follows, decomposing S into a bit string S of length liSequentially search for siIn the corresponding seed regions in the seed region table, the corresponding characters are ciThe output message M ═ c1c2…cn. The specific decoding process is explained by taking seed 000000000000101000010000000001000010001000000000011111111100 as an example (l ═ 20, n ═ 3): decomposing the seed into three 20-bit long character strings of 00000000000010100001, 00000000010000100010 and 00000000011111111100 respectively; sequentially searching corresponding seed regions, and finding corresponding characters as a, b and c; the message abc is output.
The process of encrypting the message M under the key K is: 1) firstly, coding a message M by using the coder to obtain a seed S; 2) then, expanding the key K by using the PBKDF2 to obtain a long key; 3) and encrypting the seed S by using the long key under the CTR mode by using AES to obtain a ciphertext C. The process of decrypting the ciphertext C under the key K is as follows: 1) expanding the key K by using the PBKDF2 to obtain a long key; 2) decrypting the ciphertext C by using the long key in the CTR mode by using AES to obtain a seed S; 3) and decoding the seed S by using the encoder to obtain the message M.
It is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.

Claims (10)

1. A general method for converting a generated probability model into an encoder automatically realizes an efficient and safe encoder by utilizing the generated probability model of any message, and encodes the message, thereby realizing safe and efficient encryption; the method comprises the following steps:
1) in constructing the encoder, the information is stored in the generation rule set
Figure FDA0003530074040000011
Each generates a rule prefix (r)1,r2,…,ri-1) Each of the latter generation rules riAnd the corresponding seed region specifically executes the following operations:
11) defining the generative probability model PM as a quintuple
Figure FDA0003530074040000012
Figure FDA0003530074040000013
In order to be a space for the message,
Figure FDA0003530074040000014
in order to generate the set of rules,
Figure FDA0003530074040000015
for all legal generation of a sequence of rules, the function G is
Figure FDA0003530074040000016
To
Figure FDA0003530074040000017
Represents a message generating a sequence of rules, the function P is
Figure FDA0003530074040000018
A probability distribution function of (a);
12) the sum of the probabilities of all the generation rule sequences which can generate the message M is recorded as the message space
Figure FDA0003530074040000019
Probability distribution P' (M) above;
13) using a conditional probability density function table P (r) for generating a probabilistic modeli|r1,r2,…,ri-1) Constructing a cumulative distribution function table F (r | r)1,r2,…,ri-1) Then storing the converted cumulative distribution function table to obtain the prefix (r) of each generation rule sequence1,r2,…,ri-1) A corresponding seed interval table;
2) the encoder, when encoding the message M, performs the following operations:
21) parsing all Generation rule sequences G of M-1(M)；G-1(M) is the set of all generation rule sequences RS that can generate the message M;
22) generating a regular sequence RS (r) for each of M1,r2,…,rn) Each of the generation rules riAfter generating a regular sequence prefix of (r)1,r2,…,ri-1) In the corresponding seed interval table, look up riCorresponding seed regions, calculating the length l of the seed regionsi；
23) Calculating the number of seeds corresponding to the RS according to the following formula:
Figure FDA00035300740400000110
wherein n ismaxIs composed of
Figure FDA00035300740400000111
The length of the longest generation rule sequence;
24) randomly selecting a generation rule sequence RS' according to probability distribution;
25) looking up RS ═ (r)1,r2,…,rn) Each of the generation rules riAfter generating a regular sequence prefix of (r)1,r2,…,ri-1) And randomly selecting a bit string s in the corresponding seed interval in the seed interval tablei；
26) All s areiSequentially connected and filled with random bits at the end to generate a length of nmaxl, outputting the bit string as a seed S;
3) the decoder, when decoding the seed S, performs the following operations:
31) decomposing a seed into a bit string s of length liN is total tomaxA plurality of;
32) sequentially searching and generating a regular sequence prefix of (r)1,r2,…,ri-1) In the seed interval table, search s in the tableiObtaining the corresponding generation rule r between the seed regionsi(ii) a The generation rule sequence RS' corresponding to the seed S is (r)1,r2,…,rn)；
33) Generating a message M (G) (RS) by using a generating function G, and outputting the message M;
through the steps, the generated probability model is converted into the encoder.
2. The general method for converting a generative probabilistic model into an encoder as defined in claim 1, wherein step 13) performs the operations of:
131) generating a regular sequence prefix (r) for each1,r2,…,ri-1) Using a conditional probability density function table P (r) for generating a probability modeli|r1,r2,…,ri-1) Is provided with riAll possible values are ri,1,ri,m,…,ri,mConstructing a cumulative distribution function table F (r)i|r1,r2,…,ri-1) Expressed as:
Figure FDA0003530074040000021
132) the value F (r) in the cumulative distribution function tablei,j|r1,r2,…,ri-1) Converting into a bit string of length l, which is a generating rule ri,jIn generating rule prefix (r)1,r2,…,ri-1) The upper bound of the seed interval of the seed; lower bound being the previous rule ri,j-1The upper bound of the seed interval of (1) is added, and if j is 1, the lower bound is 0;
133) storing the converted cumulative distribution function table, i.e. each generation rule sequence prefix (r)1,r2,…,ri-1) A corresponding seed compartment table.
3. The method as claimed in claim 2, wherein the step 132) is implemented by using roundl(s)＝round(2ls), round (x) represents the nearest integer to x, will accumulate the value F (r) in the distribution function tablei,j|r1,r2,…,ri-1) Into a bit string of length l.
4. The general method for converting a generative probability model into an encoder as claimed in claim 2 wherein step 22) the seed interval length liThe number of seeds in the seed region; if riThe upper and lower boundaries of the corresponding seed interval in the table are b and a, respectively, and then the seed interval is [ a, b]Length between seed zones liIs b-a + 1.
5. The general method of converting a generative probability model into an encoder as set forth in claim 1,step 24) the probability distribution is specifically
Figure FDA0003530074040000022
6. A general method of transforming a generative probability model into an encoder as claimed in claim 1 wherein the search is by a binary search method.
7. An encryption method of a low-entropy key comprises the steps of firstly converting a generated probability model into an encoder and then encrypting; the method comprises the following steps:
s1, converting the generative probability model into an encoder by adopting the method of any one of claims 1 to 6, and storing the encoder in a generative rule set
Figure FDA0003530074040000023
Each generates a rule prefix (r)1,r2,…,ri-1) Each generation rule riCorresponding seed regions are constructed, so that a probability model conversion encoder is obtained; the following operations are specifically executed:
11) defining the generative probability model PM as a quintuple
Figure FDA0003530074040000031
Figure FDA0003530074040000032
In order to be a space for the message,
Figure FDA0003530074040000033
in order to generate the set of rules,
Figure FDA0003530074040000034
for all legal generation of a sequence of rules, the function G is
Figure FDA0003530074040000035
To
Figure FDA0003530074040000036
Represents a message generating a sequence of rules, the function P is
Figure FDA0003530074040000037
A probability distribution function of (a);
12) the sum of the probabilities of all the generation rule sequences which can generate the message M is recorded as the message space
Figure FDA0003530074040000038
Probability distribution P' (M) above;
13) using a conditional probability density function table P (r) for generating a probabilistic modeli|r1,r2,…,ri-1) Constructing a cumulative distribution function table F (r)i|r1,r2,…,ri-1) Then storing the converted cumulative distribution function table to obtain the prefix (r) of each generation rule sequence1,r2,…,ri-1) A corresponding seed interval table;
s2, encrypting and executing the following operations:
21) inputting a plaintext message M and a secret key K, and converting the encoder coding message M by using the probability model obtained in S1 to obtain a seed S;
22) encrypting the seed S by using the key K to obtain a ciphertext C;
s3, carrying out decryption and executing the following operations:
31) inputting a ciphertext C and a key K, and decrypting the ciphertext C by using the key K to obtain a seed S;
32) decoding the seed S by using a probability model conversion encoder to obtain a message M;
through the steps, any message can be encoded and decoded, and safe and efficient encryption is realized.
8. The method of encrypting the low-entropy key of claim 7, wherein the low-entropy key includes but is not limited to a password.
9. The method for encrypting the low-entropy key according to claim 7, wherein the encryption method of step 22) includes a password-based encryption method, and any key can be successfully decrypted only by using the encryption method.
10. A method for encrypting a low-entropy key as claimed in claim 9, wherein the encryption method is implemented by expanding the key K with PBKDF2 to obtain a long key, and encrypting S with the long key in CTR mode with AES.
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